Digital twin calibration

Abstract

To provide a scientific instrument, method and program for facilitating improved digital twin calibration for the scientific instrument.SOLUTION: A scientific instrument module includes first, second and third logics. The first logic is for accessing digital twin of a scientific instrument, in which the digital twin is any appropriate set of mathematics- or physics-based formulas, equations or models allowed to simulate, predict or forecast any appropriate behavior mode of the scientific instrument. The second logic is for calibrating or synchronizing a parametric state of the digital twin to a physical state of the scientific instrument so as to utilize or implement a state-entirety Bayesian filter, thereby facilitating such calibration or synchronization. The third logic is for electronically notifying a user or technician of the scientific instrument of a fact that the digital twin is calibrated and prepared to correctly simulate, predict or forecast a future behavior of the scientific instrument.SELECTED DRAWING: Figure 1

Description

Technical Field

[0001] Scientific instruments can include complex configurations of operable parts, sensors, or consumables. A digital twin can simulate or predict the behavior of a scientific instrument. To make such simulations or predictions accurate, the digital twin should first be calibrated or synchronized using their respective scientific instruments.

Summary of the Invention

[0002] The following presents a summary for providing a basic understanding of one or more embodiments. This summary is not intended to identify key or critical elements or to delineate any scope of particular embodiments or any scope of the claims. Its sole purpose is to present concepts in a simplified form as a prelude to a more detailed description that is presented later. In one or more embodiments described herein, a device, system, computer-implemented method, apparatus, or computer program product is described that facilitates improved digital twin calibration for scientific instruments.

[0003] According to one or more embodiments, a scientific instrument is provided. The scientific instrument can include a non-transitory computer-readable memory capable of storing computer-executable components. The scientific instrument can further include a processor operably coupled to the non-transitory computer-readable memory and capable of executing the computer-executable components stored in the non-transitory computer-readable memory. In various embodiments, the computer-executable components can include an access component capable of accessing a digital twin of the scientific instrument. In various aspects, the computer-executable components can include a calibration component capable of synchronizing parametric states of the digital twin with physical states of the scientific instrument via execution of a full-state Bayesian filter. In various instances, the full-state Bayesian filter can include a set of calibration iterations, each of which can include a Bayesian update for an entire parametric state based on an iterative common observable that can be presented by the scientific instrument and simulated by the digital twin.

[0004] According to one or more embodiments, a computer-implemented method is provided. In various embodiments, the computer-implemented method can include synchronizing parametric states of a digital twin with physical states of a scientific instrument by a device operably coupled to a processor that executes a full-state Bayesian filter. In various aspects, the computer-implemented method can include generating, by the device, an electronic alert indicating that the digital twin is ready to predict the behavior of the scientific instrument in response to the synchronizing. In various instances, the full-state Bayesian filter can include a set of calibration iterations, each of which can include a Bayesian update for an entire parametric state based on an iterative common observable that can be presented by the scientific instrument and simulated by the digital twin.

[0005] According to one or more embodiments, a computer program product is provided for facilitating improved digital twin calibration for scientific instruments. In various embodiments, the computer program product can comprise a non-transitory computer-readable memory having program instructions incorporated therein. In various aspects, the program instructions can be executable by a processor to cause the processor to access a digital twin of a charged particle microscope. In various instances, the program instructions can be further executable by the processor to synchronize the physical state of the charged particle microscope with the parametric state of the digital twin via execution of a set of calibration iterations, where each calibration iteration can be presented by the charged particle microscope and simulated by the digital twin, and each calibration iteration includes a Bayesian update of the parametric state of the digital twin with respect to an overall parametric state based on a recurring common observable. In various cases, the program instructions can be further executable by the processor to cause the processor to predict how the charged particle microscope will respond to a proposed usage scenario by operating the digital twin after synchronization.

Brief Description of the Drawings

[0006] Various embodiments will be readily understood by the following detailed description in conjunction with the accompanying drawings. For the sake of ease of explanation, like reference numerals denote like structural elements. The embodiments are illustrated by way of example in the drawings and are not limiting. The drawings are not necessarily drawn to scale.

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DETAILED DESCRIPTION OF THE INVENTION

[0007] The following detailed description is merely exemplary and is not intended to limit the embodiments or the application / use of the embodiments. Further, it is not intended to be bound by any expressed or implied information presented in the preceding "Background Art" or "Summary of the Invention" sections, or in the "Detailed Description of the Invention" section.

[0008] Here, one or more embodiments will be described with reference to the drawings, and like reference numerals will be used throughout the drawings to refer to like elements. In the following description, for the sake of convenience of explanation, a number of specific details are set forth in order to provide a more detailed understanding of one or more embodiments. However, it is obvious that in various cases, one or more embodiments can be implemented without these specific details.

[0009] Various operations may be described in sequence as a plurality of discrete operations or as operations for the purpose of best serving to understand the subject matter disclosed herein. However, the order of description should not be construed as suggesting that these operations necessarily depend on order. In particular, these operations may be performed in a different order than presented. The operations described may be performed in a different order than the described embodiments. In additional embodiments, various additional operations may be performed or the described operations may be omitted.

[0010] Some elements may be referred to in the singular (e.g., "processing device"), but any suitable element may be represented by multiple instances of that element, and vice versa. For example, a set of operations described as being performed by a processing device may be implemented using different operations performed by different processing devices. As used herein, the phrase "based on" shall be understood to mean "based at least in part on" unless otherwise specified. at least in part on)".

[0011] A scientific instrument (e.g., a mass spectrometer, an electron microscope) can be any suitable computerized device capable of capturing electronic measurements in a scientific, laboratory, research, or clinical operating situation. A scientific instrument can include a complex configuration of operative components (e.g., an ion source, an ion lens, a heater, a cooler, a fluid valve, a fluid pump, a circuit switch, a sample stage, an aperture), sensors (e.g., an ion detector, a voltmeter, a thermistor, a potentiometer, a pressure gauge), or consumables (e.g., a carrier fluid, a calibration substance, a filter).

[0012] The digital twin of a scientific instrument can be any suitable set of mathematical or physics-based models (e.g., mass continuity equations, energy conservation equations) that can collectively simulate or predict the future behavior of the scientific instrument (e.g., calculate how the complex configuration of the scientific instrument, including its operable parts, sensors, or consumables, or any portion thereof, will be affected by any given plan or proposed use of the scientific instrument). In order for the digital twin to accurately or appropriately facilitate such simulation or prediction, the digital twin should first be calibrated or otherwise synchronized with the scientific instrument. In other words, whatever the parameters that constitute or define the digital twin are, and whatever the physical characteristics of the scientific instrument that those parameters represent are, numerical values that closely match them should be assigned. If the numerical values assigned to the parameters of the digital twin do not exactly match the physical characteristics of the scientific instrument, the simulations or predictions calculated by the digital twin may not accurately reflect the behavior of the scientific instrument.

[0013] Various parameters often represent or quantify physical characteristics of a scientific instrument that are not directly controllable or selectable (e.g., the damping coefficient can represent a type of physical characteristic of the scientific instrument that affects how the scientific instrument responds dynamically or kinematically to different inputs, but the scientific instrument generally does not have a button, knob, joystick, or other interface device that allows for the direct selection of the damping coefficient). Thus, calibration of such parameters can involve performing experiments or tests on the scientific instrument to infer or deduce what numerical values should be assigned to those parameters.

[0014] As recognized by the inventors of the various embodiments described herein, existing techniques facilitate calibration of digital twin parameters in a fragmented and non-standardized manner. In particular, when given a digital twin with a full set of parameters, existing techniques divide that full set of parameters into mutually prime subsets, identify which of those subsets depend on which others of those subsets, and calibrate those subsets in order of dependence by using subset-specific test procedures.

[0015] For example, consider a digital twin where the full set of parameters is the length, width, and height of the device, the stiffness and yield strength of the device, and the damping coefficient of the device. In such a case, existing techniques would involve determining that the stiffness and yield strength can be experimentally estimated if the shape is known, and that the damping coefficient can be experimentally estimated if the stiffness, yield strength, and shape are known. Thus, such existing techniques first measure the length, width, and height of the scientific device and assign those measurements to the length, width, and height parameters of the digital twin. Such existing techniques then estimate the stiffness and yield strength of the scientific device by performing one or more load-displacement tests on the scientific device (e.g., the data collected from those load-displacement tests can be statistically processed in conjunction with the measured shape to calculate the stiffness and yield strength), and then those estimated values would be assigned to the stiffness and yield strength parameters of the digital twin. Finally, such existing techniques estimate the damping coefficient of the scientific device by performing one or more vibration tests or initial condition tests on the scientific device (e.g., the data collected from those vibration or initial condition tests can be statistically processed in conjunction with the measured shape and the estimated stiffness and yield strength to calculate the damping coefficient), and then those estimated values would be assigned to the damping coefficient parameter of the digital twin. Note that such existing techniques perform calibration in the order of parameter dependence (e.g., the shape parameters are calibrated first, the stiffness and yield strength parameters are dependent on the shape parameters and thus are only calibrated after the shape parameters are calibrated, and the damping coefficient parameters are dependent on the shape parameters as well as the stiffness and yield strength parameters and thus are only calibrated after the shape parameters and the stiffness and yield strength parameters are calibrated). Further, note that such existing techniques use different or unique tests, metrics, or observables for each identified parameter subset (e.g., the shape parameters are directly measured, the stiffness and yield strength parameters are estimated via a load-displacement metric, and the damping coefficient parameters are estimated via a vibration metric).

[0016] Unfortunately, such existing technologies have various drawbacks.

[0017] First, as recognized by the inventors, such existing technologies cannot generalize beyond simple, well-behaved parameters. In fact, such existing technologies are only applicable to digital twin parameters that are not complex, not intricately intertwined, or have easily or clearly understood interrelationships. Simple parameters that are easily physically intuitive (such as shape, rigidity, yield strength, or damping coefficient) meet these conditions. However, more complex parameters that are not easily physically intuitive (such as optical aberration coefficients, or elements or parts of a quantum Hamiltonian) do not meet these conditions. In the field of scientific instruments, digital twins often have a very large number (e.g., dozens, hundreds, or thousands) of parameters that are high-dimensional, unclear, counterintuitive, or not well understood in terms of their interdependencies with each other. Existing technologies cannot be applied with confidence in such situations. Ultimately, when it is unclear which parameters depend on which other parameters, it is not possible to know in what order to calibrate the parameters according to existing technologies.

[0018] Furthermore, such existing technologies are vulnerable to what the inventors refer to as the parameter ambiguity problem. Specifically, the inventors have recognized that when calibrating the parameters of a digital twin by conducting experiments or tests on scientific instruments, it is possible for multiple different instantiations of the parametric state of the digital twin to correspond to, or appear to correspond to, the same acquired or measured experimental or test results, such that the parameters of the digital twin have, or appear to have, an inherent symmetry. In fact, in some cases, there may be multiple parametric state instantiations that actually correspond to a given experimental result, according to the underlying mathematical or physics-based theory of the digital twin. In other cases, noisy experimental measurements may make it appear as though multiple parametric state instantiations correspond to a given experimental result. In any case, although there is only one way to calibrate the parameters of the digital twin to match the true physical state of the scientific instrument, there may be more than one way to calibrate the parameters of the digital twin to conform to the experimental or test results.

[0019] Existing technologies do not recognize or address the problem of parameter ambiguity. Furthermore, as the inventors have recognized, existing technologies are unable to reliably handle or address the problem of parameter ambiguity. In fact, when there are multiple possible instantiations of the parametric state corresponding to experimental or test results, a dependency-ordered calibration that uses different test metrics for different parameters can be regarded as locking the digital twin to one of those possibilities earlier or arbitrarily than normal, for no good reason (e.g., without even recognizing or knowing that there are multiple other possibilities to choose from). In other words, which of those multiple possible instantiations of the parametric state is determined or selected by existing technologies can be a function of any order in which the parameters of the digital twin are calibrated.

[0020] For example, assume that the parametric state of the digital twin of a scientific instrument is composed of a first parameter and a second parameter. Assume that the first parameter is calibrated before the second parameter. In such a case, an experiment corresponding to or adjusted to the first parameter can be performed on the scientific instrument, and the result of the experiment can suggest or indicate that the value A should be assigned to the first parameter. Next, some other experiments corresponding to or adjusted to the second parameter can be performed on the scientific instrument, and the result of the experiment can suggest or indicate that the second parameter should be assigned the value B when considered together with the calibrated value A of the first parameter. Therefore, when the first parameter is calibrated before the second parameter, the parametric state of the digital twin can be calibrated to the A-B instantiation. Here, instead, assume that the second parameter is calibrated before the first parameter. In such a case, an experiment corresponding to or adjusted to the second parameter can be performed on the scientific instrument, and the result of the experiment can suggest or indicate that the value C should be assigned to the second parameter. Next, some other experiments corresponding to or adjusted to the first parameter can be performed on the scientific instrument, and the result of the experiment can suggest or indicate that the first parameter should be assigned the value D when considered together with the calibrated value C of the second parameter. Therefore, when the second parameter is calibrated before the first parameter, the parametric state of the digital twin can be calibrated to the D-C instantiation. This example shows that there can be multiple possible parametric state instantiations (e.g., A-B instantiation and D-C instantiation) that are consistent with the experiments performed on the scientific instrument, and this example also shows which of these multiple possible parametric state instantiations that are ultimately selected or chosen by the existing technology can depend on the order in which the digital twin parameters are calibrated.Letting selected or selected instantiations of the parametric state of a digital twin follow a calibration order can be considered unjustified, arbitrary, or particularly troublesome in situations where parameter interdependencies are not known or well understood from the start.

[0021] Furthermore, the inventors recognized that the inability to handle the parameter ambiguity problem can be exacerbated by using different test metrics for different parameters. Ultimately, using different experimental procedures, tests, or measurement criteria for different parameters can be considered to treat different parameters as inconsistent with each other (for example, in practice, different measurement criteria often measure with different uncertainties or resolution errors). Introducing such inconsistencies into the digital twin calibration process can reduce the likelihood of finding the true physical state of a scientific instrument among multiple possible parametric state instantiations.

[0022] As the inventors have recognized, for any given digital twin, it may be possible to attempt to identify, in an ad hoc manner, one or more specific experimental tests, observations, or metrics that are not affected by the parameter ambiguity problem. However, such an ad hoc approach would be overly costly from the perspectives of time consumption, labor, and blind experiments (e.g., for some specific digital twins representing some specific types of scientific instruments, much labor may be expended to experimentally identify tests, observations, or metrics that are not subject to the parameter ambiguity problem, and unfortunately, such efforts and experiments would then have to be repeated from the beginning for some different digital twins representing some different types of scientific instruments). Further, since it is not generally or universally guaranteed that any given digital twin has at least some experimental tests, observations, or metrics that are not affected by the parameter ambiguity problem, such an ad hoc approach may not even function. Further, such an ad hoc approach can be considered to be one that avoids or eludes the parameter ambiguity problem at a first stage, rather than addressing or solving it when the parameter ambiguity problem occurs.

[0023] Accordingly, there may be a desire for a system or technique that can improve one or more of these technical problems.

[0024] The various embodiments described herein can address one or more of these technical problems. One or more embodiments described herein can include a system, computer-implemented method, apparatus, or computer program product that can facilitate improved digital twin calibration for scientific instruments. In particular, the various embodiments described herein can include calibrating the parameters of a digital twin of a scientific instrument via an implementation of a full state Bayesian filter. More specifically, the full state Bayesian filter can be an algorithm or procedure that includes performing a plurality of calibration iterations on the digital twin. As described herein, each calibration iteration can include performing recursive Bayesian updates (e.g., via Bayes' rule) on the entirety of the parametric state of the digital twin. Further, such recursive Bayesian updates can be presented by the scientific instrument, can be simulated by the digital twin, and can be based on observables that are common or the same over a plurality of calibration iterations. At least for this reason, the observable can sometimes be referred to as an iterative common observable.

[0025] It should be noted how such embodiments can differ from the existing technology. As described above, the existing technology calibrates the parameters of the digital twin separately in the order of dependence (for example, updating the shape parameters in the first iteration, then updating the stiffness and yield strength parameters in the second iteration, and finally updating the damping coefficient parameters in the third iteration). In stark contrast, the various embodiments described herein do not include calibrating the parameters of the digital twin separately or independently. Instead, the various embodiments described herein include incrementally updating, adjusting, or otherwise modifying the numerical values of all the parameters of the digital twin during each calibration iteration (for example, if the various embodiments described herein were implemented in the above example, the shape parameters, stiffness and yield strength parameters, and damping coefficient parameters would all be incrementally updated in the first iteration, the shape parameters, stiffness and yield strength parameters, and damping coefficient parameters would all be incrementally updated again in the next iteration, and the shape parameters, stiffness and yield strength parameters, and damping coefficient parameters would all be incrementally updated again in yet another subsequent iteration). Further, as described above, the existing technology utilizes different test metrics or observables in each calibration iteration (for example, the shape parameters are directly measured in the first calibration iteration, the stiffness and yield strength parameters are estimated via a load-displacement metric in the second calibration iteration, and the damping coefficient parameters are estimated via a vibration or initial condition metric in the third calibration iteration). In stark contrast, the various embodiments described herein do not include utilizing such different test metrics or observables. Instead, the various embodiments described herein include utilizing a single, common, or universal test metric or observable throughout all calibration iterations (for example, if the various embodiments described herein were implemented in the above example, each calibration iteration would include performing a load-displacement test or, alternatively, each calibration iteration would include performing a vibration or initial condition test).

[0026] In various aspects, these differences between the existing art and the various embodiments described herein enable such embodiments to overcome the various drawbacks or problems encountered by such existing art.

[0027] Indeed, as described above, since the existing art performs calibration in the order of parameter interdependencies, such existing art is only applicable to physically intuitive digital twin parameters (such as shape parameters, stiffness and yield strength parameters, and damping coefficient parameters, etc.) that have easily understandable interdependencies. In stark contrast, the various embodiments described herein do not require or need any prior information regarding the interdependencies between digital twin parameters. In fact, all digital twin parameters can be incrementally updated in each calibration iteration as described herein, regardless of their interdependencies, rather than different parameters being updated in different iterations in the order of their dependencies. Thus, the various embodiments described herein can be considered generalizable to digital twin parameters (such as those like optical aberration coefficients or those like the numerical elements of a quantum Hamiltonian) having highly complex, complicated, or unknown interactions or interdependencies with each other.

[0028] Furthermore, as described above, existing techniques perform calibration in the order of parameter interdependence using different test metrics or observables for different subsets of parameters, and thus such existing techniques cannot appropriately handle the parameter ambiguity problem. In fact, multiple different instantiations of the parametric state of a digital twin associated with a scientific instrument can be consistent with the experimental results obtained from the scientific instrument (especially in the case of digital twin parameters having unknown or very complex interdependencies). However, only one of those multiple different instantiations can be considered to actually match the true physical state of the scientific instrument. By calibrating the parameters separately in the order of dependence and using different test metrics or observables for different parameters, existing techniques do not even recognize that such multiple different instantiations are possible and arbitrarily lock onto one of those multiple different instantiations. In stark contrast, the various embodiments described herein do not calibrate the parameters separately in the order of dependence using different observables for different parameters. Instead, the various embodiments described herein can incrementally adjust all of the parameters during each calibration iteration (rather than adjusting different parameters during different iterations), and such adjustment can be based on an experimental metric or observable that is common or universal across all of the calibration iterations (e.g., the same experiment or test can be performed on the scientific instrument during each calibration iteration rather than performing different experiments or tests for different parameters during different iterations or for different parameters). The inventors have experimentally verified that such a calibration procedure appropriately calibrates the digital twin parameters even in the presence of the parameter ambiguity problem. In other words, existing techniques tend to inaccurately or incorrectly calibrate digital twin parameters in the presence of the parameter ambiguity problem, while the various embodiments described herein accurately or correctly calibrate digital twin parameters in the presence of the parameter ambiguity problem.

[0029] Accordingly, the various embodiments described herein can be considered to facilitate improved digital twin calibration for scientific instruments.

[0030] The various embodiments described herein can be considered computerized tools (e.g., any suitable combination of computer-executable hardware or computer-executable software) that can be electronically installed on or otherwise related to a scientific instrument and that can facilitate improved digital twin calibration for the scientific instrument. In various aspects, such computerized tools can comprise an access component, a calibration component, or a post-calibration component.

[0031] In various embodiments, the scientific instrument can be any suitable computerized device capable of electronically capturing, measuring, or otherwise recording any suitable electronic information having clinical or laboratory significance (e.g., can be a mass spectrometer, can be an electron microscope). In either case, the scientific instrument can include a set of controllable instrument settings. In various aspects, the controllable instrument settings can be any suitable configurable hardware characteristic or configurable software characteristic of the scientific instrument that can be directly controlled, adjusted, or changed in response to electronic instructions or commands received from a user or technician of the scientific instrument (e.g., can be a user-controlled voltage or current setting of the scientific instrument, a user-controlled temperature setting of the scientific instrument, or a user-controlled actuator setting of the scientific instrument).

[0032] In various embodiments, there may be digital twins corresponding to or otherwise associated with scientific instruments. In various aspects, the digital twin can be any suitable mathematical model or physics-based model, or any suitable combination thereof, that numerically, computationally, or analytically predicts, anticipates, or otherwise simulates how a scientific instrument or any suitable portion thereof will respond to any given use scenario. More specifically, the digital twin can include a parametric state, a set of input variables, and a set of output variables.

[0033] In various cases, the parametric state can include any suitable number of parameters, each of which can be any suitable mathematical quantity that represents any suitable characteristic, attribute, or property (physical or theoretical) of the scientific instrument (e.g., the shape of the scientific instrument, the material properties of the scientific instrument, the aberration coefficient of the scientific instrument). In various cases, the characteristics, attributes, or properties of the scientific instrument represented by the parametric state can be non-transitory (e.g., can refrain from drifting over time) or transitory (e.g., can drift over time). In various situations, the characteristics, attributes, or properties of the scientific instrument represented by the parametric state can be indirectly affected or influenced by a set of controllable instrument settings (e.g., the attenuation coefficient of the scientific instrument can be indirectly changed by changing one or more controllable motor settings of the scientific instrument). Nevertheless, any of such characteristics, attributes, or properties may not be directly controllable by a set of controllable instrument settings (e.g., the scientific instrument does not have a button or knob that allows for a direct or explicit selection of a desired attenuation coefficient, in which case, the calibration of the attenuation coefficient parameter would be straightforward).

[0034] In various aspects, the set of input variables can include any suitable number of input variables. In various instances, the input variables can represent any suitable details or aspects of the usage scenarios that can be encountered by a scientific instrument (e.g., can represent or quantify the mass or chemical composition of a laboratory sample that can be scanned or analyzed by a scientific instrument), and can be any suitable mathematical quantity.

[0035] In various cases, the set of output variables can include any suitable number of output variables. In various aspects, the output variables can be any suitable mathematical quantity that can represent any suitable details or aspects of the scientific instrument that are desired to be calculated, predicted, or tracked (e.g., the ultimate wear or degradation accumulated by the scientific instrument or any of its parts in response to a given usage scenario).

[0036] In various aspects, the set of input variables can be collectively regarded as the operands of the digital twin, the parametric state can be collectively regarded as defining the operators of the digital twin, and the set of output variables can be calculated or computed by mathematically applying the parametric state to the set of input variables (e.g., via any suitable mathematical function or its composition). Thus, regardless of what the numerical values are that define or describe any given usage scenario, a set of input variables can be assigned, and by applying the parametric state to the set of input variables, it is possible to simulate, predict, or anticipate how the scientific instrument will behave or respond to that given usage scenario. However, if the parametric state of the digital twin does not exactly match the true physical state of the scientific instrument, such simulations, predictions, or anticipations can be inaccurate.

[0037] Therefore, it may be desirable to calibrate or synchronize the parametric state of the digital twin with the true physical state of the scientific instrument. As described herein, computerized tools can facilitate such calibration or synchronization.

[0038] In various embodiments, the access component of the computerized tool can electronically access a set of controllable device settings or a digital twin. That is, the access component can electronically interface or communicate with a set of controllable device settings or a digital twin, whereby the access component functions as a conduit through which other components of the computerized tool can electronically interact (e.g., send electronic commands, read electronic signals) with a set of controllable device settings or a digital twin.

[0039] In various embodiments, the calibration component of the computerized tool can electronically synchronize the parametric state of the digital twin to the true physical state of the scientific instrument. In other words, the calibration component can identify a calibrated instantiation of the parametric state that is presumed or expected to be an acceptable approximation of the true physical state of the scientific instrument (e.g., within any appropriate threshold margin of similarity). In particular, the calibration component can achieve this by implementing or executing a state - of - the - art Bayesian filter for both the scientific instrument and the digital twin.

[0040] In various aspects, the state-of-the-art Bayesian filter can include a plurality of calibration iterations to be performed in sequence. That is, the plurality of calibration iterations can include an initial calibration iteration and a final calibration iteration. In various cases, the plurality of calibration iterations can be driven by a recurring common observable. In various situations, the recurring common observable can be presented by a scientific instrument during or after performing a standardized or repeatable usage scenario, and can be any suitable measurable or observable behavior that can be simulated (e.g., predicted, output, calculated) by a digital twin, or can represent or otherwise refer to that. In some cases, the recurring common observable can be any set of output variables calculated in response to a standardized or repeatable usage scenario. In other cases, the recurring common observable can instead be derived from any set of output variables calculated in response to a standardized or repeatable usage scenario. In any case, each of the plurality of calibration iterations includes operating or performing the scientific instrument according to its standardized or repeatable usage scenario to measure or observe the behavior of the scientific instrument with respect to the recurring common observable, determining its standardized or repeatable usage scenario on the digital twin to predict the behavior of the scientific instrument with respect to the recurring common observable, and incrementally updating the entire parametric state of the digital twin (e.g., all of the digital twin's parameters, not just a subset thereof) based on the error between the measured or observed behavior presented by the scientific instrument and the simulated behavior predicted by the digital twin through recursive application of Bayes' rule. Note that the adjective "recurring common" is considered appropriate because the recurring common observable is used throughout all of the plurality of calibration iterations (e.g., one metric or observable is common or universal to all of the calibration iterations).

[0041] More specifically, the first or initial calibration iteration of the plurality of calibration iterations can be performed as follows.

[0042] In various aspects, the true physical state of a scientific instrument may be unknown. However, despite such an unknown true physical state, a calibration component can cause or command the scientific instrument to operate or perform according to a standardized or repeatable usage scenario, or to be commanded to operate or perform in that manner. During or after such an operation or performance, the calibration component can electronically measure (or can command the scientific instrument to electronically measure) the behavior of the scientific instrument with respect to a repetitive common observable. This may be referred to as a first measured observation of the repetitive common observable.

[0043] In various cases, the calibration component can randomly sample or randomly select a first plurality of parametric state instantiations of the digital twin from an unrestricted or unconstrained version of the state space of the digital twin. More specifically, each parameter of the digital twin can be considered a mathematical quantity that can arise from a respective defined region of values, and all of their respective defined regions can be considered to form the state space of the digital twin collectively, and any suitable number of instantiations of the parametric state can be randomly selected from such a state space.

[0044] In various instances, the calibration component can cause or simulate a standardized or repeatable usage scenario using each of the first plurality of parametric state instantiations for the digital twin, or command it to perform or simulate in that manner. In other words, for each given one of the first plurality of parametric state instantiations, the digital twin can predict how the scientific instrument will behave with respect to the repetitive common observable, assuming that the true physical state of the scientific instrument coincides with the given parametric state instantiation. This can result in a first plurality of simulated observations of the repetitive common observable.

[0045] In various aspects, for each given one of the first plurality of parametric state instantiations, the calibration component may calculate respective weights based on the error (e.g., mean absolute error (MAE), mean squared error (MSE), cross-entropy error) between the first measured observation of the iterative common observable and the one corresponding to that given parametric state instantiation among the first plurality of simulated observations. In various cases, the weight assigned to any given parametric state instantiation can be based on the reciprocal of any error calculated for that given parametric state instantiation, can be based on the complement of any such error, or can be inversely proportional to any such error.

[0046] In various instances, the calibration component can delete, remove, or otherwise discard any of the first plurality of parametric state instantiations having weights below any suitable threshold weight value. This can result in the first plurality of remaining parametric state instantiations. In various cases, the calibration component can calculate one or more variances of the first plurality of remaining parametric state instantiations, and the calibration component can compare those one or more variances to any suitable threshold variance value.

[0047] If one or more of those variances meet (e.g., fall below) a threshold variance value, the calibration component can calculate a calibrated parametric state instantiation based on the first plurality of remaining parametric state instantiations. In particular, the calibrated parametric state instantiation can be equal to or otherwise based on a weighted average of the first plurality of remaining parametric state instantiations. As described above, the calibrated parametric state instantiation can be considered an acceptable or sufficient approximation of the true physical state of the scientific instrument. Thus, in various cases, the calibration component can cause the digital twin's parameters to take on any numerical values indicated by the calibrated parametric state instantiation.

[0048] Instead, if one or more of those variances do not meet (e.g., exceed) a threshold variance value, the calibration component can apply any suitable active setting adjustment (e.g., rotation of a knob, pressing of a button, displacement of a joystick, activation or clicking of a graphical user interface) to any of the set of controllable device settings of the scientific instrument. In various aspects, the calibration component can modify each of the first plurality of remaining parametric state instantiations according to that active setting adjustment, and such modification can result in the first plurality of modified remaining parametric state instantiations. Indeed, as described above, the characteristics, attributes, or properties of the scientific instrument represented by the parameters of the digital twin cannot be directly or explicitly controlled or selected by the set of controllable device settings (e.g., otherwise, calibration would be trivial). However, nevertheless, those characteristics, attributes, or properties can be indirectly affected by the set of controllable device settings in a known or understood way or pattern. In other words, any given change to the set of controllable device settings can be expected to be commensurate with, related to, or otherwise cause a known change in those characteristics, attributes, or properties of the scientific instrument (e.g., in the unknown true physical state of the scientific instrument). Stated yet another way, changing a particular controllable device setting by a particular amount or percentage is known or can be expected to change each of one or more of those characteristics, attributes, or properties by one or more respective amounts or percentages. Thus, for each given one of the first plurality of remaining parametric state instantiations, the calibration component can adjust, modify, or change that given remaining parametric state instantiation in any way that is expected to be caused by the active setting adjustment, thereby resulting in each one of the first plurality of modified remaining parametric state instantiations.

[0049] Here, a second calibration iteration of the plurality of calibration iterations can be performed as follows.

[0050] In various aspects, the true physical state of the scientific instrument may still be unknown, but such true physical state may be altered in some known or expected way by the aforementioned active setting adjustments. Similarly, the calibration component can cause or instruct the scientific instrument to operate or perform according to a standardized or repeatable usage scenario, or otherwise command it to operate or perform, and the calibration component can then measure (or can instruct the scientific instrument to measure) the behavior of the scientific instrument with respect to the repetitive common observable. This may be referred to as a second measured observation of the repetitive common observable.

[0051] Here, in various cases, the calibration component can randomly sample or randomly select a second plurality of parametric state instantiations from the state space of the digital twin. However, rather than sampling or selecting from an unconstrained or unconstrained version of the state space, the calibration component can instead sample or select from an incrementally constrained or constrained version of the state space. In various aspects, that incrementally constrained or restricted version of the state space can be based on a first plurality of modified remaining parametric state instantiations. More specifically, the first plurality of modified remaining parametric state instantiations can be regarded as Bayesian evidence that can be used in recursive Bayesian updates to compact or shrink the state space of the digital twin. The practical effect of such recursive Bayesian updates can be to numerically approximate, numerically bring closer to, or otherwise cause the second plurality of parametric state instantiations to be selected from any region or span of the state space that is near or local to the first plurality of modified remaining parametric state instantiations (e.g., the second plurality of parametric state instantiations cannot be sampled or selected from a region or span of the state space that does not include or is far from the first plurality of modified remaining parametric state instantiations).

[0052] In various cases, the second calibration iteration can then proceed as described above. That is, the calibration component causes the digital twin to perform or simulate a standardized or repeatable usage scenario using each of the second plurality of parametric state instantiations, thereby resulting in a second plurality of simulated observations of the iterative common observable, and calculates a respective weight for each of the second plurality of parametric state instantiations based on the error between the second measured observation of the iterative common observable and the second plurality of simulated observations of the iterative common observable, and deletes any of the second plurality of parametric state instantiations having a weight below a threshold weight value, thereby resulting in a second plurality of remaining parametric state instantiations, and can compare one or more variances of the second plurality of remaining parametric state instantiations to a threshold variance value. If those one or more variances meet (e.g., are below) the threshold variance value, the calibration component can calculate a calibrated parametric state instantiation based on the second plurality of remaining parametric state instantiations (e.g., equal to or based on the weighted average of the second plurality of remaining parametric state instantiations). Alternatively, if those one or more variances do not meet (e.g., are above) the threshold variance value, the calibration component can apply any other active setting adjustment to a set of controllable device settings of the scientific instrument, and the calibration component can correspondingly modify the second plurality of remaining parametric state instantiations based on that active setting adjustment, thereby resulting in a second plurality of modified remaining parametric state instantiations. The calibration component can then proceed to a third calibration iteration of the state ensemble Bayesian filter.

[0053] The overall state Bayesian filter can proceed in this way, and each calibration iteration incrementally narrows, tightens, or shrinks the state space of the digital twin until the threshold variance value is met. When the threshold variance value is finally met in a given calibration iteration, the calibrated parametric state instantiation can be equal to the weighted average of any remaining parametric state instantiations calculated during that given calibration iteration.

[0054] In various embodiments, the post-calibration component of the computerized tool can facilitate, perform, or otherwise initiate any suitable electronic action based on the calibration or synchronization performed by the calibration component.

[0055] As a non-limiting example, the post-calibration component can generate any suitable electronic notification indicating that the digital twin is ready to accurately simulate, predict, or anticipate the future behavior of the scientific instrument in response to the calibration or synchronization performed by the calibration component. In some cases, the post-calibration component can send the electronic notification to any suitable computing device. In other cases, the post-calibration component can visually render the electronic notification on any suitable computer screen or monitor.

[0056] As another non-limiting example, the calibrated component can cause the digital twin to actually simulate, predict, or forecast the future behavior of the scientific instrument in response to calibration or synchronization performed by the calibration component, or can command it to actually simulate, predict, or forecast, or can instruct it to actually simulate, predict, or forecast. For example, a user or technician of the scientific instrument can identify a particular usage scenario via the interface of the scientific instrument (e.g., keyboard, keypad, touch screen) and can request to predict how the scientific instrument will respond or behave in that particular usage scenario. In various embodiments, the calibrated component can, in response, assign any number of values corresponding to or defining that particular usage scenario to a set of input variables (e.g., those values can be provided by the user or technician via the interface), and the calibrated component can command or instruct the digital twin to apply a calibrated parametric state instantiation to the set of input variables, thereby resulting in particular numerical values for a set of output variables. In various cases, the calibrated component can visually render any of those particular numerical values of the set of output variables on any suitable computer screen or monitor for the user or technician to see. In this way, the digital twin can be regarded as accurately or reliably simulating how the scientific instrument will behave in or during a particular usage scenario.

[0057] The various embodiments described herein are highly technical in nature, using hardware or software (e.g., to facilitate improved digital twin calibration for scientific instruments), and are not abstract and cannot be implemented as a set of mental operations by humans. Instead, some of the processes implemented can be performed by a dedicated computer (e.g., a digital twin configured to model the behavior of a mass spectrometer or an electron microscope) for performing defined operations related to a scientific instrument.

[0058] For example, such defined operations can include synchronizing the parametric state of the digital twin with the physical state of the scientific instrument via execution of a full state Bayesian filter by a device operably coupled to a processor, and generating, by the device, an electronic alert indicating that the digital twin is ready to predict the behavior of the scientific instrument in response to the synchronization. In some cases, such defined operations can include predicting, by the device, how the scientific instrument will respond to a proposed usage scenario via performing the digital twin after synchronization. In various cases, the full state Bayesian filter can include a set of calibration iterations, each of which can include a Bayesian update for the entire parametric state based on an iterative common observable that can be presented by the scientific instrument and simulated by the digital twin.

[0059] Such defined operations are essentially computerized. In fact, scientific instruments such as chromatographs, mass spectrometers, and electron microscopes are highly technical computerized devices equipped with specific computerized hardware (e.g., temperature sensors, pressure sensors, voltage sensors, ion beam emitters, ion focusing lenses, mass analyzers, ion detectors, beam apertures, fluid valves). The scientific instruments and the operations they perform cannot be implemented in any reasonable or practical way without a computer, either by the human mind or by a human with pen and paper. Similarly, a digital twin (as the word "digital" in its name suggests) is also an essentially computerized or virtual construct used to electronically predict or simulate the future behavior of a scientific instrument. A digital twin simply cannot be facilitated or executed in any reasonable or practical way without a computer, either by the human mind or by a human with pen and paper. Furthermore, the operation of calibrating or synchronizing the parameters of a digital twin with the true physical state of a scientific instrument itself is an essentially software-based and hardware-based iterative procedure involving calculating the error between the simulated behavior output by the digital twin and the actual real-world behavior measured by or with respect to the scientific instrument. Such calibration or synchronization cannot be carried out in any meaningful, reasonable, or practical way by the human mind or by a human with pen and paper.

[0060] Furthermore, the various embodiments described herein can incorporate various teachings regarding improved digital twin calibration for scientific instruments into actual applications. As explained above, existing techniques separately calibrate digital twin parameters in order of dependence (e.g., first shape parameters, then stiffness and yield strength parameters, and finally damping coefficient parameters), and use different observables for different parameters (e.g., direct measurements of shape parameters, load-displacement observations for stiffness and yield point parameters, vibration observations for damping coefficient parameters) to facilitate such calibration. Such existing techniques are applicable only to simple and physically intuitive parameters with well-understood or clear interdependencies, and such existing techniques cannot be applied to non-physically intuitive parameters with unclear or ambiguous interdependencies. In addition, such existing techniques cannot confidently or reliably handle the parameter ambiguity problem. In fact, there can be multiple possible parametric state instantiations that are consistent with a given experimental finding (as is often the case when dealing with complex and non-physically intuitive parameters such as aberration coefficients or quantum Hamiltonians). However, the dependence-based order of calibration and the use of different observables for different parameters allow the existing techniques to identify or determine any one of those multiple possible parametric state instantiations. In other words, changing the order of calibration, and thus which observable is queried when, can change which of those multiple possible parametric state instantiations is identified or determined. For at least these reasons, existing techniques are thought to suffer from various technical problems.

[0061] The various embodiments described herein can help improve one or more of such technical problems. In particular, the various embodiments described herein can include calibrating the parameters of a digital twin to the physical state of a scientific instrument by leveraging or implementing a full-state Bayesian filter. As described herein, a full-state Bayesian filter can be an algorithm or procedure that includes performing a series of calibration iterations on a scientific instrument and a digital twin, where each calibration iteration can include performing recursive Bayesian updates (e.g., evidence and prior-based posterior calculations) on the entire parametric state of the digital twin, and thus, with respect to the adjective "full-state" (e.g., for all of the parameters). Further, a full-state Bayesian filter can be presented during the operation of a scientific instrument and can be driven by iterative common observables that can be simulated or predicted by the digital twin. In various cases, iterative common observables can be queried or tested over all of a sequence of calibration iterations, and thus, with respect to the adjective "iterative common". As described herein, an implementation of a full-state Bayesian filter driven by iterative common observables can incrementally tighten, shrink, or narrow the available state space of the digital twin until one or more variances of its state space fall below any suitable threshold for each calibration iteration. In this regard, the tightened, shrunk, or narrowed state space can be considered to indicate or identify the true physical state of the scientific instrument. Unlike existing technologies, the various embodiments described herein are generalizable to any suitable digital twin parameters, regardless of how complex, unclear, or unknown their interdependencies may be. In fact, knowledge of parameter interdependencies is not required or used by the various embodiments described herein. Also, unlike existing technologies, the various embodiments described herein are not confounded, perturbed, or otherwise obstructed by the parameter ambiguity problem.In fact, the inventors have experimentally verified that, despite the existence of multiple possible solutions caused by either a fundamental physics-based theory or noisy measurements, a state-of-the-art Bayesian filter driven by iterative common observables can correctly or accurately identify the true physical state of a scientific instrument. Furthermore, the various embodiments described herein can be considered generalizable or universal parameter calibration techniques that can be applied to any suitable digital twin representing any suitable type of scientific instrument. Compare this, instead, to ad-hoc techniques that require experiments that are significantly adjusted or customized for different digital twins representing different types of scientific instruments. For at least these reasons, the various embodiments described herein can be considered a specific and tangible technical improvement in the field of digital twins. Accordingly, the various embodiments described herein are surely eligible as useful and practical applications of a computer.

[0062] Furthermore, the various embodiments described herein can control real-world tangible devices based on the disclosed teachings. For example, the various embodiments described herein can electronically activate, deactivate, or otherwise operate the real-world hardware (e.g., ion beam emitter, ion focusing lens, carrier fluid valve / pump) of real-world scientific instruments (e.g., mass spectrometer, electron microscope).

[0063] FIG. 1 shows an exemplary and non-limiting block diagram of a scientific instrument module 102 according to the various embodiments described herein.

[0064] In various embodiments, the scientific instrument module 102 can be implemented by circuitry such as a programmed computing device (e.g., including electrical or optical components). The logic of the scientific instrument module 102 can be included in a single computing device or distributed across multiple computing devices that communicate with each other as needed. Examples of computing devices that can implement the scientific instrument module 102, alone or in combination, are described herein with reference to FIGS. 24 and 26, and examples of systems or networks of interconnected computing devices across which the scientific instrument module 102 can be implemented are described herein with reference to FIGS. 25 and 27.

[0065] The scientific instrument module 102 can include a first logic 104, a second logic 106, and a third logic 108. As used herein, the term "logic" can include an apparatus that performs a set of operations related to the logic. For example, any of the logic elements included in the scientific instrument module 102 can be implemented by one or more computing devices programmed with instructions that cause one or more processing devices of the computing device to perform a set of operations associated therewith. In certain embodiments, the logic element can include one or more non-transitory computer-readable media having instructions that, when executed by one or more processing devices of one or more computing devices, cause the one or more computing devices to perform a set of associated operations. As used herein, the term "module" can refer to a collection of one or more logic elements that together perform functions associated with the module. Different ones of the logic elements within the module can take the same form or different forms. For example, some of the logic within the module can be implemented by a programmed general-purpose processing device, and other logic within the module can be implemented by an application-specific integrated circuit (ASIC). In another example, different ones of the logic elements within the module can be associated with different sets of instructions executed by one or more processing devices. The module can omit one or more of the logic elements shown in the associated drawings. For example, the module can include a subset of the logic elements shown in the associated drawings if the module performs a subset of the operations described herein with reference to that module.

[0066] In various embodiments, there may be a scientific instrument corresponding to the scientific instrument module 102. In various aspects, the scientific instrument can be any suitable computerized device that can electronically measure some scientifically relevant, clinically relevant, or research-related features, characteristics, or attributes of an analytical sample (e.g., a collection of known or unknown mixtures, compounds, or substances). As a non-limiting example, the scientific instrument can be a mass spectrometer operably coupled to a gas chromatograph or a liquid chromatograph. In such a case, the scientific instrument can measure or determine the ion spectrum of the analytical sample (e.g., the relative ion abundance as a function of mass-to-charge ratio). As another non-limiting example, the scientific instrument can be a scanning electron microscope. In such a case, the scientific instrument can measure or determine the surface topography of the analytical sample. As yet another non-limiting example, the scientific instrument can be a transmission electron microscope. In such a case, the scientific instrument can measure or determine the details of the internal structure of the analytical sample. As a more general non-limiting example, the scientific instrument can be any suitable type of charged particle microscope (e.g., some types of microscopes can use a beam of non-electronic ions to capture an image).

[0067] In various embodiments, the first logic 104 can access the digital twin of the scientific instrument. In various aspects, the digital twin can be any suitable set of mathematical or physics-based formulas, equations, or models that can simulate, predict, or otherwise anticipate any suitable behavior pattern of the scientific instrument. As a non-limiting example, the digital twin can include any suitable formula, equation, or model that can predict the amount of wear or degradation experienced or accumulated by the scientific instrument or any part thereof. As another non-limiting example, when an analytical sample is provided, the digital twin can include any suitable formula, equation, or model that can predict the scientifically relevant, clinically relevant, or research-related measurements that would be obtained by the scientific instrument when analyzing the given analytical sample.

[0068] In various embodiments, the second logic 106 can calibrate or synchronize the parametric state of the digital twin to the physical state of the scientific instrument. Ultimately, without such calibration or synchronization, the digital twin may not be able to accurately simulate, anticipate, or predict the behavior of the scientific instrument. In various aspects, the second logic 106 can facilitate such calibration or synchronization by leveraging or implementing a full state Bayesian filter. In various instances, the full state Bayesian filter can be driven by a recurrent common observable. In various cases, the recurrent common observable can be any suitable state-dependent characteristic that can be presented by or observable by the scientific instrument during operation or execution and that can be simulated, anticipated, or predicted by the digital twin. In particular, the full state Bayesian filter can include a series of calibration iterations, each calibration iteration including operating or running the scientific instrument, thereby resulting in a measurement or observed behavior corresponding to the recurrent common observable, operating or running the digital twin, thereby resulting in a simulated or predicted behavior corresponding to the recurrent common observable, and recursively updating the overall (and thus "full state") parametric state of the digital twin based on an error calculated between the measured or observed behavior and the simulated or predicted behavior.

[0069] In various embodiments, the third logic 108 can facilitate any suitable electronic action in response to the completion or implementation of the second logic 106. As a non-limiting example, the third logic 108 can electronically notify a user or technician of the scientific instrument (e.g., via a visual representation on an electronic display) that the digital twin is calibrated and thus ready to accurately simulate, predict, or anticipate the future behavior of the scientific instrument. As another non-limiting example, the third logic 108 can electronically receive (e.g., via an electronic interface of the scientific instrument) user input that identifies or indicates a proposed use scenario for the scientific instrument (e.g., analyzing one or more user-specified analytical samples within a user-specified time frame using a user-specified instrument configuration), and the third logic 108 can execute or perform the digital twin in that proposed use scenario, thereby further including simulating, predicting, or anticipating how the scientific instrument will behave or respond to that proposed use scenario.

[0070] Accordingly, the scientific instrument module 102 can facilitate improved digital twin calibration for the scientific instrument.

[0071] FIG. 2 is an exemplary and non-limiting flowchart of a computer-implemented method 200 according to various embodiments described herein. The operations of the computer-implemented method 200 can be used in any suitable context for performing any suitable operations (e.g., implemented by or used with any of the various modules, computing devices, or graphical user interfaces described with respect to FIGS. 1, 23, 24, 25, 26, and 27). The operations are shown in a specific order in FIG. 2, one time each, but the operations can be appropriately reordered or repeated as desired (e.g., different operations being performed in parallel as appropriate).

[0072] In various aspects, operation 202 may include performing a first operation of accessing a digital twin of a scientific instrument. In various cases, the first logic 104 may perform or otherwise facilitate operation 202.

[0073] In various instances, operation 204 may include performing a second operation of synchronizing a parametric state of the digital twin to a physical state of the scientific instrument via execution of a full state Bayesian filter. In various aspects, the full state Bayesian filter may be presented by the scientific instrument and driven by or otherwise based on an iterative common observable that may be simulated by the digital twin. In various cases, the second logic 106 may perform or otherwise facilitate operation 204.

[0074] In various aspects, operation 206 may include performing a third operation of predicting the behavior of the scientific instrument or otherwise notifying the user that the digital twin is prepared for such prediction in response to synchronizing the parametric state to the physical state. In various cases, the third logic 108 may perform or otherwise facilitate operation 206.

[0075] Accordingly, the computer-implemented method 200 can facilitate improved digital twin calibration for a scientific instrument.

[0076] FIG. 3 shows a block diagram of an exemplary and non-limiting scientific instrument 302 that can facilitate improved digital twin calibration according to one or more embodiments described herein.

[0077] In various aspects, the scientific instrument 302 can be as described above. That is, the scientific instrument 302 can be any suitable computerized device that can electronically measure any suitable scientifically relevant, clinically relevant, or research-related feature, attribute, or property of any suitable analytical sample. By way of non-limiting example, the scientific instrument 302 can be a mass spectrometer that can be equipped or equipped with a gas chromatograph or a liquid chromatograph. In such a case, the scientific instrument 302 can utilize its constituent hardware (e.g., injector, oven-heated column, carrier fluid valve or pump, ion beam emitter, ion optical lens or shroud, mass analyzer) to electronically determine the chemical composition or constitution of any given analytical sample. As another non-limiting example, the scientific instrument 302 can be a scanning electron microscope or a transmission electron microscope. In such a case, the scientific instrument 302 can utilize its constituent hardware (e.g., electron source, anode, condenser lens, condenser aperture, scanning coil, objective lens, objective aperture, deflector, condenser, stigmator, electron detector, X-ray detector, operable sample stage) to electronically determine or map the surface structure or internal structure of any given analytical sample.

[0078] Although not explicitly shown in the figure, the scientific instrument 302 can be electronically integrated with any suitable human-computer interface device that can be remote or local to the scientific instrument 302. Accordingly, a user or technician associated with the scientific instrument 302 can interact with or otherwise control the scientific instrument 302. Some non-limiting examples of human-computer interface devices can be a keyboard of the scientific instrument 302, a keypad of the scientific instrument 302, a touch screen of the scientific instrument 302, or a voice command system of the scientific instrument 302.

[0079] In various examples, as shown, the scientific instrument 302 can include a set of controllable instrument settings 304 and a digital twin 306. In various cases, the digital twin 306 can include a parametric state 308, a set of input variables 310, and a set of output variables 312. Various non-limiting aspects are described with respect to FIG. 4.

[0080] FIG. 4 shows an exemplary and non-limiting block diagram illustrating a set of controllable instrument settings 304, a parametric state 308, a set of input variables 310, and a set of output variables 312, according to one or more embodiments described herein.

[0081] In various aspects, a set of controllable device settings 304 can include, for any suitable positive integer n, n settings, i.e., controllable device settings 304(1) through controllable device settings 304(n). In various instances, each of the sets of controllable device settings 304 can be any suitable hardware-related or software-related characteristic of the scientific instrument 302 that can guide or affect how the scientific instrument 302 executes or operates on any given analytical sample and can be selectively configured or otherwise controlled by a user or technician (e.g., via interaction with a human-computer interface device of the scientific instrument 302). That is, controllable device setting 304(1) can be regarded as a first user-configurable hardware-related or software-related characteristic that affects how the scientific instrument 302 executes or operates on an analytical sample, and controllable device setting 304(n) can be regarded as the nth user-configurable hardware-related or software-related characteristic that affects how the scientific instrument 302 executes or operates on an analytical sample. As a non-limiting example, any of the sets of controllable device settings 304 can be a user-configurable voltage or current setting, whereby a user or technician can control the electrodes of the scientific instrument 302 to selectively increase or decrease the voltage or current within or applied by the scientific instrument 302. As another non-limiting example, any of the sets of controllable device settings 304 can be a user-configurable temperature setting that enables a user or technician to control a heater (e.g., an oven, a heating coil) or a cooler (e.g., a cooling fan, a heat pump, a refrigerator) of the scientific instrument 302 to selectively raise or lower the temperature within the scientific instrument 302 or the temperature applied by the scientific instrument 302.As yet another non-limiting example, any of the sets of controllable device settings 304 can be user-configurable radiation settings that enable a user or technician to selectively increase or decrease the level of radiation within or applied by the scientific instrument 302, such as by controlling a radiation source (e.g., an electron emitter, an ion beam emitter) of the scientific instrument 302. As yet another non-limiting example, any of the sets of controllable device settings 304 can be user-configurable mechanical actuator settings that enable a user or technician to control a mechanical actuator (e.g., an electric motor, a sample stage, a diaphragm aperture) of the scientific instrument 302 to selectively move the mechanical actuator. As yet another non-limiting example, any of the sets of controllable device settings 304 can be user-configurable optical settings that enable a user or technician to control an optical element (e.g., an optical lens, a light deflector) of the scientific instrument 302 to selectively change the optical quality (e.g., focus size or position, aberration, defocus) applied by the scientific instrument 302.

[0082] In various aspects, the digital twin 306 can be any suitable set or collection of any suitable mathematical or physics-based models that can collectively simulate, predict, or otherwise anticipate the details or aspects of any suitable behavior of the scientific instrument 302. By way of non-limiting example, the digital twin 306 can include any suitable mass continuity equations, inequalities, or formulas that are in some way related to the scientific instrument 302. As another non-limiting example, the digital twin 306 can include any suitable energy balance equations, inequalities, or formulas that are related to the scientific instrument 302 in some form. As yet another non-limiting example, the digital twin 306 can include any suitable heat transfer equations, inequalities, or formulas that are related to the scientific instrument 302 in some way. As yet another non-limiting example, the digital twin 306 can include any suitable fluid flow equations, inequalities, or formulas that are related to the scientific instrument 302 in some form. As yet another non-limiting example, the digital twin 306 can include any suitable equations, inequalities, or formulas of motion or kinematics that are related to the scientific instrument 302 in some form. As another non-limiting example, the digital twin 306 can include any suitable equations, inequalities, or formulas of Newtonian mechanics or quantum mechanics that are related to the scientific instrument 302 in some way. As yet another non-limiting example, the digital twin 306 can include any suitable equations, inequalities, or formulas of corrosion or degradation that are related to the scientific instrument 302 in some way.

[0083] In either case, the digital twin 306 can be regarded as a set or collection of mathematical or physics-based models that can simulate, predict, or forecast something related to the scientific instrument 302, and those mathematical or physics-based models can be regarded as being composed of a parametric state 308, a set of input variables 310, and a set of output variables 312. In particular, the parametric state 308 can be regarded as defining the operators or coefficients of those mathematical or physics-based models, the set of input variables 310 can be regarded as the operands or arguments of those mathematical or physics-based models, and the set of output variables 312 can be regarded as the simulated, predicted, or forecasted results calculated by those mathematical or physics-based models.

[0084] In various aspects, the parametric state 308 of the digital twin 306 can include, for any suitable positive integer m, m parameters, namely, parameters 308(1) through 308(m). In various cases, each parameter of the parametric state 308 can be any suitable mathematical quantity that can represent a respective physical or theoretical characteristic, attribute, or property of the scientific instrument 302. For example, parameter 308(1) can be a scalar, vector, matrix, tensor, or any suitable combination thereof that can represent a first physical or theoretical characteristic, attribute, or property of the scientific instrument 302. Similarly, parameter 308(m) can be a scalar, vector, matrix, tensor, or any suitable combination thereof that can represent the mth physical or theoretical characteristic, attribute, or property of the scientific instrument 302.As some non-limiting examples, any parameter of the parametric state 308 can represent the length of the scientific instrument 302 or any of its parts or components, the width of the scientific instrument 302 or any of its parts or components, the height of the scientific instrument 302 or any of its parts or components, the thickness of the scientific instrument 302 or any of its parts or components, the radius of curvature of the scientific instrument 302 or any of its parts or components, the mass or density of the scientific instrument 302 or any of its parts or components, the rigidity of the scientific instrument 302 or any of its parts or components, the attenuation coefficient of the scientific instrument 302 or any of its parts or components, the electrical resistance of the scientific instrument 302 or any of its parts or components, the electrical impedance of the scientific instrument 302 or any of its parts or components, the thermal resistance of the scientific instrument 302 or any of its parts or components, the thermal conductivity of the scientific instrument 302 or any of its parts or components, the heat capacity of the scientific instrument 302 or any of its parts or components, the optical opacity of the scientific instrument 302 or any of its parts or components, the optical aberration coefficient of the scientific instrument 302 or any of its parts or components (e.g., defocus coefficient, second-order spherical aberration coefficient), the decoherence time of the scientific instrument 302 or any of its parts or components, or the quantum Hamiltonian element of the scientific instrument 302 or any of its parts or components.

[0085] In some cases, any parameter of the parametric state 308 can represent a physical or theoretical characteristic, attribute, or property that is expected to be non-temporary, constant, or fixed. That is, the value of such a physical or theoretical characteristic, attribute, or property is expected not to drift, decay, or otherwise change over time or with the use of the scientific instrument 302. However, in other cases, any parameter of the parametric state 308 can represent a physical or theoretical characteristic, attribute, or property that is expected to be transient, not fixed, or not constant. That is, the value of such a physical or theoretical characteristic, attribute, or property is expected to slowly or rapidly drift, decay, or otherwise change over time or with the use of the scientific instrument 302.

[0086] Note that in various aspects, any parameter of the parametric state 308 may not be directly or explicitly controlled or selected by any of the sets of controllable device settings 304. Despite this lack of direct and explicit control, any parameter of the parametric state 308 may be indirectly affected or modified by one or more of the sets of controllable device settings 304. As a non-limiting example, assume that the scientific instrument 302 is an electron microscope and the parametric state 308 includes an aberration coefficient parameter. The aberration coefficient can be considered a useful theoretical property that helps quantitatively describe the optical performance or behavior of the electron microscope, but an electron microscope equipped with an aberration coefficient knob, slider, joystick, physical button, or software button that would enable the explicit direct selection of a particular desired aberration coefficient value has not been made or manufactured. However, nonetheless, the configurable knobs, sliders, joysticks, physical buttons, or software buttons that the electron microscope has (e.g., defocus knob, stigmator knob, sample stage actuator joystick, voltage knob, temperature knob) can nonetheless indirectly affect the aberration coefficient of the electron microscope (e.g., adjusting any of the defocus knob, stigmator knob, sample stage actuator joystick, voltage knob, or temperature knob can increase or decrease the aberration coefficient of the electron microscope).

[0087] In various aspects, the set 310 of input variables of the digital twin 306 can include, for any suitable positive integer s, s variables, i.e., input variables 310(1) through input variable 310(s). In various cases, each of the sets of input variables 310 can be any suitable mathematical quantity that can represent any suitable dimension, feature, detail, or aspect of a usage scenario that the scientific instrument 302 can encounter or experience. For example, input variable 310(1) can be a scalar, vector, matrix, tensor, or any suitable combination thereof that can represent a first dimension, feature, detail, or aspect of a usage scenario that can be encountered by the scientific instrument 302. Similarly, input variable 310(s) can be a scalar, vector, matrix, tensor, or any suitable combination thereof that can represent the s-th dimension, feature, detail, or aspect of a usage scenario that can be encountered by the scientific instrument 302. As some non-limiting examples, any of the sets of input variables 310 can be the mass or density of an analytical sample that the scientific instrument 302 can analyze, the chemical composition of an analytical sample that the scientific instrument 302 can analyze, the crystal structure of an analytical sample that the scientific instrument 302 can analyze, the absorption coefficient of an analytical sample that the scientific instrument 302 can analyze, the warm-up time given or assigned to the scientific instrument 302 for the analysis of an analytical sample, the execution time given or assigned to the scientific instrument 302 for the analysis of an analytical sample, the cool-down time given or assigned to the scientific instrument 302 for the analysis of an analytical sample, the maximum or minimum voltage level used by the scientific instrument 302 for the analysis of an analytical sample, the maximum or minimum radiation level used by the scientific instrument 302 for the analysis of an analytical sample, the maximum or minimum fluid flow rate used by the scientific instrument 302 for the analysis of an analytical sample, or the highest or lowest temperature level used by the scientific instrument 302 for the analysis of an analytical sample.

[0088] In various aspects, the set 312 of output variables of the digital twin 306 can include, for any suitable positive integer t, t variables, namely, output variables 312(1) through output variable 312(t). In various cases, each of the sets of output variables 312 can be any suitable mathematical quantity that can represent any suitable characteristic, attribute, property, feature, detail, or aspect of behavior of the scientific instrument 302 that is desired to be simulated, predicted, or forecasted. For example, output variable 312(1) can be a scalar, vector, matrix, tensor, or any suitable combination thereof that can represent a first simulated, predicted, or forecasted characteristic, attribute, property, feature, detail, or aspect of behavior of the scientific instrument 302. Similarly, output variable 312(t) can be a scalar, vector, matrix, tensor, or any suitable combination thereof that can represent the t-th simulated, predicted, or forecasted characteristic, attribute, property, feature, detail, or aspect of behavior of the scientific instrument 302. As a non-limiting example, any of the sets of output variables 312 can represent an electronic measurement value that can be captured or generated by the scientific instrument 302 in response to any given use scenario. For example, if the scientific instrument 302 is a mass spectrometer, one or more output variables can represent a material composition result or percentage that can be output by the scientific instrument 302. As another example, if the scientific instrument 302 is an electron microscope, one or more output variables can represent an image (e.g., a pixel array or voxel array) that can be output by the scientific instrument 302. As another non-limiting example, any of the sets of output variables 312 can represent the total or limiting amount of degradation or wear that the scientific instrument 302, or any of its parts or components, can experience or accumulate in response to any given use scenario. As yet another non-limiting example, any of the sets of output variables 312 can represent the total or limiting amount of fuel, calibration substance, or electricity that can be consumed by the scientific instrument 302 in response to any given use scenario. As yet another non-limiting example, any of the sets of output variables 312 can represent the amount of useful life (e.g., represented in terms of time or operation) of the scientific instrument 302 that remains or is left in response to any given use scenario.

[0089] Thus, the digital twin 306 can simulate, predict, or forecast how the scientific instrument 302 will respond to any particular usage scenario. Specifically, a set of input variables 310 can be assigned any suitable numerical values corresponding to or defining that particular usage scenario, the parametric state 308 can be applied to the set of input variables 310 (e.g., according to whatever mathematical functions, operations, or equations make up the digital twin 306), and the set of output variables 312 can equal the calculation result of such application (e.g., product, difference, sum, quotient).

[0090] Referring back to FIG. 3, it should be noted that the digital twin 306 can accurately or reliably simulate, predict, or forecast the behavior of the scientific instrument 302 only when the parametric state 308 is assigned numerical values that exactly match the true physical state of the scientific instrument 302. However, that true physical state can be unknown and can vary with the set of controllable instrument settings 304. Thus, it may be desirable to calibrate or synchronize the parametric state 308 of the digital twin 306 with that unknown true physical state of the scientific instrument 302. As described herein, the scientific instrument 302 can comprise a system 314 that can facilitate such calibration or synchronization.

[0091] In various aspects, system 314 can include a processor 316 (e.g., a computer processing unit, a microprocessor), and a non-transitory computer-readable memory 318 that is operably or communicably connected or coupled to the processor 316. The non-transitory computer-readable memory 318 can store computer-executable instructions that, when executed by the processor 316, can cause the processor 316 or other components of the system 314 (e.g., access component 320, calibration component 322, post-calibration component 324) to perform one or more operations. In various embodiments, the non-transitory computer-readable memory 318 can store computer-executable components (e.g., access component 320, calibration component 322, post-calibration component 324), and the processor 316 can execute the computer-executable components.

[0092] In various embodiments, system 314 can include an access component 320. In various aspects, the access component 320 can electronically communicate or otherwise electronically interact (e.g., send electronic instructions or commands, receive electronic data) with a set of controllable device settings 304 or a digital twin 306. Accordingly, any other component of the system 314 can communicate or interact with the set of controllable device settings 304 or the digital twin 306 through or via the access component 320 (e.g., the access component 320 can function as an intermediary between any other component of the system 314 and the set of controllable device settings 304 or the digital twin 306). However, this is merely a non-limiting example. In other cases, the access component 320 can be omitted, and any other component of the system 314 can communicate or interact directly with the set of controllable device settings 304 or the digital twin 306.

[0093] In various embodiments, system 314 can include a calibration component 322. In various aspects, as described herein, calibration component 322 can electronically calibrate or synchronize parametric state 308 of digital twin 306 with an unknown true physical state of scientific instrument 302 by leveraging a full state Bayesian filter.

[0094] In various embodiments, system 314 can include a post - calibration component 324. In various cases, as described herein, post - calibration component 324 can perform or initiate any suitable electronic action in response to parametric state 308 of digital twin 306 being properly calibrated or synchronized with an unknown true physical state of scientific instrument 302.

[0095] FIG. 5 shows a block diagram of an exemplary and non - limiting scientific instrument that can facilitate improved digital twin calibration, including a full state Bayesian filter and a calibrated parametric state instantiation, according to one or more embodiments described herein.

[0096] In various embodiments, calibration component 322 can electronically identify a calibrated parametric state instantiation 504 for digital twin 306 based on full state Bayesian filter 502. In various aspects, calibrated parametric state instantiation 504 can be considered to be any particular numerical value of the parameters of parametric state 308 that is determined or inferred to be equal to or close to (e.g., within any suitable margin of similarity) the unknown true physical state of scientific instrument 302. In various cases, full state Bayesian filter 502 can be an iterative procedure or algorithm that utilizes the actual behavior exhibited by scientific instrument 302, the simulated behavior predicted by digital twin 306, and recursive Bayesian updates to ultimately identify calibrated parametric state instantiation 504. Various non - limiting aspects are described with respect to FIGS. 6 - 12.

[0097] FIG. 6 shows an illustrative and non-limiting block diagram showing a global state Bayesian filter 502 according to one or more embodiments described herein.

[0098] In various embodiments, as described above, the global state Bayesian filter 502 can be an iterative procedure or algorithm. In particular, the global state Bayesian filter 502 can include a plurality of correction iterations 602. In various aspects, the plurality of correction iterations 602 can include z iterations, where for any suitable positive integer z>1, the correction iterations 602(1) through 602(z). In various instances, the plurality of correction iterations 602 can be performed in sequence. Thus, correction iteration 602(1) can be considered the first, initial, or starting iteration of the plurality of correction iterations 602, and correction iteration 602(z) can be considered the final, last, or terminal iteration of the plurality of correction iterations 602.

[0099] In various cases, the plurality of calibration iterations 602 can be driven by the iterative common observable 604. In other words, the operations performed within each of the plurality of calibration iterations 602 can depend on the iterative common observable 604. In various aspects, the iterative common observable 604 can correspond to or be associated with a standard, repeatable, or baseline usage scenario of the scientific instrument 302. More specifically, the iterative common observable 604 can be any suitable measurable, trackable, recordable, or quantifiable detail, concept, aspect, or behavior that can be presented by or generated by the scientific instrument 302 during or after the execution of its standard, repeatable, or baseline usage scenario and that can be simulated, predicted, or anticipated by the digital twin 306. Thus, the iterative common observable 604 can be considered to be any suitable state-dependent quantity (e.g., one or more scalars, one or more vectors, one or more matrices, one or more tensors, or any suitable combination thereof) that is equal to or equivalent to any one of the set of output variables 312 or equal to or equivalent to any suitable function of one or more of the set of output variables 312.

[0100] As a non-limiting example, assume that the scientific instrument 302 is an electron microscope. In such a case, the scientific instrument 302 may be capable of measuring or generating a convergent beam electron diffraction (CBED) pattern by performing or operating on an analysis sample, and the CBED pattern may be regarded as a two-dimensional pixel array depicting the inside or outside of the analysis sample. In various aspects, the standard, repeatable, or baseline usage scenario may be to capture the CBED patterns of some defined analysis samples (e.g., amorphous carbon) using some defined instrument setting configurations (e.g., using defined or baseline optical, voltage, or power settings). Further, given the CBED pattern of an analysis sample, the Fourier transform of the given CBED pattern can be calculated. Thus, in various cases, the repeat common observable 604 can refer to the application of the Fourier transform to the CBED pattern generated by scanning an amorphous carbon sample according to defined or baseline optical, voltage, or power settings.

[0101] In any case, the repeat common observable 604 can be utilized, exploited, or otherwise referenced in each of the plurality of calibration repeats 602 (rather than using different observables in each repeat). In particular, each of the plurality of calibration repeats 602 operates the scientific instrument 302 according to a standard, repeatable, or baseline usage scenario, thereby enabling the behavior of the scientific instrument 302 with respect to the repeat common observable 604 to be measured or observed, simulating a standard, repeatable, or baseline usage scenario on the digital twin 306, thereby enabling the behavior of the scientific instrument 302 with respect to the repeat common observable 604 to be predicted, and incrementally updating the entire parametric state 308 (not just that subset) via Bayes' theorem based on the error between the measured or observed behavior and the predicted behavior. Various non-limiting aspects are described with respect to FIGS. 7-12.

[0102] Figures 7-12 show exemplary and non-limiting block diagrams 700, 800, 900, 1000, 1100, and 1200 illustrating iterations of the overall state Bayes filter 502 according to one or more embodiments described herein. In particular, FIGS. 7-12 can be considered to show how the j-th calibration iteration among a plurality of calibration iterations 602 can be implemented or facilitated by the calibration component 322 for any suitable positive integer j≥1.

[0103] First, consider FIG. 7. In various aspects, the scientific instrument 302 can be considered to have some unknown true physical state at the start of the j-th calibration iteration. As described above, that true physical state can be indirectly affected by a set of controllable instrument settings 304, but that true physical state cannot be directly or explicitly selected or commanded by the set of controllable instrument settings 304 (otherwise, calibration would be trivial).

[0104] In various cases, regardless of the true physical state of the scientific instrument 302, the calibration component 322 can electronically command the scientific instrument 302 to be standard, repeatable, or operate according to the baseline usage scenario corresponding to the iterative common observable 604, or to perform, do, or otherwise be able to operate according to the usage scenario, or to electronically command it to perform, do, or otherwise be able to operate according to the usage scenario, or otherwise cause it to be electronically implemented, performed, or operated according to the usage scenario. Such implementation, execution, or operation can cause the scientific instrument 302 to exhibit some measurable behavior regarding the iterative common observable 604, and the calibration component 322 can electronically record or cause to be electronically recorded such measurable behavior. This can result in the measured observation value 702. In other words, the measured observation value 702 can be any suitable mathematical quantity (e.g., scalar, vector, matrix, tensor, or any suitable combination thereof) representing how the scientific instrument 302 behaved with respect to the iterative common observable 604 during or as a result of the j-th calibration iteration, the standard, repeatable, or baseline usage scenario.

[0105] As a non-limiting example, as described above, assume that the scientific instrument 302 is an electron microscope and the iterative common observable 604 refers to the Fourier-transformed CBED pattern of an amorphous carbon sample. In such a case, the amorphous carbon sample can be inserted into the scientific instrument 302 (e.g., placed on the sample stage of the scientific instrument 302). The calibration component 322 can cause the scientific instrument 302 to capture or generate the CBED pattern of the amorphous carbon sample during the j-th calibration iteration. The calibration component 322 can apply a Fourier transform to the captured CBED pattern, and any mathematical quantity resulting from such Fourier transform can be considered as the measured observation value 702.

[0106] Here, consider FIG. 8. In various aspects, the parametric state 308 can be considered to have a state space or to correspond to a state space at any place where a particular instantiation of the parametric state 308 can be selected. More specifically, the parametric state 308 can include m distinct parameters. Each of such m distinct parameters can be considered to correspond to a respective domain, and all of such domains can be collectively considered to form or define the state space of the digital twin 306. As a non-limiting example, parameter 308(1) can be considered to correspond to a first domain, and such first domain can be considered to be a set of all possible numerical values or combinations of numerical values that can be assigned to parameter 308(1). As another non-limiting example, parameter 308(m) can be considered to correspond to an mth domain, and such mth domain can be considered to be a set of all possible numerical values or combinations of numerical values that can be assigned to parameter 308(m). In either case, all of such m domains can be collectively considered to constitute the state space of the digital twin 306.

[0107] In various cases, the calibration component 322 can probabilistically sample the state space of the digital twin 306 during the jth calibration iteration. This can result in a plurality of sampled parametric state instantiations 802. In various situations, the plurality of sampled parametric state instantiations 802 can include x instantiations, where for any suitable positive integer x>1, from the sampled parametric state instantiation 802(1) to the sampled parametric state instantiation 802(x). In various aspects, each of the plurality of sampled parametric state instantiations 802 can be a particular version of the parametric state 308, and its parameters are assigned particular numerical values that are probabilistically selected from their respective regions.

[0108] As a non-limiting example, the sampled parametric state instantiation 802(1) can be regarded as the first specific version of the parametric state 308. Thus, the sampled parametric state instantiation 802(1) can include a first specific numerical value probabilistically selected from the region of the parameter 308(1) (for example, if the parameter 308(1) represents the attenuation coefficient of the scientific instrument 302 that can vary from a minimum attenuation value to a maximum attenuation value, the sampled parametric state instantiation 802(1) can include a specific attenuation coefficient value probabilistically selected from the interval formed by those minimum and maximum attenuation values). Similarly, the sampled parametric state instantiation 802(1) can include an m-th specific numerical value probabilistically selected from the region of the parameter 308(m) (for example, if the parameter 308(m) represents the aberration coefficient of the scientific instrument 302 that can vary from a minimum aberration value to a maximum aberration value, the sampled parametric state instantiation 802(1) can include a specific aberration coefficient value probabilistically selected from the interval formed by those minimum and maximum aberration values).

[0109] As another non-limiting example, the sampled parametric state instantiation 802(x) can be regarded as the x-th specific version of the parametric state 308. Thus, the sampled parametric state instantiation 802(x) can include a first specific numerical value probabilistically selected from the region of the parameter 308(1). Similarly, the sampled parametric state instantiation 802(x) can include an m-th specific numerical value probabilistically selected from the region of the parameter 308(m).

[0110] In various aspects, when j = 1 (e.g., during the first, start, or initial calibration iteration), the calibration component 322 can probabilistically select a plurality of sampled parametric state instantiations 802 from an unconstrained or unrestricted version of the state space of the digital twin 306. In contrast, when j > 1 (e.g., during any non-initial calibration iteration), the calibration component 322 can probabilistically select a plurality of sampled parametric state instantiations 802 from a constrained or restricted version of the state space of the digital twin 306, and such a constrained or restricted version of the state space can be calculated by performing recursive Bayesian updates on any version of the state space sampled in the (j - 1)th calibration iteration (e.g., in a previous calibration iteration).

[0111] More specifically, it is recalled that recursive Bayesian updates can include calculating a posterior distribution (e.g., via Bayes' theorem, Bayes' rule, or Bayesian inference) when both a prior distribution and evidence are given. In various aspects, the calibration component 322 can select a plurality of sampled parametric state instantiations 802 from any suitable prior distribution over the state space of the digital twin 306. When j = 1, that prior distribution can be a uniform distribution (e.g., such that all possible parametric state instantiations within the state space have an equal likelihood of being selected by the calibration component 322), or any desired or defined distribution over the state space, such as a normal or Gaussian distribution (e.g., such that parametric state instantiations with extreme or out-of-range parameter values have a lower likelihood of being selected by the calibration component 322). However, when j > 1, that prior distribution can be equal to or based on whatever the posterior distribution calculated during the (j - 1)th calibration iteration is. This is further clarified below with respect to FIG. 12.

[0112] In either case, the calibration component 322 can probabilistically select a plurality of sampled parametric state instantiations 802 from the state space of the digital twin 306.

[0113] In various aspects, the calibration component 322 can electronically command, electronically instruct, or otherwise electronically cause the digital twin 306 to simulate, for each of the plurality of sampled parametric state instantiations 802, the respective execution of a standard, repeatable, or baseline usage scenario corresponding to the iterative common observable 604. Such simulations can cause the digital twin 306 to predict or anticipate what measurable or observable behavior the scientific instrument 302 will exhibit with respect to the iterative common observable 604, assuming that the true physical state of the scientific instrument 302 matches what is presented by each of the plurality of sampled parametric state instantiations 802. This can result in a plurality of simulated observations 804.

[0114] For example, calibration component 322 can perform digital twin 306 for the sampled parametric state instantiation 802(1). That is, calibration component 322 can command, instruct, or cause digital twin 306 to simulate, anticipate, or predict how scientific instrument 302 will behave with respect to recurring common observable 604 during a standard, repeatable, or baseline usage scenario, assuming that the true physical state of scientific instrument 302 matches whatever specific numerical value is indicated by the sampled parametric state instantiation 802(1). The simulated observation 804(1) can be any suitable mathematical quantity (e.g., scalar, vector, matrix, tensor, or any suitable combination thereof) representing such simulated, anticipated, or predicted behavior. Consider again the above non-limiting example where scientific instrument 302 is an electron microscope and recurring common observable 604 refers to the Fourier-transformed CBED pattern of an amorphous carbon sample. In such a case, digital twin 306 can simulate, predict, or anticipate the synthetic CBED image of that amorphous carbon sample that scientific instrument 302 would capture if the true physical state of scientific instrument 302 matches the numerical value indicated by the sampled parametric state instantiation 802(1). Thus, calibration component 322 can apply a Fourier transform to its simulated, predicted, or anticipated CBED pattern, and any mathematical quantity resulting from such Fourier transform can be regarded as the simulated observation 804(1).

[0115] Similarly, calibration component 322 can perform digital twin 306 for the sampled parametric state instantiation 802(x). That is, calibration component 322 can command, instruct, or cause digital twin 306 to simulate, anticipate, or predict how scientific instrument 302 will behave with respect to repetitive common observable 604 during a standard, repeatable, or baseline usage scenario, assuming that the true physical state of scientific instrument 302 matches whatever specific numerical value is indicated by the sampled parametric state instantiation 802(x). The simulated observation 804(x) can be any suitable mathematical quantity (e.g., scalar, vector, matrix, tensor, or any suitable combination thereof) representing such simulated, anticipated, or predicted behavior. Once again, consider the above non-limiting example where scientific instrument 302 is an electron microscope and repetitive common observable 604 refers to the Fourier-transformed CBED pattern of an amorphous carbon sample. In such a case, digital twin 306 can simulate, predict, or anticipate the synthetic CBED image of that amorphous carbon sample captured by scientific instrument 302 if the true physical state of scientific instrument 302 matches the numerical value indicated by the sampled parametric state instantiation 802(x). Accordingly, calibration component 322 can apply a Fourier transform to its simulated, anticipated, or predicted CBED pattern, and any mathematical quantity resulting from such Fourier transform can be regarded as the simulated observation 804(x).

[0116] In various cases, the simulated observations 804(1) through 804(x) can be collectively considered as forming a plurality of simulated observations 804.

[0117] Here, consider FIG. 9. In various aspects, calibration component 322 can electronically calculate or compute a plurality of weights 902 based on the measured observation value 702 and the plurality of simulated observation values 804(1). More specifically, calibration component 322 can calculate the respective error between the measured observation value 702 and each of the plurality of simulated observation values 804, and the plurality of weights 902 can be any suitable function of those respective errors.

[0118] As a non-limiting example, calibration component 322 can calculate any suitable error (e.g., MAE, MSE, cross-entropy error, Euclidean distance error) between the measured observation 702 and the simulated observation 804(1). In various aspects, calibration component 322 can then calculate weight 902(1) based on that error. In various cases, weight 902(1) can be any suitable scalar whose magnitude can range from any suitable minimum value (e.g., 0) to any suitable maximum value (e.g., 1). In various aspects, weight 902(1) can be any suitable function of the error between the measured observation 702 and the simulated observation 804(1), and the magnitude of weight 902(1) is inversely proportional to the magnitude of that error (e.g., the magnitude of weight 902(1) can increase as the error between the measured observation 702 and the simulated observation 804(1) decreases). The magnitude of weight 902(1) can decrease as the error between the measured observation 702 and the simulated observation 804(1) increases. For example, in some cases, weight 902(1) can be equal to or otherwise based on the reciprocal of the error between the measured observation 702 and the simulated observation 804(1). In other cases, weight 902(1) can be equal to or otherwise based on the complement of the error between the measured observation 702 and the simulated observation 804(1). In either case, weight 902(1) can be calculated based on the simulated observation 804(1), and since the simulated observation 804(1) can be obtained based on the sampled parametric state instantiation 802(1), weight 902(1) can be considered to indicate the degree to which the sampled parametric state instantiation 802(1) matches the true physical state of the scientific instrument 302.

[0119] As another non-limiting example, the calibration component 322 can calculate any suitable error (e.g., MAE, MSE, cross-entropy error, Euclidean distance error) between the measured observation 702 and the simulated observation 804(x). In various aspects, the calibration component 322 can then calculate the weight 902(x) based on that error. Similar to the above, the weight 902(x) can be any suitable scalar whose magnitude can range from any suitable minimum value (e.g., 0) to any suitable maximum value (e.g., 1). Also, as above, the weight 902(x) can be any suitable function of the error between the measured observation 702 and the simulated observation 804(x), such that the magnitude of the weight 902(x) is inversely proportional to the magnitude of that error (e.g., the weight 902(x) is equal to or otherwise based on the reciprocal or complement of the error between the measured observation 702 and the simulated observation 804(x)). In any case, the weight 902(x) can be calculated based on the simulated observation 804(x), and since the simulated observation 804(x) can be obtained based on the sampled parametric state instantiation 802(x), the weight 902(x) can be considered to indicate the degree to which the sampled parametric state instantiation 802(x) is likely to match the true physical state of the scientific instrument 302.

[0120] In various cases, the weights 902(1) through 902(x) can be considered to collectively form a plurality of weights 902, and the plurality of weights 902 can be considered to each correspond to a plurality of sampled parametric state instantiations 802.

[0121] Here, consider FIG. 10. In various aspects, the calibration component 322 can electronically delete, electronically discard, or otherwise electronically ignore any of the plurality of sampled parametric state instantiations 802 that do not meet (e.g., fall below) any suitable threshold weight value. In other words, the calibration component 322 can remove any of the plurality of sampled parametric state instantiations 802 that are insufficiently weighted. In various cases, this can result in a plurality of remaining parametric state instantiations 1002 and a plurality of remaining weights 1004.

[0122] In various cases, the plurality of remaining parametric state instantiations 1002 can include y instantiations, where for any suitable positive integer y < x, the remaining parametric state instantiations 1002 range from the remaining parametric state instantiation 1002(1) to the remaining parametric state instantiation 1002(y). In various aspects, the plurality of remaining weights 1004 can each correspond to the plurality of remaining parametric state instantiations 1002. Thus, since the plurality of remaining parametric state instantiations 1002 can include y instantiations, the plurality of remaining weights 1004 can similarly include y weights, i.e., from the remaining weight 1004(1) to the remaining weight 1004(y). As a non-limiting example, the remaining parametric state instantiation 1002(1) can be any distinct one of the plurality of sampled parametric state instantiations 802 whose weight exceeds the threshold weight value, and the remaining weight 1004(1) can be that weight (e.g., the weight of the remaining parametric state instantiation 1002(1)). As another non-limiting example, the remaining parametric state instantiation 1002(y) can be any distinct one of the plurality of sampled parametric state instantiations 802 whose weight exceeds the threshold weight value, and the remaining weight 1004(y) can be that weight (e.g., the weight of the remaining parametric state instantiation 1002(y)).

[0123] Here, in various aspects, calibration component 322 can electronically calculate or compute the variance for each parameter based on a plurality of remaining parametric state instantiations 1002. In fact, as described above, each of the plurality of remaining parametric state instantiations 1002 can include m specific numerical values respectively corresponding to the m parameters of parametric state 308. Thus, for each given parameter of parametric state 308, calibration component 322 can calculate the variance of the specific numerical values assigned to that given parameter across the plurality of remaining parametric state instantiations 1002, thereby resulting in m variances. Such m variances can collectively be regarded as the variances for each parameter of the plurality of remaining parametric state instantiations 1002.

[0124] As a non-limiting example, each of the plurality of remaining parametric state instantiations 1002 can include a specific numerical value assigned to parameter 308(1). Thus, the plurality of remaining parametric state instantiations 1002 can collectively be regarded as having a total of y specific numerical values assigned to parameter 308(1). In various cases, calibration component 322 can calculate the variance of those y specific numerical values. Such variance can be regarded as the variance for each parameter of the first parameter of the plurality of remaining parametric state instantiations 1002.

[0125] As another non-limiting example, each of the plurality of remaining parametric state instantiations 1002 can include a specific numerical value assigned to parameter 308(m). Thus, the plurality of remaining parametric state instantiations 1002 can collectively be regarded as having a total of y specific numerical values assigned to parameter 308(m). In various cases, calibration component 322 can calculate the variance of those y specific numerical values. Such variance can be regarded as the variance for each parameter of the m-th parameter of the plurality of remaining parametric state instantiations 1002.

[0126] In either case, the calibration component 322 can calculate the variance for each parameter across the plurality of remaining parametric state instantiations 1002. In various aspects, the calibration component 322 can compare each of those variances for each parameter to any suitable threshold variance value. FIG. 11 shows how the j-th calibration iteration can proceed if each of those variances for each parameter meets (e.g., is below) the threshold variance value. In contrast, FIG. 12 shows how the j-th calibration iteration can proceed if at least one of those variances for each parameter does not meet (e.g., exceeds) the threshold variance value.

[0127] Consider FIG. 11. If each of the variances for each parameter meets the threshold variance value, the calibration component 322 can electronically calculate or compute the calibrated parametric state instantiation 504 based on the plurality of remaining parametric state instantiations 1002. In particular, the calibrated parametric state instantiation 504 can be equal to, or otherwise based on, the weighted average of the plurality of remaining parametric state instantiations 1002. That is, each of the plurality of remaining parametric state instantiations 1002 can be multiplied by its respective one of the plurality of remaining weights 1004 (e.g., the remaining parametric state instantiation 1002(1) can be multiplied by the remaining weight 1004(1)). The remaining parametric state instantiation 1002(y) can be multiplied by the remaining weight 1004(y), thereby resulting in y products, and the calibrated parametric state instantiation 504 can be made equal to the arithmetic mean of such y products.

[0128] In other words, if the variance for each parameter meets the threshold variance value, the plurality of remaining parametric state instantiations 1002 can be considered to be closely grouped or clustered around the unknown true physical state of the scientific instrument 302, and thus, the unknown true physical state can be estimated by a weighted average.

[0129] Now, consider FIG. 12. If at least one of the variances for each parameter does not meet the threshold variance value, the calibration component 322 can electronically perform (or otherwise cause to be electronically performed) an active setting adjustment 1202 on the scientific instrument 302 in various ways. In various instances, the active setting adjustment 1202 can be any suitable change or modification to one or more of the set of controllable device settings 304 (e.g., pressing or selecting any suitable button, rotating any suitable knob by any suitable degree, shifting any suitable slider by any suitable amount, displacing any suitable joystick in any suitable direction by any suitable amount). Thus, the active setting adjustment 1202 can be considered to change one or more user-configurable aspects of the scientific instrument 302 (e.g., voltage, current, temperature, stage height, focus size, flow rate, radiation level) by one or more known amounts.

[0130] In fact, the true physical state of the scientific instrument 302 may still be unknown at this point, but the active setting adjustment 1202 can be considered to change the true physical state of the scientific instrument by some known method, by some known amount, or otherwise in some known direction. It should be noted that in a subsequent calibration iteration (e.g., the (j + 1)-th calibration iteration), the calibration component 322 can cause the scientific instrument 302 to perform or carry out, or command, a standard, repeatable, or baseline usage scenario in this newly changed but still unknown true physical state, or using it.

[0131] Referring back to the j-th calibration iteration, the calibration component 322 can, in various cases, electronically modify or adjust each of the plurality of remaining parametric state instantiations 1002 according to, or otherwise based on, the active setting adjustment 1202. Ultimately, as explained above, the true physical state of the scientific instrument 302 (e.g., whatever the characteristics, attributes, or properties of the scientific instrument 302 represented by the parametric state 308 are) cannot be directly or explicitly controlled or selected by a set of controllable instrument settings 304 (otherwise calibration would be trivial in this case). However, nevertheless, the true physical state can potentially be indirectly affected by a set of controllable instrument settings 304 in a known manner or through known relationships. For example, assume that the active setting adjustment 1202 shifts one or more of the set of controllable instrument settings 304 by one or more specific amounts or percentages, or in one or more respective directions. In various cases, it is known or can be expected that such a shift will correspondingly shift one or more respective characteristics, attributes, or properties that make up the true physical state of the scientific instrument 302 by one or more respective amounts or percentages, or in one or more respective directions. Thus, the calibration component 322 can electronically adjust, modify, change, or otherwise shift the plurality of remaining parametric state instantiations 1002 according to, or in accordance with, the active setting adjustment 1202, thereby resulting in a plurality of modified remaining parametric state instantiations 1204.

[0132] As a non-limiting example, calibration component 322 can electronically adjust, modify, or change the numerical values of the remaining parametric state instantiations 1002(1) in any amount or percentage, or in any direction, in any way that is expected to be caused by the active setting adjustment 1202. This can result in a modified remaining parametric state instantiation 1204(1). In other words, the modified remaining parametric state instantiation 1204(1) can be considered to indicate whatever the specific numerical values of the parametric state 308 are that the scientific instrument 302 is expected to have after the active setting adjustment 1202, assuming that the true physical state of the scientific instrument 302 before the active setting adjustment 1202 matches what is indicated by the remaining parametric state instantiation 1002(1).

[0133] As another non-limiting example, calibration component 322 can electronically adjust, modify, or change the numerical values of the remaining parametric state instantiations 1002(y) in any amount or percentage, or in any direction, in any way that is expected to be caused by the active setting adjustment 1202. This can result in a modified remaining parametric state instantiation 1204(y). That is, the modified remaining parametric state instantiation 1204(y) can be considered to indicate whatever the specific numerical values of the parametric state 308 are that the scientific instrument 302 is expected to have after the active setting adjustment 1202, assuming that the true physical state of the scientific instrument 302 before the active setting adjustment 1202 matches what is indicated by the remaining parametric state instantiation 1002(y).

[0134] In some embodiments, it should be understood that in addition to the active setting adjustment 1202, the scientific instrument 302 can undergo passive temporal evolution (e.g., the internal temperature of the scientific instrument 302 can cool or warm up naturally or passively over time). Similarly, its passive temporal evolution can be considered to change the true physical state of the scientific instrument 302 by some known method, by some known amount or percentage, or in some known direction. In such embodiments, the calibration component 322 can take into account its passive temporal evolution to generate a plurality of corrected remaining parametric state instantiations 1204. It should be noted that in some cases, the passive temporal evolution of the scientific instrument 302 may not be observed, not measured, or otherwise unknown. Even in such cases, when the state - of - the - whole Bayesian filter 502 is implemented as described herein, it can be considered to catch up with such unobserved passive temporal evolution.

[0135] In any case, the plurality of corrected remaining parametric state instantiations 1204 can be regarded as, or treated as, Bayesian evidence that can be utilized to incrementally constrain or limit the state space of the digital twin 306 during the (j + 1) - th calibration iteration (e.g., during the next or subsequent calibration iteration).

[0136] In particular, as described above, the calibration component 322 can select a plurality of sampled parametric state instantiations 802 according to a prior distribution over the state space during the j-th calibration iteration. In various aspects, the calibration component 322 can perform recursive Bayesian updates (e.g., via Bayes' theorem) on its prior distribution by leveraging a plurality of modified remaining parametric state instantiations 1204 as Bayesian evidence during the j-th calibration iteration. This can result in a posterior distribution over the state space, which is narrower or more stringent (and thus the terms "constrained" or "restricted") than the prior distribution. In fact, the posterior distribution can be shaped according to a plurality of modified remaining parametric state instantiations 1204. In various aspects, the posterior distribution computed during the j-th calibration iteration can be treated as the prior distribution during the (j + 1)-th calibration iteration. Conversely, for j > 1, the prior distribution sampled during the j-th calibration iteration can be whatever the posterior distribution computed during the (j - 1)-th calibration iteration was. If j = 1, the prior distribution sampled during the j-th calibration iteration can be any suitable initial prior distribution over the state space (e.g., a uniform distribution or a Gaussian distribution), as desired.

[0137] Accordingly, calibration component 322 can perform each of a plurality of calibration iterations 602, as described with respect to FIGS. 7-12. Ultimately, there may be some calibration iterations where the variance for each parameter meets a threshold variance value. Such calibration iterations can be considered the last, terminal, or final of the plurality of calibration iterations 602 (e.g., can be considered calibration iteration 602(z)). During such an iteration, a calibrated parametric state instantiation 504 can be calculated and considered to indicate, estimate, or approximate a particular numerical value of the true physical state of scientific instrument 302. In various aspects, calibration component 322 can electronically command, instruct, or otherwise cause the parametric state 308 of digital twin 306 to be assigned whatever particular numerical value is indicated by calibrated parametric state instantiation 504.

[0138] Note that the formulation or structure of the overall state Bayesian filter 502 as described with respect to FIGS. 6-12 can be considered a type of particle filter technique. However, this is merely a non-limiting example for ease of explanation and illustration. In various other cases, the overall state Bayesian filter 502 can exhibit any other suitable formulation or structure, such as a Kalman filter technique.

[0139] In various embodiments, post-calibration component 324 can facilitate any suitable electronic action in response to the parametric state 308 of digital twin 306 being assigned the particular numerical value indicated by calibrated parametric state instantiation 504.

[0140] As a non-limiting example, the calibrated component 324 can electronically generate any suitable electronic notification or alert indicating that the digital twin 306 has been successfully calibrated or synchronized with the scientific instrument 302. In other words, the electronic notification or alert can be regarded as conveying that the digital twin 306 is ready or prepared to accurately, correctly, or reliably simulate, predict, or anticipate the future implementation or behavior of the scientific instrument 302. In some cases, the calibrated component 324 can electronically transmit the electronic notification or alert to any suitable computing device. In other examples, the calibrated component 324 can electronically render the electronic notification or alert on any suitable electronic display (e.g., a computer screen, a computer monitor, a head-up display, a holographic display).

[0141] As another non-limiting example, the calibrated component 324 can electronically instruct, command, or cause the digital twin 306 to simulate, predict, or anticipate the implementation or behavior of the scientific instrument 302 based on any suitable usage scenario indicated, identified, or selected by a user or technician of the scientific instrument 302. For example, the user or technician can numerically define a proposed or desired usage scenario using the human-computer interface device of the scientific instrument 302. In response to receiving such a numerical definition, the calibrated component 324 can cause the digital twin 306 to perform the proposed or desired usage scenario using the calibrated parametric state instantiation 504. Thereby, the digital twin 306 can accurately simulate, predict, or anticipate how the scientific instrument 302 would actually behave or be implemented if it were operated according to the proposed or desired usage scenario.

[0142] Figures 13 - 15 illustrate exemplary and non - limiting computer - implemented methods 1300, 1400, and 1500 that can facilitate improved digital twin calibration, according to one or more embodiments described herein. In various cases, system 314 can facilitate computer - implemented methods 1300, 1400, and 1500.

[0143] First, consider Figure 13. In various embodiments, operation 1302 can include accessing a digital twin (e.g., 306) of a scientific instrument (e.g., 302) by a device operably coupled to a processor (e.g., via 320).

[0144] In various aspects, operation 1304 can include initializing a prior parametric state distribution over the state space of the digital twin by a device (e.g., via 322). In some cases, the prior parametric state distribution can be initialized as a uniform distribution or a normal distribution / Gaussian distribution over the state space.

[0145] In various instances, operation 1306 can include defining a state - dependent observable (e.g., 604) that can be presented by the scientific instrument during operation and simulated by the digital twin by a device (e.g., via 322). In some cases, the state - dependent observable can be associated with a standard, repeatable, or baseline execution, usage scenario, or sample of the scientific instrument.

[0146] In various aspects, operation 1308 can include operating the scientific instrument by a device (e.g., via 322).

[0147] In various instances, operation 1310 can include measuring an observed value (e.g., 702) presented by the scientific instrument during its operation with respect to the state - dependent observable by a device (e.g., via 322).

[0148] In various cases, operation 1312 may include the device (e.g., via 322) randomly sampling a plurality of parametric state instantiations (e.g., 802) of the digital twin from a previous parametric state distribution.

[0149] In various aspects, operation 1314 may include the device (e.g., via 322) calculating a plurality of simulated observations (e.g., 804) by performing each of a plurality of parametric state instantiations on the digital twin with respect to a state-dependent observable. In various cases, computer-implemented method 1300 may proceed to operation 1402 of computer-implemented method 1400.

[0150] Now, consider FIG. 14. In various embodiments, operation 1402 may include the device (e.g., via 322) assigning a respective weight (e.g., 902) to each of a plurality of parametric state instantiations based on the respective error between an observation and a plurality of simulated observations.

[0151] In various aspects, operation 1404 may include the device (e.g., via 322) removing any of the plurality of parametric state instantiations that have a weight below a threshold weight value. This can result in a plurality of remaining parametric state instantiations (e.g., 1002).

[0152] In various instances, operation 1406 may include the device (e.g., via 322) calculating the variance for each parameter across the plurality of remaining parametric state instantiations.

[0153] In various cases, operation 1408 may include determining, by the device (e.g., via 322), whether all of the per-parameter variances satisfy (e.g., are below) a threshold variance value. If so, computer-implemented method 1400 may proceed to operation 1410. If not, computer-implemented method 1400 may proceed to operation 1502 of computer-implemented method 1500.

[0154] In various aspects, operation 1410 may include generating, by the device (e.g., via 324), an electronic notification indicating that the digital twin and the scientific instrument are synchronized or calibrated with a weighted average (e.g., 504) of a plurality of remaining parametric state instantiations.

[0155] Now, consider FIG. 15. In various embodiments, operation 1502 may include applying, by the device (e.g., via 322), an active adjustment (e.g., 1202) to one or more controllable settings (e.g., 304) of the scientific instrument.

[0156] In various aspects, operation 1504 may include modifying, by the device (e.g., via 322), each of the plurality of remaining parametric state instantiations based on the active adjustment. Optionally, such modification may further be based on the passive temporal evolution of the scientific instrument. In any case, such modification may result in a plurality of modified remaining parametric state instantiations (e.g., 1204).

[0157] In various instances, operation 1506 may include calculating, by the device (e.g., via 322), a posterior parametric state distribution by applying recursive Bayesian updates to a prior parametric state distribution based on the plurality of modified remaining parametric state instantiations (e.g., the plurality of modified remaining parametric state instantiations may be considered to provide Bayesian evidence in the application of Bayes' theorem).

[0158] In various cases, operation 1508 may include the device (e.g., via 322) redefining the previous parametric state distribution to be equal to the subsequent parametric state distribution.

[0159] In various aspects, operation 1510 may include the device (e.g., via 322) returning to operation 1308 of computer-implemented method 1300.

[0160] The inventors have experimentally verified various embodiments described herein. Some results of such experimental verification are shown in FIGS. 16-22.

[0161] In particular, the inventors have grouped together various embodiments in which the scientific instrument 302 is a transmission electron microscope; the parametric state 308 is a two-parameter vector, one parameter representing the microscope defocus aberration coefficient (e.g., measured in nanometers (nm)) and the other parameter representing the microscope spherical aberration coefficient (e.g., measured in nm); and the iterative common observable 604 refers to the Fourier transform applied to the CBED pattern of an amorphous carbon sample.

[0162] FIG. 16 shows the CBED pattern 1602 of an amorphous carbon sample. In the inventors' experiments, such a CBED pattern could actually be captured with a transmission electron microscope, but such a CBED pattern could also be synthesized or simulated with a digital twin of the transmission electron microscope. FIG. 16 further shows the amplitude of the Fourier-transformed CBED pattern 1604. The Fourier-transformed CBED pattern 1604 was obtained by applying a Fourier transform to the CBED pattern 1602 and taking the amplitude of the resulting complex number.

[0163] FIG. 17 shows a heat map 1700 illustrating a real-world example of the parameter ambiguity problem. Specifically, the horizontal axis of the heat map 1700 represents at least a portion of the domain of the microscope defocus aberration coefficient parameter (e.g., the possible numerical values that can be assigned to it). In addition, the vertical axis of the heat map 1700 represents at least a portion of the domain of the microscope 2-fold aberration coefficient parameter (e.g., the possible numerical values that can be assigned to it). These two regions can both be regarded as defining the state space of the digital twin of the transmission electron microscope.

[0164] Here, the inventors caused the transmission electron microscope to capture the actual CBED pattern of an amorphous carbon sample using a certain unknown true physical state, and applied a Fourier transform to the actual CBED pattern. Further, the inventors spanned the state space of the digital twin using approximately 400 unique equidistant parametric state instantiations. For each of these parametric state instantiations, the digital twin calculated a simulated CBED pattern of the amorphous carbon sample, and a Fourier transform was applied to each of such simulated CBED patterns.

[0165] Finally, the mean squared error was calculated between the Fourier-transformed versions of the actual CBED patterns and the Fourier-transformed versions of each of those simulated CBED patterns. These mean squared errors are shown in heatmap 1700, where darker colors represent lower mean squared errors and lighter colors represent higher mean squared errors. As indicated by the dark regions of heatmap 1700, there are many possible parametric state instantiations of the digital twin that result in low mean squared errors (e.g., predicting a simulated CBED pattern that is close to or similar to the actual CBED pattern). However, the true physical state of the transmission electron microscope only coincides with one of these many possible parametric state instantiations. Determining which of these many possible parametric state instantiations is closest to the true physical state of the transmission electron microscope (e.g., calibrating the digital twin to the transmission electron microscope) is a difficult and non-trivial task. The inventors have demonstrated that the various embodiments described herein can, despite such difficulties or non-trivialities, enable such a determination to be made correctly, accurately, or reliably and easily.

[0166] Indeed, the inventors calibrated or synchronized the aberration coefficient parameter of the digital twin to the true physical state of the transmission electron microscope by leveraging one embodiment of the state ensemble Bayesian filter 502.

[0167] Figure 18 shows a graph 1800 illustrating a first calibration iteration implemented by an embodiment of the overall state Bayesian filter 502. In graph 1800, the “+” represents the ground truth physical state of a transmission electron microscope estimated using the optiSTEM (registered trademark) software platform. Also in graph 1800, each circle represents one of a plurality of sampled parametric state instantiations 802, and the shading or color of each circle represents the weight (e.g., one of 902) corresponding to one of the plurality of sampled parametric state instantiations 802. Specifically, it indicates that the darker the color, the greater the weight, and the lighter the color, the smaller the weight. As shown, the plurality of sampled parametric state instantiations 802 in the first calibration iteration exhibit wide dispersion / variability (e.g., they are dispersed or not close to each other).

[0168] Figure 19 shows a graph 1900 illustrating a second calibration iteration implemented by an embodiment of the overall state Bayesian filter 502. As shown in graph 1900, the true physical state of the transmission electron microscope has moved due to the active setting adjustment 1202 performed in the first calibration iteration. Also as shown in graph 1900, the plurality of sampled parametric state instantiations 802 have moved closer to each other and are incrementally more densely packed around or near the true physical state.

[0169] Figure 20 shows a graph 2000 illustrating a third calibration iteration implemented by an embodiment of the overall state Bayesian filter 502. As shown in graph 2000, the true physical state of the transmission electron microscope has moved again due to the active setting adjustment 1202 performed in the second calibration iteration. Also as shown in graph 2000, the plurality of sampled parametric state instantiations 802 have moved even closer to each other and are even more densely packed around or near the true physical state.

[0170] FIG. 21 shows a graph 2100 illustrating a fourth calibration iteration implemented by an embodiment of the overall state Bayesian filter 502. As shown in graph 2100, the true physical state of the transmission electron microscope has moved again due to the active setting adjustment 1202 implemented in the third calibration iteration. Also, as shown in graph 2100, the plurality of sampled parametric state instantiations 802 have moved closer to each other and are more densely packed around or near the true physical state.

[0171] FIG. 22 shows a graph 2200 illustrating a fifth calibration iteration implemented by an embodiment of the overall state Bayesian filter 502. As shown in graph 2200, the true physical state of the transmission electron microscope has moved again due to the active setting adjustment 1202 implemented in the fourth calibration iteration. Also, as shown in graph 2200, the plurality of sampled parametric state instantiations 802 are now very close to each other and are close enough to the true physical state.

[0172] Thus, FIGS. 16-22 can be considered to show how the various embodiments described herein were able to accurately calibrate or synchronize the digital twin's microscope aberration coefficient parameters with the true physical state of the transmission electron microscope despite the problem of parameter ambiguity. As explained throughout this disclosure, such accurate calibration or synchronization is achieved not by updating different parameters in different iterations in order of dependence, but rather by the overall state Bayesian filter 502 that incrementally updates all of the parameters of the digital twin 306 in each calibration iteration, and by the overall state Bayesian filter 502 that uses a single common observable (e.g., the Fourier-transformed CBED pattern) in all of the calibration iterations rather than different observables in different iterations.

[0173] The various embodiments described herein include the iterative common observable 604, which is the Fourier-transformed version of a CBED pattern (e.g., a Ronchigram) that represents an amorphous carbon sample, but these are merely non-limiting examples for ease of explanation and illustration. In various aspects, the iterative common observable 604 can take any other form or be represented according to any other data representation. In fact, in some cases, the iterative common observable 604 can be a CBED pattern that has undergone some transformation other than a Fourier transform. Non-limiting examples of such other types of transformation can be any suitable feature extraction such as edge, shift, power spectrum, or patching. In still other cases, the iterative common observable 604 can be a CBED pattern that has not undergone any transformation at all. In still other cases, the iterative common observable 604 can be a CBED pattern of any suitable non-carbon sample or non-amorphous sample.

[0174] The figures in this specification show that the system 314 can be within or local to the scientific instrument 302, but this is merely a non-limiting example for ease of explanation and illustration. In various other embodiments, the system 314 can instead be remote from the scientific instrument 302. In fact, in some cases, the system 314 can be implemented on a dedicated computer designed or configured to control one or more scientific instruments, perform post-measurement analysis of one or more scientific instruments, or otherwise computationally support one or more scientific instruments.

[0175] It should be noted that the aberration coefficient of a charged particle microscope cannot be regarded as a global characteristic of the charged particle microscope in various aspects. In fact, the substantial content or meaning of the aberration coefficient of a charged particle microscope can vary depending on different positions along the optical axis of the charged particle microscope. As a non-limiting example, when the beam of a charged particle microscope is focused on a sample, the aberration coefficient can be defined at the condenser aperture plane of the charged particle microscope. In such a case, the aberration coefficient may be referred to as the probe aberration of the charged particle microscope. As another non-limiting example, when the beam of a charged particle microscope is instead parallel to the sample, the aberration coefficient can be defined within the sample plane of the charged particle microscope. In such a case, the aberration coefficient may be referred to as the image aberration. Therefore, as described herein, the term "aberration coefficient" can be considered as a superordinate or inclusive term that includes or encompasses any suitable type of aberration defined with respect to any suitable position along the optical axis of the charged particle microscope.

[0176] In some aspects, it should be noted that system 314 may be implemented, activated, or otherwise invoked periodically, continuously, or persistently so as to more frequently synchronize the parametric state 308 of digital twin 306 with the physical state of scientific instrument 302, or otherwise calibrate it. However, in other aspects, system 314 can instead be implemented, activated, or otherwise invoked in an aperiodic or ad hoc manner so as to reduce the frequency of synchronizing the parametric state 308 of digital twin 306 with the physical state of scientific instrument 302, or otherwise calibrating it.

[0177] The scientific instrument systems, methods, or technologies disclosed herein may involve interactions with a human user (e.g., via the user local computing device 2520 described herein with reference to FIG. 25). These interactions may include providing information to the user (e.g., information regarding the operation of a scientific instrument such as the scientific instrument 2510 of FIG. 25, information regarding the sample being analyzed or other tests or measurements being performed by the scientific instrument, information read from a local or remote database, or other information), or providing options for the user to input commands (e.g., to control the operation of a scientific instrument such as the scientific instrument 2510 of FIG. 25 or to control the analysis of data generated by the scientific instrument), queries (e.g., to a local or remote database), or other information. In some embodiments, these interactions may be implemented via a graphical user interface (GUI) that includes visual displays on a display device (e.g., the display device 2410 described herein with reference to FIG. 24) that provide output to the user and / or prompt the user to provide input via one or more input devices (e.g., a keyboard, mouse, trackpad, or touch screen included in other I / O devices 2412 described herein with reference to FIG. 24). The scientific instrument systems, methods, or technologies disclosed herein may include any suitable GUI for interaction with the user.

[0178] Figure 23 shows an exemplary graphical user interface 2300 (hereinafter, "GUI 2300") that can be used in some or all implementations of the support methods or techniques disclosed herein according to various embodiments. In various aspects, the GUI 2300 can be provided on any suitable electronic display (e.g., the display device 2410 described herein with reference to FIG. 24) of a computing device (e.g., the computing device 2400 described herein with reference to FIG. 24) of a scientific instrument support system (e.g., the scientific instrument support system 2500 described herein with reference to FIG. 25), and a user or technician can interact with the GUI 2300 using any suitable input device (e.g., any of the other I / O devices 2412 described herein with reference to FIG. 24) and input techniques (e.g., cursor movement, motion capture, face recognition, gesture detection, voice recognition, button activation).

[0179] The GUI 2300 can include a data display area 2302, a data analysis area 2304, a scientific instrument control area 2306, and a settings area 2308. The specific number and configuration of the areas shown in FIG. 23 are merely exemplary, and any number and configuration of areas including any desired features can be included in other embodiments of the GUI 2300.

[0180] The data display area 2302 can display data generated by a scientific instrument (e.g., the scientific instrument 2510 described herein with reference to FIG. 25).

[0181] The data analysis area 2304 can display any suitable data analysis results (e.g., the results of analyzing the data shown in the data display area 2302 or other data). In some embodiments, the data display area 2302 and the data analysis area 2304 can be combined within the GUI 2300 (e.g., to include both the data output from the scientific instrument and some analysis of the data within a common graph or area).

[0182] The scientific instrument control area 2306 can include options that enable a user or technician to control a scientific instrument (e.g., the scientific instrument 2510 described herein with reference to FIG. 25). For example, the scientific instrument control area 2306 can include configurable parameters that manage the operation of such a scientific instrument (e.g., configurable parameters that manage the voltage or current of the scientific instrument, manage the internal temperature of the scientific instrument, or manage the fluid flow rate of the scientific instrument).

[0183] The settings area 2308 can include options that enable a user or technician to control any feature or function of the GUI 2300 (or other GUI), or to perform common computing operations (e.g., saving data to a storage device such as the storage device 2404 described herein with reference to FIG. 24, sending data to another user, labeling data) with respect to the data display area 2302 and the data analysis area 2304.

[0184] As described above, the scientific instrument module 102 can be implemented by one or more computing devices. FIG. 24 is a block diagram of a computing device 2400 that can implement some or all of the scientific instrument methods or techniques disclosed herein according to various embodiments. In some embodiments, the scientific instrument module 102 can be implemented by a single instance of the computing device 2400, or by multiple instances of the computing device 2400. Further, as discussed below, the computing device 2400 (or multiple instances thereof) implementing the scientific instrument module 102 can be a part of one or more of the scientific instrument 2510 of FIG. 25, the user local computing device 2520, the service local computing device 2530, or the remote computing device 2540.

[0185] Computing device 2400 is shown as having several components, but any one or more of these components can be omitted or duplicated as suitable for the application and settings. In some embodiments, some or all of the components included in computing device 2400 can be attached to one or more motherboards and enclosed in a housing (e.g., including plastic, metal, or other materials). In some embodiments, some of these components can be fabricated on a single system-on-a-chip (SoC) (e.g., the SoC can include one or more instances of processing device 2402 and one or more instances of storage device 2404). Further, in various embodiments, computing device 2400 can omit one or more of the components shown in FIG. 24, but can include an interface circuit (not shown) for coupling to one or more omitted components using any suitable interface (e.g., Universal Serial Bus (USB) interface, High-Definition Multimedia Interface (HDMI (registered trademark)) interface, Controller Area Network (CAN) interface, Serial Peripheral Interface (SPI) interface, Ethernet interface, wireless interface, or any other suitable interface). For example, computing device 2400 can omit display device 2410, but can include a display device interface circuit (e.g., a connector and driver circuit) to which display device 2410 can be coupled.

[0186] The computing device 2400 can include a processing device 2402 (e.g., one or more processing devices). As used herein, the term "processing device" can refer to any device or portion of a device that processes electronic data from a register or memory and converts that electronic data into other electronic data that can be stored in a register or memory. The processing device 2402 can include one or more digital signal processors (DSPs), application-specific integrated circuits (ASICs), central processing units (CPUs), graphics processing units (GPUs), cryptographic processors (dedicated processors that execute cryptographic algorithms within hardware), server processors, or any other suitable processing device. integrated circuit, ASIC), central processing unit, CPU), graphics processing unit (GPU), cryptographic processor (a dedicated processor that executes encryption algorithms within hardware), server processor, or any other suitable processing device.

[0187] The computing device 2400 can include a storage device 2404 (e.g., one or more storage devices). The storage device 2404 can include random access memory (RAM) (e.g., static One or more memory devices, such as random access memory (RAM) devices (e.g., static RAM (SRAM) devices, magnetic RAM (MRAM) devices, dynamic RAM (DRAM) devices, resistive RAM (RRAM) devices, or conductive-bridging RAM (CBRAM) devices), hard drive-based memory devices, solid state memory devices, network drives, cloud drives, or any combination of memory devices, can be included. In some embodiments, the storage device 2404 can include memory that shares a die with the processing device 2402. In such embodiments, the memory can be used as cache memory and can include, for example, embedded dynamic random access memory (eDRAM) or spin transfer torque magnetic random access memory (STT-MRAM). In some embodiments, the storage device 2404 can include a non-transitory computer-readable medium having thereon instructions that, when executed by one or more processing devices (e.g., the processing device 2402), cause the computing device 2400 to perform any suitable one or more of the methods disclosed herein.

[0188] The computing device 2400 can include an interface device 2406 (e.g., one or more instances of the interface device 2406). The interface device 2406 can include one or more communication chips, connectors, or other hardware and software to manage communication between the computing device 2400 and other computing devices. For example, the interface device 2406 can include circuitry to manage wireless communication for transferring data between the computing device 2400. The term “wireless” and its derivatives can be used to describe a circuit, device, system, method, technique, or communication channel that can communicate data using electromagnetic radiation modulated through a non-solid medium. This term does not mean that the associated device does not include any wiring, although in some embodiments it may not. The circuitry included in the interface device 2406 to manage wireless communication can implement any of several wireless standards or protocols, including, but not limited to, Institute for Electrical and Electronic Engineers (IEEE) standards including Wi-Fi (IEEE 802.11 family), IEEE 802.16 standards (e.g., IEEE 802.16-2005 Amendment), Long Term Evolution (LTE) projects (e.g., Advanced LTE project, Ultra Mobile Broadband (UMB) project (also referred to as “3GPP (registered trademark) 2”)) with any amendments, updates, and / or revisions.In some embodiments, the circuitry included in the interface device 2406 for managing wireless communications can operate in accordance with a Global System for Mobile Communication (GSM), General Packet Radio Service (GPRS), Universal Mobile Telecommunications System (UMTS), High Speed Packet Access (HSPA), Evolved HSPA (E-HSPA), or Long Term Evolution (LTE) network. In some embodiments, the circuitry included within the interface device 2406 for managing wireless communications can operate in accordance with Enhanced Data for GSM Evolution (EDGE), GSM EDGE Radio Access Network (GERAN), Universal Terrestrial Radio Access Network (UTRAN), or Evolved UTRAN (E-UTRAN). In some embodiments, the circuitry included in the interface device 2406 for managing wireless communications can operate in accordance with Code Division Multiple Access (CDMA), Time Division Multiple Access (TDMA), Digital Enhanced Cordless Telecommunications (DECT), or any other suitable wireless communication standard or protocol. It can operate in accordance with Enhanced Cordless Telecommunication (DECT), Evolution-Data Optimized (EV-DO), and their derivatives, as well as any other wireless protocol designated as 3G, 4G, 5G, and beyond. In some embodiments, the interface device 2406 can include one or more antennas (e.g., one or more antenna arrays) for receiving and / or transmitting wireless communication.

[0189] In some embodiments, the interface device 2406 can include circuitry for managing wired communication, such as electrical, optical, or any other suitable communication protocol. For example, the interface device 2406 can include circuitry for supporting communication in accordance with Ethernet technology. In some embodiments, the interface device 2406 can support both wireless and wired communication, or support multiple wired communication protocols or multiple wireless communication protocols. For example, a first set of circuits of the interface device 2406 may be dedicated to short-range wireless communication such as Wi-Fi or Bluetooth, and a second set of circuits of the interface device 2406 may be dedicated to long-range wireless communication such as global positioning system (GPS), EDGE, GPRS, CDMA, WiMAX, LTE, EV-DO. In some embodiments, a first set of circuits of the interface device 2406 can be dedicated to wireless communication, and a second set of circuits of the interface device 2406 can be dedicated to wired communication.

[0190] Computing device 2400 can include a battery / power circuit 2408. The battery / power circuit 2408 can include one or more energy storage devices (e.g., a battery or a capacitor), or a circuit for coupling components of the computing device 2400 to an energy source separate from the computing device 2400 (e.g., alternating current line power).

[0191] Computing device 2400 can include a display device 2410 (e.g., multiple display devices). The display device 2410 can include any visual indicator such as a head-up display, a computer monitor, a projector, a touch screen display, a liquid crystal display (LCD), a light emitting diode display, or a flat panel display.

[0192] Computing device 2400 can include other input / output (I / O) devices 2412. The other I / O devices 2412 can include, for example, one or more audio output devices (e.g., speakers, headsets, earphones, alarms), one or more audio input devices (e.g., a microphone or a microphone array), a positioning device (e.g., a GPS device that communicates with a satellite-based system to receive the position of the computing device 2400), an audio codec, a video codec, a printer, a sensor (e.g., a thermocouple or other temperature sensor, a humidity sensor, a pressure sensor, a vibration sensor, an accelerometer, a gyroscope), an image capture device such as a camera, a cursor control device such as a keyboard, a mouse, a stylus, a trackball, or a touchpad, a barcode reader, a Quick Response (QR) code reader, or a radio frequency identification (RFID) reader.

[0193] Computing device 2400 can have any suitable form factor for its applications and settings, such as a handheld or mobile computing device (e.g., a cellular phone, smartphone, mobile Internet device, tablet computer, laptop computer, netbook computer, ultrabook computer, personal digital assistant (PDA), ultra-mobile personal computer), a desktop computing device, or a server computing device or other networked computing component.

[0194] One or more computing devices implementing any of the scientific instrument modules, methods, or techniques disclosed herein can be part of a scientific instrument support system. FIG. 25 is a block diagram of an exemplary scientific instrument support system 2500 in which some or all of the scientific instrument support methods disclosed herein can be implemented according to various embodiments. The scientific instrument modules, methods, or techniques disclosed herein (e.g., scientific instrument module 102, computer-implemented method 200, system 314, computer-implemented methods 1300-1500) can be implemented by one or more of scientific instrument 2510, user local computing device 2520, service local computing device 2530, or remote computing device 2540 of scientific instrument support system 2500.

[0195] Any one of the scientific instrument 2510, the user local computing device 2520, the service local computing device 2530, or the remote computing device 2540 can include any of the embodiments of the computing device 2400, and any one of the scientific instrument 2510, the user local computing device 2520, the service local computing device 2530, or the remote computing device 2540 can take the form of any suitable one of the embodiments of the computing device 2400.

[0196] The scientific instrument 2510, the user local computing device 2520, the service local computing device 2530, or the remote computing device 2540 may each include a processing device 2502, a storage device 2504, and an interface device 2506. The processing device 2502 can take any suitable form including any form of the processing device 2402, and the processing devices 2502 included in different ones of the scientific instrument 2510, the user local computing device 2520, the service local computing device 2530, or the remote computing device 2540 can take the same form or different forms. The storage device 2504 can take any suitable form including any form of the storage device 2404, and the storage devices 2504 included in different ones of the scientific instrument 2510, the user local computing device 2520, the service local computing device 2530, or the remote computing device 2540 can take the same form or different forms. The interface device 2506 can take any suitable form including any form of the interface device 2406, and the interface devices 2506 included in different ones of the scientific instrument 2510, the user local computing device 2520, the service local computing device 2530, or the remote computing device 2540 can take the same form or different forms.

[0197] The scientific instrument 2510, the user local computing device 2520, the service local computing device 2530, and the remote computing device 2540 can communicate with other elements of the scientific instrument support system 2500 via the communication path 2508. As shown, the communication path 2508 may communicatively couple interface devices 2506 of different ones of the elements of the scientific instrument support system 2500 and may be a wired or wireless communication path (e.g., by any of the communication technologies described herein with reference to interface device 2406). The particular scientific instrument support system 2500 shown in FIG. 25 includes communication paths between each pair of the scientific instrument 2510, the user local computing device 2520, the service local computing device 2530, and the remote computing device 2540, but this “fully connected” implementation is merely exemplary and in various embodiments, various ones of the communication paths 2508 may not be present. For example, in some embodiments, the service local computing device 2530 can lack a direct communication path 2508 between its interface device 2506 and the interface device 2506 of the scientific instrument 2510 and instead can communicate with the scientific instrument 2510 via a communication path 2508 between the service local computing device 2530 and the user local computing device 2520 and a communication path 2508 between the user local computing device 2520 and the scientific instrument 2510.

[0198] The scientific instrument 2510 can include any suitable scientific instrument such as the scientific instrument 302.

[0199] The user local computing device 2520 can be a computing device that is local to the user of the scientific instrument 2510 (e.g., according to any of the embodiments of the computing device 2400). In some embodiments, the user local computing device 2520 may be local to the scientific instrument 2510, but it does not have to be. For example, the user local computing device 2520 at the user's home or office may be remote from the scientific instrument 2510 but communicate with it so that the user can control or access data from the scientific instrument 2510 using the user local computing device 2520. In some embodiments, the user local computing device 2520 can be a laptop, smartphone, or tablet device. In some embodiments, the user local computing device 2520 can be a portable computing device.

[0200] The service local computing device 2530 can be a computing device that is local to an entity that provides services to the scientific instrument 2510 (e.g., according to any of the embodiments of the computing device 2400). For example, the service local computing device 2530 can be local to the manufacturer of the scientific instrument 2510 or a third-party service company. In some embodiments, the service local computing device 2530 receives data regarding the operation of the scientific instrument 2510, the user local computing device 2520, and / or the remote computing device 2540 (e.g., the results of a self-diagnostic test of the scientific instrument 2510, the calibration coefficients used by the scientific instrument 2510, the measurements of sensors associated with the scientific instrument 2510, etc.) from the scientific instrument 2510, the user local computing device 2520, and / or the remote computing device 2540 (e.g., via the direct communication path 2508 as described above, or via a plurality of "indirect" communication paths 2508). In some embodiments, the service local computing device 2530 communicates with the scientific instrument 2510, the user local computing device 2520, or the remote computing device 2540 (e.g., via the direct communication path 2508 as described above, or via a plurality of "indirect" communication paths 2508) to send data to the scientific instrument 2510, the user local computing device 2520, or the remote computing device 2540 (e.g., to update programmed instructions such as the firmware in the scientific instrument 2510, to initiate a test or calibration sequence in the scientific instrument 2510, to update programmed instructions such as the software in the user local computing device 2520 or the remote computing device 2540).Users of the scientific instrument 2510 can communicate with the service local computing device 2530 using the scientific instrument 2510 or the user local computing device 2520 to report problems with the scientific instrument 2510 or the user local computing device 2520, request a visit from a technician to improve the operation of the scientific instrument 2510, order consumables or replacement parts related to the scientific instrument 2510, or perform other purposes.

[0201] The remote computing device 2540 can be a computing device (e.g., according to any of the embodiments of the computing device 2400 described herein) remote from the scientific instrument 2510 or the user local computing device 2520. In some embodiments, the remote computing device 2540 can be included in a data center or other large-scale server environment. In some embodiments, the remote computing device 2540 can include network-connected storage (e.g., as part of the storage device 2504). The remote computing device 2540 can store data generated by the scientific instrument 2510, perform analysis of the data generated by the scientific instrument 2510 (e.g., according to programmed instructions), facilitate communication between the user local computing device 2520 and the scientific instrument 2510, or facilitate communication between the service local computing device 2530 and the scientific instrument 2510.

[0202] In some embodiments, one or more of the elements of the scientific instrument support system 2500 shown in FIG. 25 can be omitted. Further, in some embodiments, there can be a plurality of various ones of the elements of the scientific instrument support system 2500 of FIG. 25. For example, the scientific instrument support system 2500 can include a plurality of user local computing devices 2520 (e.g., different user local computing devices 2520 associated with different users or located in different locations). In another example, the scientific instrument support system 2500 can include a plurality of scientific instruments 2510 all of which communicate with a service local computing device 2530 and / or a remote computing device 2540. In such embodiments, the service local computing device 2530 can monitor these plurality of scientific instruments 2510, the service local computing device 2530 can cause an update, or can "broadcast" other information to the plurality of scientific instruments 2510 simultaneously. Different ones of the scientific instruments 2510 within the scientific instrument support system 2500 can be located close to each other (e.g., in the same room) or far from each other (e.g., on different floors of a building, in different buildings, in different cities, etc.). In some embodiments, the scientific instrument 2510 can connect to an Internet of Thing (IoT) stack that enables command and control of the scientific instrument 2510 via a web-based application, a virtual or augmented reality application, a mobile application, or a desktop application. Any of these applications can be accessed by a user who operates a user local computing device 2520 that communicates with the scientific instrument 2510 via an intervening remote computing device 2540. In some embodiments, the scientific instrument 2510 can be sold by a manufacturer as part of a local scientific instrument computing unit 2512 together with one or more associated user local computing devices 2520.

[0203] In some embodiments, different ones of the scientific instruments 2510 included in the scientific instrument support system 2500 may be different types of scientific instruments 2510. For example, one scientific instrument 2510 may be a mass spectrometer, and another scientific instrument 2510 may be a chromatograph or an autosampler. In some such embodiments, the remote computing device 2540 or the user local computing device 2520 may be able to combine data from different types of scientific instruments 2510 included in the scientific instrument support system 2500.

[0204] In various cases, machine learning algorithms or models can be implemented in any suitable way to facilitate any suitable aspect described herein. To facilitate some of the above-described aspects of machine learning in various embodiments, consider the following description of artificial intelligence (AI). The various embodiments described herein can facilitate the use of artificial intelligence to automate one or more features or functions. Components can use various AI-based schemes to perform the various embodiments / examples disclosed herein. To provide or assist in providing a number of decisions (e.g., determining, verifying, inferring, calculating, predicting, foreseeing, estimating, deriving, anticipating, detecting, computing) described herein, the components described herein can examine all or a subset of the data to which it is permitted access and provide or determine inferences about the state of a system or environment from a set of observations as captured via events or data. Decisions can be employed, for example, to identify a particular context or action, or can generate a probability distribution over states. Decisions can be probabilistic. That is, a calculation of a probability distribution over the state of an object based on the consideration of data and events. Decisions can also refer to techniques used to compose higher-level events from a set of events or data.

[0205] Such a determination can result in the construction of new events or actions from a set of observed or remembered event data, regardless of whether the events are temporally proximate and correlated, and regardless of whether the events and data are from one or more event and data sources. The components disclosed herein may relate to various classification (explicitly trained (e.g., via training data), as well as implicitly trained (e.g., via observing behavior, preferences, history information, receiving external information, etc.)) schemes or systems (e.g., support vector machines, neural networks, expert systems, Bayesian belief networks, fuzzy logic, data fusion engines, etc.) in relation to performing automatic or determined actions related to the claimed subject matter. Thus, classification schemes or systems can be used to automatically learn and perform some functions, actions, or decisions.

[0206] A classifier can map an input attribute vector z = (z1, z2, z3, z4, z n ) to a confidence that the input belongs to a class, such as f(z) = confidence(class). Such classification can employ probability or statistics-based analysis (e.g., taking into account analysis utilities and costs) to determine actions to be automatically performed. A support vector machine (SVM) can be an example of a classifier that can be used. An SVM operates by finding a hypersurface within the space of possible inputs, where the hypersurface attempts to divide trigger criteria from non-trigger events. Intuitively, this corrects classification for test data that is close to but not identical to the training data. Other directed and undirected model classification techniques include, for example, naive Bayes, Bayesian networks, decision trees, neural networks, fuzzy logic models, or probabilistic classification models that provide for different patterns of independence, and any of these can be used. Classification as used herein also includes statistical regression utilized to develop a model of priorities.

[0207] To provide additional context to the various embodiments described herein, FIGS. 26 and the following description are intended to provide a brief, general description of a suitable computing environment 2600 in which the various embodiments described herein can be implemented. The embodiments are described in the general context of computer-executable instructions that can be performed on one or more computers, but those skilled in the art will recognize that the embodiments can also be implemented in combination with other program modules or as a combination of hardware and software.

[0208] In general, program modules include routines, programs, components, data structures, etc. that perform particular tasks or implement particular abstract data types. Further, those skilled in the art will understand that the methods of the present invention can be implemented in other computer system configurations including single-processor or multiprocessor computer systems, minicomputers, mainframe computers, monolithic Internet of Things (IoT) devices, distributed computing systems, and personal computers, handheld computing devices, microprocessor-based or programmable consumer electronics, etc., each of which can be operably coupled to one or more associated devices.

[0209] The illustrated embodiments of the embodiments herein can also be implemented in a distributed computing environment where certain tasks are performed by remote processing devices linked through a communications network. In a distributed computing environment, program modules can be located in both local and remote memory storage devices.

[0210] A computing device can typically include various media that can include a computer-readable storage medium, a machine-readable storage medium, or a communication medium, and these two terms are used differently from each other as follows in this specification. A computer-readable storage medium or a machine-readable storage medium can be any available storage medium that can be accessed by a computer, and includes both volatile and non-volatile media, and both removable media and non-removable media. By way of non-limiting example, a computer-readable storage medium or a machine-readable storage medium can be implemented in connection with any method or technology for storing information such as computer-readable or machine-readable instructions, program modules, structured data or unstructured data.

[0211] A computer-readable storage medium includes, but is not limited to, random access memory (random access memory, RAM), read only memory (ROM), electrically erasable programmable read only memory (EEPROM), flash memory or other memory technologies, compact disk read only memory (CD ROM), digital versatile disk (DVD), Blu-ray (registered trademark) disc (BD) or other optical disk storage, magnetic cassette, magnetic tape, magnetic disk storage or other magnetic storage devices, solid state drive or other solid state storage devices, or other tangible or non-transitory media that can be used to store desired information. In this regard, the terms "tangible" or "non-transitory" as applied to storage, memory, or computer-readable media herein should be understood to exclude only the transient signals themselves that propagate as a modifier, and do not waive rights to all standard storage, memory, or computer-readable media that are not only the transient signals themselves that propagate.

[0212] A computer-readable storage medium can be accessed by one or more local or remote computing devices via, for example, access requests, queries, or other data retrieval protocols for various operations related to the information stored by the medium.

[0213] A communication medium typically embodies computer-readable instructions, data structures, program modules, or other structured or unstructured data in a data signal, such as a modulated data signal like a carrier wave or other transmission mechanism, and includes any information delivery or transmission medium. The term "modulated data signal" or signal refers to a signal in which one or more characteristics are set or changed so as to encode information in one or more signals. By way of example and not limitation, communication media include wired media such as wired networks or direct wired connections, and wireless media such as acoustic, RF, infrared, and other wireless media.

[0214] Referring again to FIG. 26, an exemplary environment 2600 for implementing various embodiments of the aspects described herein includes a computer 2602, which includes a processing unit 2604, a system memory 2606, and a system bus 2608. The system bus 2608 couples system components including, but not limited to, the system memory 2606 to the processing unit 2604. The processing unit 2604 can be any of a variety of commercially available processors. Dual microprocessors and other multiprocessor architectures can also be used as the processing unit 2604.

[0215] The system bus 2608 can be any of several types of bus structures including, without limitation, a memory bus (with or without a memory controller), a peripheral bus, and a local bus using any of a variety of commercially available bus architectures. The system memory 2606 includes ROM 2610 and RAM 2612. A basic input / output system (BIOS) can be stored in non-volatile memory such as ROM, erasable programmable read-only memory (EPROM), EEPROM, and includes basic routines that help transfer information between elements within the computer 2602 during startup, etc. The RAM 2612 can also include high-speed RAM such as static RAM for caching data.

[0216] The computer 2602 has an internal hard disk drive The environment 2600 further includes an internal hard disk drive (HDD) 2614 (e.g., EIDE, SATA), one or more external storage devices 2616 (e.g., a magnetic floppy disk drive (FDD) 2616, a memory stick or flash drive reader, a memory card reader, etc.), and a drive 2620, e.g., a solid state drive, optical disk drive, etc., that can read from or write to a disk 2622, such as a CD-ROM disk, DVD, BD, etc. Alternatively, if a solid state drive is included, the disk 2622 is not included unless it is separate. Although the internal HDD 2614 is shown as being located within the computer 2602, the internal HDD 2614 can also be configured for external use within a suitable chassis (not shown). Additionally, although not shown in the environment 2600, a solid state drive (SSD) can be used in addition to or in place of the HDD 2614. HDD 2614, external storage device 2616, and drive 2620 can be connected to system bus 2608 by HDD interface 2624, external storage interface 2626, and drive interface 2628, respectively. Interface 2624 for external drive implementations may include at least one or both of Universal Serial Bus (USB) and Institute of Electrical and Electronics Engineers (IEEE) 1394 interface technologies. Other external drive connection technologies are within the contemplation of the embodiments described herein.

[0217] Drives and their associated computer-readable storage media provide non-volatile storage of data, data structures, computer-executable instructions, and the like. In the case of computer 2602, the drives and storage media accommodate storage of any data in a suitable digital format. The foregoing description of computer-readable storage media refers to each type of storage device, but other types of storage media that are computer-readable, whether currently existing or to be developed in the future, may also be used in exemplary operating environments. Further, it should be understood by those skilled in the art that any such storage media may contain computer-executable instructions for implementing the methods described herein.

[0218] Several program modules, including operating systems 2630, one or more application programs 2632, other program modules 2634, and program data 2636, can be stored on the drives and in RAM 2612. All or part of an operating system, application, module, or data can also be cached in RAM 2612. The systems and methods described herein may be implemented using a variety of commercially available operating systems or combinations of operating systems.

[0219] Computer 2602 can optionally include emulation technology. For example, a hypervisor (not shown) or other medium can emulate the hardware environment of operating system 2630, and the emulated hardware can optionally be different from the hardware shown in FIG. 26. In such an embodiment, operating system 2630 can include one of a plurality of virtual machines (VMs) hosted on computer 2602. Further, operating system 2630 can provide a runtime environment such as a Java runtime environment or a.NET framework for application 2632. The runtime environment is a consistent execution environment that enables application 2632 to run on any operating system that includes the runtime environment. Similarly, operating system 2630 can support containers, and application 2632 can be in the form of a container, which is a lightweight, stand-alone executable package of software that includes, for example, code, runtime, system tools, system libraries, and settings for the application.

[0220] Furthermore, computer 2602 can enable the use of a security module such as a trusted processing module (TPM). For example, using the TPM, a boot component hashes the next boot component in time and waits for the result to match a secure value before loading the next boot component. This process can be performed at any layer within the code execution stack of computer 2602 and can be applied, for example, at the application execution level or the operating system (OS) kernel level, thereby enabling security at any level of code execution.

[0221] The user can input commands and information into the computer 2602 via one or more wired / wireless input devices, such as a keyboard 2638, a touch screen 2640, and a pointing device such as a mouse 2642. Other input devices (not shown) can include a microphone, an infrared (IR) remote control, a radio frequency (RF) remote control, or other remote controls, a joystick, a virtual reality controller or virtual reality headset, a gamepad, a stylus pen, an image input device such as a camera, a gesture sensor input device, a visual motion sensor input device, an emotion or face detection device, a biometric input device such as a fingerprint or iris scanner, etc. These and other input devices are often connected to the processing unit 2604 via an input device interface 2644 that can be coupled to the system bus 2608, but can also be connected by other interfaces such as a parallel port, an IEEE 1394 serial port, a game port, a USB port, an IR interface, a BLUETOOTH (registered trademark) interface, etc.

[0222] A monitor 2646 or other type of display device can also be connected to the system bus 2608 via an interface such as a video adapter 2648. In addition to the monitor 2646, the computer typically includes other peripheral output devices (not shown) such as speakers, printers, etc.

[0223] Computer 2602 can operate in a networked environment using a logical connection via wired or wireless communication to one or more remote computers, such as remote computer 2650. Remote computer 2650 can be a workstation, server computer, router, personal computer, portable computer, microprocessor-based entertainment device, peer device, or other common network node, and typically includes many or all of the elements described with respect to computer 2602, but for simplicity only memory / storage device 2652 is shown. The illustrated logical connections include wired / wireless connections to local area network (LAN) 2654 or a larger network, such as wide area network (WAN) 2656. Such LAN and WAN networking environments are common in offices and enterprises, facilitating enterprise-scale computer networks such as intranets, all of which can be connected to a global communication network such as the Internet.

[0224] When used in a LAN networking environment, computer 2602 can be connected to local network 2654 via a wired or wireless communication network interface or adapter 2658. Adapter 2658 can facilitate wired or wireless communication to LAN 2654, and LAN 2654 can also include a wireless access point (AP) disposed thereon for communicating with adapter 2658 in wireless mode.

[0225] When used in a WAN networking environment, computer 2602 can include a modem 2660 or can be connected to a communication server on WAN 2656 via other means for establishing communication via WAN 2656, such as via the Internet. Modem 2660 can be internal or external and can be a wired or wireless device and can be connected to system bus 2608 via input device interface 2644. In a networked environment, program modules shown with respect to computer 2602 or portions thereof can be stored in remote memory / storage device 2652. The network connections shown are examples, and it will be appreciated that other means of establishing a communication link between computers can be used.

[0226] When used in either a LAN or WAN networking environment, computer 2602 can access a cloud storage system or other network-based storage system in addition to, or instead of, external storage device 2616 as described above, such as a network virtual machine that provides one or more aspects of information storage or processing, but is not limited thereto. Generally, the connection between computer 2602 and the cloud storage system can be established via LAN 2654 or WAN 2656, for example, by adapter 2658 or modem 2660, respectively. When computer 2602 is connected to an associated cloud storage system, external storage interface 2626 can manage the storage provided by the cloud storage system in the same manner as other types of external storage, with the help of adapter 2658 or modem 2660. For example, external storage interface 2626 can be configured to provide access to cloud storage sources as if those sources were physically connected to computer 2602.

[0227] Computer 2602 can be any wireless device or entity operably arranged in wireless communication, such as a printer, scanner, desktop or laptop computer, personal digital assistant, communication satellite, any device or location associated with a wirelessly detectable tag (e.g., kiosk, newsstand, store shelf, etc.), and can be operable to communicate with a telephone. This can include wireless fidelity (Wi-Fi) and BLUETOOTH (registered trademark) wireless technologies. Thus, the communication can be in a pre-defined structure similar to a conventional network or simply ad-hoc communication between at least two devices.

[0228] FIG. 27 is a schematic block diagram of a sample computing environment 2700 with which the disclosed subject matter can interact. The sample computing environment 2700 includes one or more clients 2710. The client 2710 can be hardware or software (e.g., thread, process, computing device). The sample computing environment 2700 also includes one or more servers 2730. The server 2730 can also be hardware or software (e.g., thread, process, computing device). The server 2730 can accommodate threads for performing conversions, for example, by adopting one or more embodiments as described herein. One possible communication between the client 2710 and the server 2730 can be in the form of data packets adapted to be transmitted between two or more computer processes. The sample computing environment 2700 includes a communication framework 2750 that can be used to facilitate communication between the client 2710 and the server 2730. The client 2710 is operably connected to one or more client data stores 2720 that can be used to store information local to the client 2710. Similarly, the server 2730 is operably connected to one or more server data stores 2740 that can be used to store information local to the server 2730.

[0229] Various embodiments can be a system, a method, an apparatus, or a computer program product in the integration of any possible technical detail level. The computer program product can include a computer-readable storage medium having computer-readable program instructions for causing a processor to perform aspects of various embodiments. The computer-readable storage medium can be a tangible device that can hold and store instructions for use by an instruction execution device. The computer-readable storage medium can be, for example, but not limited to, an electronic storage device, a magnetic storage device, an optical storage device, an electromagnetic storage device, a semiconductor storage device, or any suitable combination of the foregoing. A non-exhaustive list of more specific examples of the computer-readable storage medium can also include a portable computer diskette, a hard disk, a random access memory (RAM), a read-only memory (ROM), an erasable programmable read-only memory (EPROM or flash memory), a static random access memory (SRAM), a portable compact disc read-only memory (CD-ROM), a digital versatile disc (DVD), a memory stick, a floppy disk, a mechanically encoded device such as a punched card or raised structures in grooves having instructions recorded thereon, and any suitable combination of the foregoing. The computer-readable storage medium used herein should not be construed to be a transient signal per se, such as a radio wave or other freely propagating electromagnetic wave, an electromagnetic wave propagating through a waveguide or other transmission medium (e.g., an optical pulse passing through an optical fiber cable), or an electrical signal transmitted through a wire.

[0230] The computer-readable program instructions described herein can be downloaded from a computer-readable storage medium to respective computing / processing devices, or to an external computer or external storage device via a network, such as the Internet, a local area network, a wide area network, or a wireless network. The network can include copper transmission cables, optical transmission fibers, wireless transmission, routers, firewalls, switches, gateway computers, or edge servers. A network adapter card or network interface within each computing / processing device receives the computer-readable program instructions from the network and transfers the computer-readable program instructions for storage in a computer-readable storage medium within each respective computing / processing device. The computer-readable program instructions for carrying out operations of various embodiments can be source code or object code written in any combination of one or more programming languages, including assembler instructions, instruction-set-architecture (ISA) instructions, machine instructions, machine-dependent instructions, microcode, firmware instructions, state-setting data, configuration data for integrated circuits, or object-oriented programming languages such as Smalltalk, C++, and procedural programming languages such as the "C" programming language or similar programming languages. The computer-readable program instructions can execute entirely on the user's computer, partly on the user's computer, as a stand-alone software package, partly on the user's computer and partly on a remote computer, or entirely on the remote computer or server. In the latter scenario, the remote computer can be connected to the user's computer via any type of network, including a local area network (LAN) or a wide area network (WAN), or can be connected to an external computer (e.g., via the Internet using an Internet service provider).In some embodiments, for example, an electronic circuit including a programmable logic circuit, a field-programmable gate array (FPGA), or a programmable logic array (PLA) can execute computer-readable program instructions by personalizing the electronic circuit using the state information of the computer-readable program instructions to implement various aspects.

[0231] Various aspects are described herein with reference to flowcharts or block diagrams of methods, apparatus (systems), and computer program products according to various embodiments. It will be understood that each block of the flowcharts or block diagrams, and combinations of blocks in the flowcharts or block diagrams, can be implemented by computer-readable program instructions. These computer-readable program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, or other programmable data processing apparatus to create means for implementing the functions / operations specified in one or more blocks of the flowchart or block diagram by causing the instructions executed via the processor of the computer or other programmable data processing apparatus. These computer-readable program instructions can also be stored in a computer-readable storage medium that includes instructions for implementing aspects of the functions / operations specified in one or more blocks of the flowchart or block diagram, so that the computer-readable storage medium can be configured to cause a computer, programmable data processing apparatus, or other device to function in a particular manner. The computer-readable program instructions can also be loaded onto a computer, other programmable apparatus, or other device to generate a computer-implemented process for implementing the functions / operations specified in one or more blocks of the flowchart or block diagram by causing a series of operational steps to be performed on the computer, other programmable apparatus, or other device.

[0232] The flowcharts and block diagrams in the figures illustrate the architecture, functionality, and operation of possible implementations of systems, methods, and computer program products according to various embodiments. In this regard, each block in the flowchart or block diagram can represent a module, segment, or portion of a program that includes one or more executable instructions for implementing the specified logical function. In some alternative implementations, the functions noted in the blocks may be performed in an order different than that noted in the figures. For example, two blocks shown in succession may, in fact, be executed substantially simultaneously, or the blocks may sometimes be executed in the reverse order, depending upon the functionality involved. It should also be noted that each block of the block diagrams or flowchart diagrams, and combinations of blocks in the block diagrams or flowchart diagrams, can be implemented by a dedicated hardware-based system that performs the specified functions or operations, or by a combination of dedicated hardware and computer instructions.

[0233] The subject matter has been described above in the general context of computer-executable instructions of a computer program product that runs on one or more computers, and those skilled in the art will recognize that the present disclosure may be implemented in combination with other program modules. In general, program modules include routines, programs, components, data structures, etc. that perform particular tasks or implement particular abstract data types. Further, those skilled in the art will understand that various aspects may be implemented using other computer system configurations, including single-processor or multi-processor computer systems, minicomputing devices, mainframe computers, and computers, handheld computing devices (e.g., PDAs, telephones), microprocessor-based or programmable home or industrial electronic devices, etc. The illustrated aspects may also be implemented in a distributed computing environment where tasks are performed by remote processing devices linked through a communications network. However, although not all of the present disclosure, some aspects may be implemented on a stand-alone computer. In a distributed computing environment, program modules may be located in both local and remote memory storage devices.

[0234] As used in this application, terms such as "component", "system", "platform", "interface", etc. can refer to, or can include, computer-related entities or entities related to an operating machine having one or more specific functions. The entities disclosed herein can be any of hardware, a combination of hardware and software, software, or software in execution. For example, a component can be, but is not limited to, a process running on a processor, a processor, an object, an executable file, an execution thread, a program, or a computer. By way of example, both an application running on a server and the server can be components. One or more components can exist within a process or execution thread, and a component can be localized on one computer or distributed between two or more computers. In another example, each component can be executed from various computer-readable media in which various data structures are stored. A component can communicate through a local process or a remote process, such as by following a signal having one or more data packets (e.g., data from one component interacting with another component in a local system, a distributed system, or with another system via a network such as the Internet). As another example, a component can be a device having a specific function provided by a mechanical part operated by an electrical or electronic circuit operated by software or a firmware application executed by a processor. In such a case, the processor can be inside or outside the device and can execute at least a portion of the software or firmware application. As yet another example, a component can be a device that provides a specific function through an electronic component without a mechanical part, and the electronic component can include a processor or other means for executing software or firmware that at least partially provides the function of the electronic component.In one aspect, a component may emulate an electronic component, for example, via a virtual machine within a cloud computing system.

[0235] Furthermore, the term "or" means an inclusive "or" rather than an exclusive "or". That is, unless otherwise specified or clear from the context, "X employs A or B" means any natural inclusive substitution. That is, if X employs A, X employs B, or if X employs both A and B, "X employs A or B" is satisfied in any of the foregoing cases. As used herein, the term "and / or" is intended to have the same meaning as "or". Further, the articles "a" and "an" used in this specification and the accompanying drawings should generally be construed to mean "one or more" unless specifically stated otherwise or clear from the context. As used herein, the term "example" or "exemplary" is utilized to mean serving as an example, instance, or illustration. To avoid misunderstanding, the subject matter disclosed herein is not limited by such examples. Further, any aspect or design described herein as "example" or "exemplary" should not necessarily be construed as more preferable or advantageous than other aspects or designs, nor does it mean excluding equivalent exemplary structures and techniques known to those skilled in the art.

[0236] The disclosure of this specification describes non-limiting examples. For ease of description or explanation, various parts of the disclosure of this specification use the terms "each", "all", or "all" when discussing various examples. The use of such terms as "each", "any", or "all" is non-limiting. In other words, when the disclosure of this specification provides an explanation applicable to "each", "all", or "all" of some specific objects or components, it is to be understood that this is a non-limiting example, and in various other examples, it is further to be understood that such an explanation may apply to less than "each", "all", or "all" of that specific object or component.

[0237] As used herein, the term "processor" can refer to substantially any computing processing unit or device, including but not limited to a single-core processor, a single processor with software multithreading capabilities, a multi-core processor, a multi-core processor with software multithreading capabilities, a multi-core processor with hardware multithreading technology, and a parallel platform with distributed shared memory. Further, a processor can refer to an integrated circuit, an application-specific integrated circuit (ASIC), a digital signal processor (DSP), a field-programmable gate array (FPGA), a programmable logic controller (PLC), a complex programmable logic device (CPLD), discrete gates or transistor logic, discrete hardware components, or any combination thereof designed to perform the functions described herein. Further, a processor can utilize nanoscale architectures such as, but not limited to, molecular and quantum dot-based transistors, switches, and gates to optimize space usage or improve the performance of user equipment. A processor can also be implemented as a combination of computing processing units. In the present disclosure, terms such as "store", "storage", "data store", "data storage", "database", and substantially any other information storage component related to the operation and function of a component are used to refer to an entity incorporated within a "memory component", "memory", or a component having a memory. It should be understood that the memory or memory component described herein can be either volatile memory or non-volatile memory, or can include both volatile memory and non-volatile memory.By way of example and not limitation, non-volatile memory can include read-only memory (ROM), programmable ROM (PROM), electrically programmable ROM (EPROM), electrically erasable ROM (EEPROM), flash memory, or non-volatile random access memory (RAM) (e.g., ferroelectric RAM (FeRAM)). Volatile memory can include, for example, RAM that can function as an external cache memory. By way of example and not limitation, RAM is available in many forms such as synchronous RAM (SRAM), dynamic RAM (DRAM), synchronous DRAM (SDRAM), double data rate SDRAM (DDR SDRAM), enhanced SDRAM (ESDRAM), Synchlink DRAM (SLDRAM), direct Rambus RAM (DRRAM), direct Rambus dynamic RAM (DRDRAM), and Rambus dynamic RAM (RDRAM). Additionally, the disclosed memory components of the systems or computer-implemented methods of this specification are intended to include these and any other suitable types of memory, but are not limited to including them. data rate SDRAM, DDR SDRAM), enhanced SDRAM (ESDRAM), Synchlink DRAM (SLDRAM), direct Rambus RAM, DRRAM), direct Rambus dynamic RAM, DRDRAM), and Rambus dynamic RAM (RDRAM) and are available in many forms. Additionally, the disclosed memory components of the systems or computer-implemented methods of this specification are intended to include these and any other suitable types of memory, but are not limited to including them.

[0238] What has been described above includes merely examples of systems and computer-implemented methods. Of course, for the purpose of describing the present disclosure, it is impossible to describe all possible combinations of components or computer-implemented methods, but many further combinations and permutations of the present disclosure are possible. Further, as used in the detailed description, the claims, the appendices, and the drawings, terms such as "including," "having," "possessing," etc., are intended to be as encompassing as the term "comprising" as interpreted when the term "comprising" is used as a transitional term in the claims.

[0239] The descriptions of the various embodiments are presented for purposes of illustration but are not intended to be exhaustive or limited to the disclosed embodiments. Many modifications and variations will be apparent without departing from the scope and spirit of the described embodiments. The terms used herein are chosen in order to best explain the principles of the embodiments, the practical application to technologies found in the marketplace, or the technical improvement, or to enable others of ordinary skill in the art to understand the embodiments disclosed herein.

[0240] Various non-limiting aspects are described in the examples below.

[0241] Example 1: A scientific instrument can comprise a processor capable of executing computer-executable components stored in a non-transitory computer-readable memory. In various aspects, the computer-executable components can include an access component capable of accessing a digital twin of the scientific instrument. In various cases, the computer-executable components can include a calibration component capable of synchronizing the parametric state of the digital twin with the physical state of the scientific instrument via execution of a state-of-the-art Bayesian filter.

[0242] Example 2: The scientific instrument of any preceding example can be implemented, and the state-of-the-art Bayesian filter can include a set of calibration iterations, each of which can be presented by the scientific instrument and can include Bayesian updates for the entire parametric state based on iterative common observables that can be simulated by the digital twin.

[0243] Example 3: The scientific instrument of any preceding example can be implemented, and during the current calibration iteration of the set of calibration iterations, the calibration component measures the observed values of the iterative common observables presented during the operation of the scientific instrument, and from the state space of the digital twin, where the state space can be incrementally constrained via recursive Bayesian updates based on previous calibration iterations, a plurality of parametric state instantiations are randomly sampled, and based on performing a plurality of parametric state instantiations on the digital twin, a plurality of simulated observed values of the iterative common observables are calculated, weights are respectively assigned to the plurality of parametric state instantiations based on the difference between the observed values and the plurality of simulated observed values, and any of the plurality of parametric state instantiations having a weight below a threshold weight value are deleted, thereby resulting in a plurality of remaining parametric state instantiations, checking whether the variance of the plurality of remaining parametric state instantiations is below a threshold variance value, in response to a determination that the variance of the plurality of remaining parametric state instantiations is below the threshold variance value, determining that the parametric state of the digital twin and the physical state of the scientific instrument are synchronized in the weighted average of the plurality of remaining parametric state instantiations, and in response to a determination that the variance of the plurality of remaining parametric state instantiations does not fall below the threshold variance value, applying an active setting adjustment to the scientific instrument, modifying the plurality of remaining parametric state instantiations based on the active setting adjustment, thereby resulting in a plurality of modified remaining parametric state instantiations that can be used to incrementally constrain the state space via recursive Bayesian updates during subsequent calibration iterations.

[0244] Example 4: The scientific instrument of any preceding example can be implemented, and the calibration component can further modify the plurality of remaining parametric state instantiations based on the passive temporal evolution associated with the scientific instrument.

[0245] Example 5: The scientific instrument of any preceding example can be implemented, and the scientific instrument can be a charged particle microscope.

[0246] Example 6: The scientific instrument of any preceding example can be implemented, and the parametric state of the digital twin can be the aberration coefficient vector of the charged particle microscope.

[0247] Example 7: The scientific instrument of any preceding example can be implemented, and the iterative common observable can be based on the convergent beam electron diffraction pattern of an amorphous carbon sample captured by a charged particle microscope.

[0248] Example 8: The scientific instrument of any preceding example can be implemented, and the active setting adjustment can be the lens setting adjustment, deflector setting adjustment, temperature setting adjustment, or stage actuator adjustment of the charged particle microscope.

[0249] Example 9: The scientific instrument of any preceding example can be implemented, and the full-state Bayesian filter can be based on particle filter technology or Kalman filter technology.

[0250] In various embodiments, any one or more combinations of Examples 1-9 can be implemented.

[0251] Example 10: The computer-implemented method can include synchronizing the parametric state of the digital twin with the physical state of the scientific instrument by a device operably coupled to a processor that executes a full-state Bayesian filter. In various aspects, the computer-implemented method can include generating, by the device, an electronic alert indicating that the digital twin is ready to predict the behavior of the scientific instrument in response to the synchronization.

[0252] Example 11: It is possible to implement the computer-implemented method of any preceding example, and the state-of-the-art Bayesian filter can include a set of calibration iterations, each of which can be presented by a scientific instrument and can include Bayesian updates for the entire parametric state based on a recurrent common observable that can be simulated by a digital twin.

[0253] Example 12: It is possible to implement the computer-implemented method of any preceding example, and the current calibration iteration among the set of calibration iterations measures, by the device, the observed values of the iterative common observables presented during the operation of the scientific instrument, and samples, by the device, a plurality of parametric state instantiations randomly from a state space of the digital twin, where the state space can be incrementally constrained via recursive Bayesian updates based on previous calibration iterations, and calculates, by the device, a plurality of simulated observed values of the iterative common observables based on performing a plurality of parametric state instantiations on the digital twin, and assigns, by the device, weights to the plurality of parametric state instantiations respectively based on the difference between the observed values and the plurality of simulated observed values, and deletes, by the device, any of the plurality of parametric state instantiations having weights below a threshold weight value, thereby resulting in a plurality of remaining parametric state instantiations, and checks, by the device, whether the variance of the plurality of remaining parametric state instantiations is below a threshold variance value, and determines, by the device, in response to the determination that the variance of the plurality of remaining parametric state instantiations is below the threshold variance value, that the parametric state of the digital twin and the physical state of the scientific instrument are synchronized in the weighted average of the plurality of remaining parametric state instantiations, and applies, by the device, an active setting adjustment to the scientific instrument in response to the determination that the variance of the plurality of remaining parametric state instantiations does not fall below the threshold variance value, and modifies, by the device, the plurality of remaining parametric state instantiations based on the active setting adjustment, thereby resulting in a plurality of modified remaining parametric state instantiations that can be used to incrementally constrain the state space via recursive Bayesian updates during subsequent calibration iterations.

[0254] Example 13: It is possible to implement the computer-implemented method of any preceding example, and the device can further modify a plurality of remaining parametric state instantiations based on the passive temporal evolution associated with the scientific instrument.

[0255] Example 14: It is possible to implement the computer-implemented method of any preceding example, and the scientific instrument can be a charged particle microscope.

[0256] Example 15: It is possible to implement the computer-implemented method of any preceding example, and the parametric state of the digital twin can be the aberration coefficient vector of the charged particle microscope.

[0257] Example 16: It is possible to implement the computer-implemented method of any preceding example, and the iterative common observable can be based on the convergent beam electron diffraction pattern of an amorphous carbon sample captured by a charged particle microscope.

[0258] Example 17: It is possible to implement the computer-implemented method of any preceding example, and the active setting adjustment can be a lens setting adjustment, deflector setting adjustment, temperature setting adjustment, or stage actuator adjustment of the charged particle microscope.

[0259] In various embodiments, any one or more combinations of Examples 10 to 17 can be implemented.

[0260] Example 18: A computer program product for facilitating improved digital twin calibration for a scientific instrument can comprise a non-transitory computer-readable memory having program instructions incorporated therein. In various aspects, the program instructions can cause a processor to access a digital twin of a charged particle microscope and synchronize a physical state of the charged particle microscope with a parametric state of the digital twin via execution of a set of calibration iterations, each calibration iteration including a Bayesian update to the parametric state of the digital twin based on a recurring common observable that can be presented by the charged particle microscope and simulated by the digital twin, and after synchronization, cause the digital twin to be executed by the processor to predict how the charged particle microscope would respond to a proposed usage scenario.

[0261] Example 19: The computer program product of any preceding example can be implemented, and the parametric state of the charged particle microscope can be an aberration coefficient vector.

[0262] Example 20: The computer program product of any preceding example can be implemented, and the recurring common observable can be based on a convergent beam electron diffraction pattern of an amorphous carbon sample.

[0263] In various embodiments, any combination of one or more of Examples 18 - 20 can be implemented.

[0264] In various embodiments, any combination of one or more of Examples 1 - 20 can be implemented.

Claims

1. A scientific instrument, comprising: a processor that executes computer-executable components stored in a non-transitory computer-readable memory, the computer-executable components comprising: an access component that accesses a digital twin of the scientific instrument; and a calibration component that synchronizes parametric states of the digital twin with physical states of the scientific instrument via execution of a full-state Bayesian filter.

2. The scientific instrument according to claim 1, wherein the full-state Bayesian filter includes a set of calibration iterations, each of the calibration iterations including a Bayesian update for an entirety of the parametric state based on an iterative common observable that can be presented by the scientific instrument and simulated by the digital twin.

3. During a current calibration iteration of the set of calibration iterations, the calibration component: measures an observed value of the iterative common observable presented during operation of the scientific instrument; randomly samples a plurality of parametric state instantiations from a state space of the digital twin, the state space being incrementally constrained via recursive Bayesian updates based on previous calibration iterations; calculates a plurality of simulated observed values of the iterative common observable based on performing the plurality of parametric state instantiations on the digital twin; assigns weights to the plurality of parametric state instantiations respectively based on a difference between the observed value and the plurality of simulated observed values; deletes any of the plurality of parametric state instantiations having weights below a threshold weight value, thereby resulting in a plurality of remaining parametric state instantiations; checks whether a variance of the plurality of remaining parametric state instantiations is below a threshold variance value; and in response to determining that the variance of the plurality of remaining parametric state instantiations is below the threshold variance value, determines that the parametric state of the digital twin and the physical state of the scientific instrument are synchronized in a weighted average of the plurality of remaining parametric state instantiations. In response to a determination that the spread of the plurality of remaining parametric state instantiations does not fall below the threshold spread value, apply an active setting adjustment to the scientific instrument, Modify the plurality of remaining parametric state instantiations based on the active setting adjustment, thereby resulting in a plurality of modified remaining parametric state instantiations, the plurality of modified remaining parametric state instantiations being used to incrementally constrain the state space via recursive Bayesian updates during subsequent calibration iterations, the scientific instrument of claim 2. **Claim 4** The scientific instrument of claim 3, wherein the calibration component further modifies the plurality of remaining parametric state instantiations based on passive temporal evolution associated with the scientific instrument. **Claim 5** The scientific instrument of claim 3, wherein the scientific instrument is a charged particle microscope. **Claim 6** The scientific instrument of claim 5, wherein the parametric state of the digital twin is an aberration coefficient vector of the charged particle microscope. **Claim 7** The scientific instrument of claim 5, wherein the iterative common observable is based on a convergent beam electron diffraction pattern of an amorphous carbon sample captured by the charged particle microscope. **Claim 8** The scientific instrument of claim 5, wherein the active setting adjustment is a lens setting adjustment, a deflector setting adjustment, a temperature setting adjustment, or a stage actuator adjustment of the charged particle microscope. **Claim 9** The scientific instrument of claim 1, wherein the state ensemble Bayesian filter is based on particle filter technology or Kalman filter technology. **Claim 10** A computer-implemented method comprising: Synchronizing a parametric state of a digital twin with a physical state of a scientific instrument by a device operatively coupled to a processor that executes a state ensemble Bayesian filter; and Generating, by the device, an electronic alert indicating that the digital twin is ready to predict the behavior of the scientific instrument in response to the synchronizing. **Claim 11** The overall state Bayesian filter includes a set of calibration iterations, each of the calibration iterations including a Bayesian update for the overall parametric state based on an iterative common observable that can be presented by the scientific instrument and simulated by the digital twin, the computer-implemented method of claim 10.

12. The current calibration iteration of the set of calibration iterations measures, by the device, an observed value of the iterative common observable presented during operation of the scientific instrument, samples, by the device, a plurality of parametric state instantiations randomly from a state space of the digital twin, the state space being incrementally constrained via recursive Bayesian updates based on previous calibration iterations, computes, by the device, a plurality of simulated observed values of the iterative common observable based on performing the plurality of parametric state instantiations on the digital twin, assigns, by the device, weights to the plurality of parametric state instantiations respectively based on a difference between the observed value and the plurality of simulated observed values, removes, by the device, any of the plurality of parametric state instantiations having a weight below a threshold weight value, thereby resulting in a plurality of remaining parametric state instantiations, checks, by the device, whether a variance of the plurality of remaining parametric state instantiations is below a threshold variance value, determines, by the device, in response to a determination that the variance of the plurality of remaining parametric state instantiations is below the threshold variance value, that the parametric state of the digital twin and the physical state of the scientific instrument are synchronized in a weighted average of the plurality of remaining parametric state instantiations, applies, by the device, an active setting adjustment to the scientific instrument in response to a determination that the variance of the plurality of remaining parametric state instantiations does not fall below the threshold variance value The device modifies the plurality of remaining parametric state instantiations based on the active setting adjustment, thereby resulting in a plurality of modified remaining parametric state instantiations that are used to incrementally constrain the state space via recursive Bayesian updates during subsequent calibration iterations. The computer-implemented method according to claim 11 includes this.

13. The computer-implemented method according to claim 12, wherein the device further modifies the plurality of remaining parametric state instantiations based on a passive temporal evolution associated with the scientific instrument.

14. The computer-implemented method according to claim 12, wherein the scientific instrument is a charged particle microscope.

15. The computer-implemented method according to claim 14, wherein the parametric state of the digital twin is an aberration coefficient vector of the charged particle microscope.

16. The computer-implemented method according to claim 14, wherein the iterative common observable is based on a convergent beam electron diffraction pattern of an amorphous carbon sample captured by the charged particle microscope.

17. The computer-implemented method according to claim 14, wherein the active setting adjustment is a lens setting adjustment, a deflector setting adjustment, a temperature setting adjustment, or a stage actuator adjustment of the charged particle microscope.

18. A computer program product for facilitating improved digital twin calibration for a scientific instrument, the computer program product comprising a non-transitory computer-readable memory having program instructions incorporated therein, the program instructions causing a processor to access a digital twin of a charged particle microscope, synchronize with a physical state of the charged particle microscope via execution of a set of calibration iterations that include Bayesian updates to an entirety of the parametric state based on an iterative common observable, wherein each of the calibration iterations can be presented by the charged particle microscope and simulated by the digital twin. A computer program product, executable by the processor, to predict how the charged particle microscope will respond to a proposed usage scenario by performing the digital twin after synchronization. **Claim 19** The computer program product according to claim 18, wherein the parametric state of the charged particle microscope is an aberration coefficient vector. **Claim 20** The computer program product according to claim 19, wherein the iterative common observable is based on a convergent beam electron diffraction pattern of an amorphous carbon sample.

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