Systems, apparatus, and methods for controlling physical or chemical processes.

Abstract

To provide a system, device, and method for controlling a physical or chemical process.SOLUTION: The method includes: obtaining a second posterior model representing a relationship between an input variable and an output variable of a physical process or a chemical process on the basis of a first posterior model representing a relationship between an input variable and an output variable of a process related to the physical process or the chemical process. Obtaining the second posterior model includes: obtaining each Gauss process by deriving a function from a first posterior model and forming an expected value of the Gauss process and obtaining a plurality of Gauss processes using a common covariance function; and obtaining a prior model as an average value of the plurality of Gauss processes, and obtaining the second posterior model by adjusting the prior model according to a known measuring point or obtaining the second posterior model as an average value of the plurality of adjusted Gauss processes by adjusting each Gauss process according to the known measuring point.SELECTED DRAWING: None

Description

[Technical Field]

[0001] The various embodiments generally relate to systems, apparatus, and methods for controlling physical or chemical processes. [Background technology]

[0002] In production and processing processes (e.g., drilling, milling, heat treatment), process parameters such as process temperature, process time, vacuum or gas atmosphere are adjusted to obtain desired properties such as the hardness, strength, thermal conductivity, electrical conductivity, density, microstructure, macrostructure, and chemical composition of the workpiece. These process parameters can be determined by model-based optimization methods, such as Bayesian optimization. In this process, a model relating to the production or processing process can be determined based on measurement data. However, this can require a large amount of measurement data and, consequently, significant costs (e.g., time costs and / or expenditures). Such costs can be reduced by determining a model in relation to these measurement data based on a pre-trained model representing the process related to the production or processing process (also known as transfer learning). For example, two models can represent drilling or milling in various different machines (and with equivalent process parameters). In this case, a pre-trained model can be used as the basis for the model to be trained, thus reducing the amount of measurement data required.

[0003] The publication "Google Vizier: A Service for Black-Box Optimization" by D. Golovin et al. (KDD 2017 Applied Data Science Paper, 2017) (hereinafter referred to as reference [1]) describes hierarchical transfer learning, in which a model is obtained as a Gaussian process based on a model that has already been trained as a Gaussian process, and also based on measured data.

[0004] To train a model according to Bayesian optimization, a new measurement point can be obtained in each iteration using an acquisition function. Examples of acquisition functions are described in the publication "Efficient global optimization of expensive black-box functions" by D. Jones et al. (Journal of Global Optimization, 1998) (hereinafter referred to as reference [2]) and in the publication "Gaussian process optimization in the bandit setting: No regret and experimental design" by N. Srinivas et al. (Proc. International Conference on Machine Learning (ICML), 2010) (hereinafter referred to as reference [3]). [Prior art documents] [Non-patent literature]

[0005] [Non-Patent Document 1] Publication “Google Vizier: A Service for Black-Box Optimization” by D. Golovin et al. (KDD 2017 Applied Data Science Paper, 2017) [Non-Patent Document 2] Publication: "Efficient global optimization of expensive black-box functions," by D. Jones et al. (Journal of Global Optimization, 1998) [Non-Patent Document 3] Publication “Gaussian process optimization in the bandit setting: No regret and experimental design” by N. Srinivas et al. (Proc. International Conference on Machine Learning (ICML), 2010) [Overview of the project] [Problems that the invention aims to solve]

[0006] Measurements characterizing at least one characteristic of a production or processing process, and / or at least one effect of this process on a workpiece, can vary even when process parameters are identical. Such variations can arise from the process itself, from the workpiece, or from measurement errors. Such variations and / or relatively few measurement data can cause a trained model to have high inaccuracies and / or uncertainties in areas with little or no measurement data. In various embodiments, it has been recognized that the learning cost (e.g., optimization efficiency) in transfer learning can be reduced when both the uncertainty of the already trained model and the uncertainty of the model to be trained are taken into consideration. [Means for solving the problem]

[0007] A method having the features of independent claim 1, an apparatus having the features of independent claim 5, and a system having the features of independent claim 6 enable efficient model optimization. In this case, the number of measurement data required is reduced, thereby reducing the cost of training the model (e.g., time cost and / or expenditure). Specifically, within the framework of transfer learning, only a small number of measurements are required to adapt a model already trained for a similar process to a new process. Furthermore, the consideration of uncertainty in the already trained model, as described herein, improves the accuracy of the trained model for the new process (e.g., improved accuracy of the expected value of the trained model, and improved accuracy of the considered uncertainty regarding this expected value). In various embodiments, it is possible to train the model even when only a small amount of data is available and / or when the model already trained for a similar process has high uncertainty.

[0008] A method having the features of independent claim 1 constitutes a first example. In this case, specifically, at least one (e.g., exactly one or more) hyperparameter of the first post-model cannot be optimized again.

[0009] The models described herein may be statistical models, or any kind of mathematical representation of a relationship between input and output variables of a physical or chemical process using a Gaussian process. The input and / or output variables of the physical or chemical process may be input or output variables of another system. For example, the input variables may be parameters of a simulation (e.g., of the physical or chemical process). For example, the output variables may be approximation errors. For example, the output variables may be hyperparameters and one or more loss values ​​of a machine learning-based model.

[0010] When obtaining the second posterior model, all hyperparameters of the covariance function of the first posterior model can be kept unchanged. The features described in this paragraph, combined with the first example, constitute the second example. Specifically, the second posterior model can be obtained by optimizing the hyperparameters of the second model and adjusting it to a known second measurement point, where the hyperparameters of the first posterior model can be kept unchanged. Here, specifically, it is not possible to optimize all the hyperparameters of the first posterior model again.

[0011] These two methods for obtaining the second posterior model, as in the first example, enable a reduction in computational complexity and, consequently, computational cost by defining the hyperparameters of the first posterior model (see, for example, Table 1 and its accompanying explanation).

[0012] This method further, Based on a second posterior model, this may include using an acquisition function to select a new input parameter value for at least one input variable of a physical or chemical process. This may include measuring the output value assigned to an input parameter value for at least one output variable, wherein the selected new input parameter value and the measured new output value form a new measurement point. This may include adapting a second post-hoc model using these new measurement points, where the adapted second post-hoc model represents a physical or chemical process for known and new measurement points. A second, adapted post-hoc model is used to control a physical or chemical process. The features described in this paragraph are combined with the first or second example to form a third example.

[0013] These two methods for obtaining a second posterior model, as in the first or second example, may have reduced computational complexity compared to other methods that similarly enable uncertainty transmission (see, for example, Table 1 and its accompanying description).

[0014] A third post-hoc model can represent a relationship between at least one input variable and at least one output variable of yet another process related to a physical or chemical process, where each other measurement point of other known measurement points may have an input parameter value of at least one input variable of the other process and an output value of at least one output variable of the other process that is assigned to the input parameter value. This delicious, This may include deriving the first posterior model by incorporating the third posterior model, and deriving the first posterior model by incorporating the third posterior model is The function is derived from a third posterior model, and each Gaussian process is found by forming the expectation value of the Gaussian process, and multiple other Gaussian processes are found using another common covariance function. Alternatively, one could obtain a first posterior model by estimating another pre-model as the average of several other Gaussian processes and then adjusting this pre-model to match other known measurement points, or This involves adjusting each individual Gaussian process to match several other Gaussian processes to other known measurement points, and obtaining the first posterior model as the average of the adjusted multiple other Gaussian processes. This may include the following. The features described in this paragraph can be combined with one or more of the first to third examples to form a fourth example. Selectively, the first posterior model can be obtained by other means. For example, the first posterior model can be obtained using the hierarchical Gaussian process according to reference [1], where β=1.

[0015] The second posterior model can specifically be obtained as a sequence of multiple other models (e.g., a third posterior model and the first posterior model). These two methods for obtaining the second posterior model using one or more examples from the first to third examples can significantly improve the efficiency of training a model based on multiple other models compared to other methods (see, for example, Illustration 352 in Figure 3B).

[0016] Using a second post-hoc model to control a physical or chemical process is This may include determining the input parameter values ​​of at least one input variable that are assigned to a desired output value of at least one output variable of a physical or chemical process, according to a second post-hoc model. This may include controlling a physical or chemical process according to the required input parameter values. The features described in this paragraph can be combined with one or more of the first to fourth examples to form a fifth example.

[0017] Specifically, the second posterior model can take into account the uncertainty of the first posterior model (and the third posterior model in the fourth example), which leads to an improvement in the accuracy of the second posterior model (e.g., information about expected values ​​and / or uncertainty).

[0018] The apparatus may be configured to carry out this method according to one or more of the first to fifth examples. An apparatus having the features described in this paragraph constitutes a sixth example.

[0019] The apparatus for performing (e.g., physical or chemical) processes described herein may be any kind of computer-controlled apparatus, such as robots (e.g., manufacturing robots, maintenance robots, household robots, medical robots, etc.), vehicles (e.g., autonomous vehicles), household appliances, production machinery, personal assistants, access control systems, etc. However, the apparatus for performing (e.g., physical or chemical) processes described herein may also be non-computer-controlled apparatus. For example, the apparatus may be manually controlled by a user to perform (e.g., physical or chemical) processes. Generally, the apparatus may be, for example, production equipment for manufacturing products or processing equipment for processing workpieces (e.g., drilling or milling equipment), for example, robotic equipment for performing motion, for example, equipment for designing active ingredients in pharmaceuticals, for example, equipment for designing systems for aeronautics and spaceflight, etc.

[0020] The system is An apparatus configured to perform a physical or chemical process, A control device configured to use a second post-process model obtained according to one or more of the first to fifth examples to determine the input parameter values ​​assigned to a desired output value for at least one output variable of a physical or chemical process, and to control the apparatus to execute the physical or chemical process according to the determined input parameter values, This may include the following. A system with the features described in this paragraph constitutes the seventh example.

[0021] In this system, physical or chemical processes are Processing of workpieces, Adjustment (e.g., calibration) of equipment (e.g., instruments and / or measuring instruments), Manufacturing of products, or, Robot arm movement It may be assumed that this is the case. The features described in this paragraph, when combined with the seventh example, constitute the eighth example.

[0022] A computer program may contain instructions that cause the processor to perform actions according to one or more of the first to fifth examples when executed by the processor. A computer program having the characteristics described in this paragraph constitutes the ninth example. Here, it should be understood that the processor may generate instructions for controlling a physical or chemical process (for example, instructions for controlling a device).

[0023] Computer-readable media (e.g., computer program products, non-temporary storage media, non-transient storage media, non-volatile storage media) can store instructions that cause a processor to perform actions according to one or more of the first to fifth examples when executed by a processor. Computer-readable media having the characteristics described in this paragraph constitute a tenth example.

[0024] Embodiments of the present invention are shown in the drawings and will be described in more detail below. [Brief explanation of the drawing]

[0025] [Figure 1A] This figure shows the learning of a first post-process model representing a process performed by a first apparatus according to various embodiments. [Figure 1B] This figure shows the learning of a first post-process model representing a process performed by a first apparatus according to various embodiments. [Figure 1C] This figure shows the control of the first device by a trained first post-process model according to various embodiments. [Figure 2A] This figure shows the execution of a physical or chemical process using the second apparatus according to various embodiments. [Figure 2B] This figure shows the control of a second device by a trained second post-model according to various embodiments. [Figure 2C] This figure shows the adaptation of the second post-hoc model using various embodiments. [Figure 2D] This figure shows the control of the second device by an adapted second post-model according to various embodiments. [Figure 3A] This figure shows exemplary visualizations of various models or the optimization process based on various models, according to various embodiments. [Figure 3B] This figure shows exemplary visualizations of various models or the optimization process based on various models, according to various embodiments. [Figure 4] This figure shows methods for controlling physical or chemical processes according to various embodiments. [Modes for carrying out the invention]

[0026] In one embodiment, “computer” may be understood as any kind of logic implementation entity that can be hardware, software, firmware, or a combination thereof. Thus, in one embodiment, “computer” may be a hardwired logic circuit or a programmable logic circuit, such as a programmable processor, such as a microprocessor (e.g., CISC (a processor with a large instruction stock) or RISC (a processor with a reduced instruction stock)). “Computer” may include one or more processors. “Computer” may also be software implemented or run by a processor, such as any kind of computer program, such as a computer program that uses virtual machine code, such as Java. Each implementation of each of the functions described in detail below may be understood as “computer” in agreement with optional embodiments.

[0027] Various embodiments relate to systems, apparatus, and methods for controlling physical or chemical processes. Here, the training of a model representing a physical or chemical process may be performed using transfer learning based on another already trained model representing a process related to the physical or chemical process, where both the uncertainty of the other already trained model and the uncertainty of the model to be trained are taken into consideration. Specifically, this can significantly increase training efficiency. This allows the model to be trained with a significantly smaller amount of data and / or reduces the computational cost of obtaining the model. This not only reduces the time cost and / or expenditure of training but also improves the accuracy of the trained model with respect to the physical or chemical process.

[0028] According to various embodiments, the second apparatus 208 can perform (e.g., complete) a physical or chemical process. Figure 1A shows a first system 100 comprising the first apparatus 108. The first apparatus 108 may be configured to perform another process related to a physical or chemical process.

[0029] Physical or chemical processes as used herein may be any kind of technical process, such as manufacturing processes (e.g., manufacturing of products or intermediate products), processing processes (e.g., processing of workpieces), control processes (e.g., movement of robot arms), and adjustment processes (e.g., calibration of measuring instruments). For example, it may be necessary to adjust various operating variables of a device (e.g., within a calibration range), and a physical or chemical process may be such an adjustment. For example, a physical or chemical process during heat treatment using a furnace may be the calibration of the furnace temperature and / or vacuum.

[0030] It should be understood that other processes related to physical or chemical processes may also be physical or chemical processes as described herein.

[0031] Two processes may be related in different ways. For example, they may be similar general processes, such as drilling or milling a component, performed by different machines. It should be understood that similar general processes on different machines may also yield different results. Two processes performed on the same machine may similarly be related. For example, one process may be drilling a metal component, and the other may be drilling a ceramic component. Generally, two processes may be related if their input variables overlap at least partially and their output variables overlap at least partially. Specifically, two related processes may have one or more identical input variables (e.g., process temperature, process time, and / or vacuum pressure in the case of heat treatment) and one or more identical output variables (e.g., hardness, strength, density, microstructure, macrostructure, and / or chemical composition in the case of heat treatment). Two processes may be related if their respective models are suitable for transfer learning.

[0032] The first system 100 may include a first control device 106. The first control device 106 may be configured to control the first device 108 according to each (provided) first input parameter value 102 of at least one (i.e., strictly one or more) input variables. Specifically, the first control device 106 can control the interaction between the first device 108 and its surroundings according to one (or more) first input parameter values ​​102. Since each input variable (of at least one input variable) can be provided with each first input parameter value 102, this will also be referred to below as at least one first input parameter value 102.

[0033] The term “control device” (also referred to as “control mechanism”) can be understood as any kind of logical implementation unit that can execute, for example, software, firmware, or a combination thereof stored in a storage medium, and further, may include, for example in this example, circuits and / or processors that can instruct the device to execute a process. The control device may be configured to control a system, for example, a production system, a processing system, or the operation and / or adjustment (e.g., calibration) of a robot, for example, by program code (e.g., software).

[0034] Input parameter values ​​used herein may be parameter values ​​representing input variables, such as physical or chemical variables, applied voltage, valve opening, etc. For example, input variables may be process-related properties of one or more materials, such as hardness, thermal conductivity, electrical conductivity, density, microstructure, macrostructure, chemical composition, etc.

[0035] The first apparatus 108 may be configured to perform another process related to a physical or chemical process according to at least one first input parameter value 102.

[0036] The first system 100 may include one or more first sensors 110. One or more first sensors 110 may be configured to detect the result of a process. The result of the process may be, for example, the properties of a manufactured product or a processed workpiece (e.g., hardness, strength, density, microstructure, macrostructure, chemical composition, etc.), the success or failure of a robot's skill (e.g., object picking), the resolution of an image captured by a camera, etc. The result of the process can be represented using at least one (i.e., strictly one or more) output variables. One or more first sensors 110 may be configured to detect a first output value 112 of at least one output variable. For example, each first output value 112 for each of the multiple output variables is detectable. Since each first output value 112 for each output variable (of at least one output variable) is detectable, this will also be referred to below as at least one first output value 112.

[0037] As described herein, the detection of process results using one or more sensors may be performed during the process (e.g., in-situ) and / or after the process (e.g., ex-situ). For example, this model can represent a relationship between one or more input variables and at least two output variables, where the output value of one of the at least two output variables can be detected during the process, and the output value of another of the at least two output variables can be detected after the process. As a specific example of detecting output values ​​after the process, the process may be the hardening of a workpiece in a furnace with temperature as the input variable. In this case, the output variable may be the hardness of the workpiece at room temperature after the hardening process.

[0038] The output values ​​used herein may be values ​​representing process output variables. Process output variables may be characteristics of a product, workpiece, captured image, or other deliverable. However, process output variables may also be success or failure (e.g., robot skill). Specifically, at least one first output value 112 can be obtained as a result from at least one first input parameter value 102. Output variables may include application-specific quality criteria. Output variables may be parameters related to a component, such as dimensions or layer thickness, or parameters related to a material, such as hardness, thermal conductivity, electrical conductivity, density, chemical composition, etc.

[0039] At least one first input parameter value 102 and at least one first output value 112 can form a first measurement point 130. The first control device 106 may be configured to control the first device 108 sequentially for each (e.g., mutually different) input parameter value of at least one input variable. One or more first sensors 110 can each detect at least one first output value 112. Specifically, multiple first measurement points can be determined. The determined first measurement points are known first measurement points D s(2) (that is, D s or D s2 It is also called ).

[0040] Known first measurement point D s(2) This can be expressed by equation (1).

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[0041] The first system 100 may include a storage device having at least one memory. Known first measurement point D s(2) It may be considered to be stored in memory, or can be stored in memory. Memory can be used when processing is performed by the processor.

[0042] The memory used in this embodiment may be a volatile memory, such as DRAM (Dynamic Random Access Memory), or a non-volatile memory, such as PROM (Programmable ROM), EPROM (Erasable PROM), EEPROM (Electrically Erasable PROM), or a flash memory, such as a floating-gate memory device, a charge-trap memory device, MRAM (Magnetoresistive Memory), or PCRAM (Phase-Change Memory).

[0043] In various embodiments, model training or learning is described (see, for example, algorithms 1, 2, 4, and 5). During model training or learning, a prior model (also called the model a priori) is defined. Specifically, this prior model may exist without data (e.g., without known measurement points). The model may include hyperparameters that specify the general characteristics of the distribution represented by this model. During model training or learning, the model's hyperparameters can be optimized (also called hyperparameter optimization). Hyperparameter optimization of the model can be performed based on known measurement points (e.g., measured measurement points and / or simulated measurement points). A model with optimized hyperparameters may also be called a hyperparameter optimized model. Specifically, the hyperparameters can be fitted using known measurement points. For example, if it becomes clear from known measurement points that when the input parameter values ​​are changed, the output values ​​change relatively large, the model can be fitted to increase the probability of functions that change more rapidly. During model training or learning, a posterior model (also called the a posteriori model) can be obtained by further adjusting the model (e.g., a hyperparameter-optimized model) to known measurement points. Here, the posterior distribution of random variables related to the hyperparameters can be obtained (e.g., calculated). In this case, the hyperparameters can be kept unchanged. According to various embodiments, the values ​​of the hyperparameters can be optimized based on known measurement points. According to various embodiments, at least one first model and a second model can be trained or learned in this way (see, for example, algorithms 1, 2, 4, and 5). According to various embodiments, the second model can be learned based on the first model, and the pre-optimized hyperparameters of the first model can be kept unchanged during the training or learning of the second model.

[0044] When adapting a learned or trained posterior model to new measurement points, as described above, hyperparameter optimization and adjustment can also be performed.

[0045] According to various embodiments, a known first measurement point D s(2) can be used to obtain a first posterior model 114 (also referred to as the aposteriori of the first model). The first posterior model 114 can represent the relationship between at least one input variable and at least one output variable of another process. Specifically, even when the input parameter value or output value is not part of the known first measurement point, the first posterior model 114 can be used to obtain the expected output value assigned to the input parameter value, and for the output value, the probability density of belonging to the input parameter value can be obtained. Subsequently, for example, the input value with the highest probability density can be selected. Specifically, the first posterior model 114 represents another process.

[0046] For each first measurement point, by the user respectively selecting at least one first input parameter value 102, the known first measurement point D s(2) can be measured. However, it is also possible to measure a subset of the known first measurement point D s(2) . As shown in FIG. 1B, for a subset of the known first measurement point D s(2) , a temporary first posterior model 113 can be obtained. The temporary first posterior model 113 is based on the known first measurement point D s(2)This can represent a relationship between at least one input variable and at least one output variable of another process for a subset of . According to various embodiments, the first control device 106 may be configured to determine at least one input parameter value 116 (also referred to as the new input parameter value) for a new measurement point 132 using an acquisition function (for example, according to References [2] and / or [3]). The first control device 106 can control the first device 108 according to the determined at least one input parameter value 116, and one or more first sensors 110 can detect the output value 118 to which the new measurement point 132 belongs. For example, in this way, a known first measurement point D s(2) One or more measurement points can be determined. In this case, in order to determine the first post-model 114, a temporary adaptation of the first post-model 113 can be performed based on the newly determined measurement points. Thus, the first post-model 114 can be determined from all known first measurement points D of another process. s(2) This allows us to represent the relationship between at least one input variable and at least one output variable.

[0047] However, the known first measurement point D s(2)This can also be determined using simulation. In this case, system 100 may include a computer. In the first example, the simulation may include determining input parameter values ​​116 for a new measurement point 132, or simulating a physical or chemical process. In this case of the first example, the first control device 106, the first device 108, and one or more first sensors 110 are not required. In the second example, the simulation may include only the simulation of a physical or chemical process. In this case of the second example, for example, the first control device 106 can further determine input parameter values ​​116 for a new measurement point 132, and the first device 108 and one or more first sensors 110 are not required. The computer can use memory during processing. The computer may be any kind of circuit, as described above, that is, any kind of logic implementation entity. The computer may be configured to simulate another process and thus determine multiple times an output value 112 to which at least one input parameter value 102 belongs. Specifically, a known first measurement point D s(2) The output value may be considered simulated rather than measured.

[0048] Figure 1C shows the control of the first device 108 by a learned first post-model 114 in various embodiments. For example, the first post-model 114 can be used to determine an input parameter value 126 to which at least one input variable belongs, based on a desired output value 122 of at least one output variable of another process. The first control device 106 may be configured to control the first device 108 according to the determined input parameter value 126. Optionally, one or more first sensors 110 may detect an output value that substantially corresponds to the desired output value 122.

[0049] Figure 2A shows a second system 200, which includes a second apparatus 208 capable of carrying out a physical or chemical process.

[0050] The second system 200 may be similar to the first system 100. Thus, the second system 200 may include a second control device 206 and one or more second sensors 210. The second control device 206 may be configured to control the second device 208 according to each (provided) second input parameter value 202 of at least one (i.e., strictly one or more) input variable. Specifically, the second control device 206 can control the interaction between the second device 208 and its surroundings according to one (or more) second input parameter values ​​202. Since each input variable (of at least one input variable) can have its own second input parameter value 202, this is also referred to below as at least one second input parameter value 202. The second device 208 may be configured to perform a physical or chemical process according to at least one second input parameter value 202.

[0051] One or more second sensors 210 may be configured to detect the results of a physical or chemical process. The results of a physical or chemical process may be, for example, the properties of a manufactured product or a processed workpiece (e.g., hardness, strength, density, microstructure, macrostructure, chemical composition, etc.), the success or failure of a robot's skill (e.g., object picking), or the resolution of an image captured by a camera, as described with respect to Figure 1A, for example. The results of a process can be represented using at least one (i.e., strictly one or more) output variables. For example, the results of another process can be represented using a plurality of first output variables, and the results of a physical or chemical process can be represented using a plurality of second output variables. In this case, the plurality of first output variables may have one or more (e.g., all) output variables of the second output variables, or vice versa. For example, one or more output variables of the plurality of first output variables may coincide with one or more output variables of the plurality of second output variables. These results can be obtained during or following a physical or chemical process, as described in relation to one or more sensors 110.

[0052] One or more second sensors 210 may be configured to detect a second output value 212 of at least one output variable. For example, it is possible to detect each second output value 212 for each of the multiple output variables. At least one second input parameter value 202 and at least one second output value 212 can form a second measurement point 230. According to various embodiments, multiple second measurement points may be known as second measurement points D t It can be calculated as follows.

[0053] Known second measurement point D t This can be expressed by equation (2).

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[0054] Similar to the first system 100, the second system 200 has a known second measurement point D t It may include a storage device having at least one memory for storing the following.

[0055] Both the first posterior model 114 and the second posterior model 214 may have uncertainty regarding the precision of at least one output variable, and consequently the precision of each model, for at least one specific input variable. These uncertainties relate to known measurement points. The predictions of each model may include both an expected value and a measure of uncertainty regarding this expected value. That is, the predictions of each model may include a distribution of values ​​(e.g., a normal distribution) for each output value. Specifically, the posterior models can represent the relationship between the input and output variables with respect to known measurement points, where the regions between known measurement points are also predicted. It should be understood that these predicted regions h have some degree of uncertainty, and that this uncertainty can decrease as the number of measurement points increases. Such uncertainty can be extremely important, for example, when there are only a few measurement points. It should also be understood that each measurement point may have uncertainty due to noise and / or interference.

[0056] According to various embodiments, a first post-model 114 and a known second measurement point D t By incorporating this, a second post-model 214 can be obtained. According to various embodiments, when obtaining the second post-model 214, a known first measurement point D s(2) The uncertainty of the first posterior model 114 regarding the known second measurement point D is also tThe uncertainty of the second post-post model 214 is also considered. Here, the uncertainty of the first post-post model at measurement points where no measured first output value exists (i.e., the input parameter values ​​of one or more input variables) can be extremely important. Below, two concepts (also called approaches) that can take into account the uncertainty of the two post-post models 114, 214 are described. According to various embodiments, the system 200 may include a computer configured to determine the second post-post model 214.

[0057] I) The first concept for obtaining the second posterior model 214 (also known as a sequential hierarchical Gaussian process): The first posterior model 114 is the first posterior probability distribution p(f s(2) |D s(2) It may be considered to include ).

[0058] The computer uses the first posterior probability distribution p(f s(2) |D s(2) )(For example, p(f s |D s It is often configured to find a Gaussian process based on the first posterior probability distribution p(f s |D s ) (and consequently the first posterior model 114) from the function

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[0059] The computer calculates the average of multiple Gaussian processes (for example, using Bayesian Model Averaging).

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[0060] The computer uses a known second measurement point D t In conjunction with this, the second pre-model f t The second posterior model 214 (also called the a posteriori of the second model) may be constructed to be obtained by adjusting the second posterior probability distribution p(f t |D t It may be considered to include ).

[0061] Generally, a prior model can be considered a prior belief before the model is adjusted to known measurement points. The prior belief of a prior model can be expressed as a Gaussian process gp(m,k) with an expectation function m(·) and a covariance function (also called a kernel function) k(·,·). The posterior model can be obtained by adjusting the prior model to known measurement points. The posterior model is determined by one evaluation point X of the posterior model. * The Gaussian process having a posterior expectation function and a posterior covariance function may include a posterior probability distribution. Generally, the covariance between two points may be defined. In particular, these two points may be considered to be the same point. Evaluation point X* The posterior expectation function of the Gaussian process at a known second measurement point D is, exemplarily, t A second pre-model f tailored to the new model t The adjustment for this is shown in equation (3), and the posterior covariance function to which it belongs is shown in equation (4).

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[0062] The covariance function of the second posterior model 214 is given by the covariance function k of the first posterior model. s (Also called the first kernel function) and the common covariance function k t It can be expressed based on the second kernel function of multiple Gaussian processes, also known as the common covariance function. The common covariance function of the first and second models can be expressed according to equation (5).

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[0063] During Bayesian optimization, the hyperparameters of the kernel function (e.g., the first kernel function and / or the second kernel function) can be adapted (also called hyperparameter optimization). For example, the hyperparameter adaptation (e.g., optimization) of the first prior model can be performed at a known first measurement point D s The probability that this is represented by the first prior model can be increased (e.g., maximized). For example, the hyperparameters of the second prior model can be adapted (e.g., optimized) to a known second measurement point D. t The probability that k is represented by this second prior model can be increased (e.g., maximized). In this case, the hyperparameters of the first prior model can be kept constant. s By fixing the hyperparameters, the uncertainty of the first post-model 114 can be maintained when the second pre-model is adjusted to a known second measurement point.

[0064] According to various embodiments, the known first measurement point D s, the known second measurement point D t , the first kernel function k s and the second kernel function k t , based on the first posterior model 114 can be incorporated to obtain the second posterior model 214 according to Algorithm 1.

[0065] Algorithm 1: Learning of the second posterior model 214 according to the first concept Input: D s , D t , k s , k t Output: p(f t |D t ) 1. (If the known first measurement point is pre-normalized, for example,

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[0066] Here, as described above, the second prior model f t is defined as the average value of multiple Gaussian processes

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[0067] As described above, the hyperparameters of the first kernel function k s can be kept invariant. Specifically, for new measurement points, the second posterior model 214 can be learned by Bayesian optimization by only executing step 4 of Algorithm 1.

[0068] By transmitting the uncertainty of the first posterior model 114 to the second prior model and the second posterior model (also referred to as uncertainty propagation), both the data efficiency and the optimization efficiency are improved. This is because the number of required measurement data is reduced, thereby reducing the cost (e.g., time cost and / or cost expenditure) associated with model learning.

[0069] II) Second concept for obtaining the second posterior model 214 (also referred to as enhanced hierarchical Gaussian process): Similar to the first concept, in the second concept, multiple Gaussian processes are obtained according to a common covariance function k t by

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[0070] The common kernel function of the two models is the first kernel function k of the first posterior model. s and the second kernel function k t Based on this, it can be expressed according to equation (6).

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[0071] The second posterior model 214 can be trained according to algorithm 2.

[0072] Algorithm 2: Training the second posterior model according to the second concept Input: D s , D t , k s , k t Output: p(f t |D t ) 1. (If the known first measurement point has been normalized in advance, for example,

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[0073] Figure 2B shows the control of the second apparatus 208 by a learned second post-model 214 according to various embodiments. The second control device 206 may be supplied with a desired output value 222 for at least one output variable. Selectively, the control device 206 can determine the desired output value based on other parameter values ​​and / or adjustments. The control device 206 may be configured to determine an input parameter value 226 for at least one input variable, which is assigned to the desired output value 222 according to the second post-model 214. The control device 206 can control the second apparatus 208 according to the determined input parameter value of at least one input variable in order to perform a physical or chemical process. Optionally, one or more second sensors 210 can detect an output value that substantially corresponds to the desired output value 222.

[0074] Figure 2C shows the adaptation of the second post-hoc model 214 according to various embodiments. According to various embodiments, the adaptation of the second post-hoc model 214 can be performed using Bayesian optimization. Here, additional second measurement points can be obtained using Bayesian optimization, and additionally, the second post-hoc model 214 can be adjusted to match the additional second measurement points. The new second measurement points are obtained using the acquisition function α(f) based on the second post-hoc model 214. t |x,D t Using (for example, the acquisition function according to references [2] and / or [3]), selection can be made, for example, according to equation (8).

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[0075] For example, the control device 206 can use an acquisition function to select an input parameter value 216 for a new second measurement point 232. The control device 206 can control the second device 208 according to the obtained input parameter value 216, and one or more second sensors 210 can detect the output value 218 to which the new second measurement point 232 belongs. According to various embodiments, the second post-model 214 can be additionally adjusted to match the new second measurement point 232. This adapted second post-model 234 defines the relationship between at least one input variable and at least one output variable as a previously known second measurement point D t And it can be expressed with respect to a new second measurement point 232. Specifically, the known second measurement point D t Similarly, this may include a new second measurement point 232. In this way, a new second measurement point can be obtained at any frequency, and in each iteration, each second posterior model can be adjusted to match the newly known second measurement point. Here again, in the first and second concepts, the first kernel function k sThe hyperparameters can be kept constant. This increases the efficiency of Bayesian optimization. It is not necessary to explicitly determine multiple Gaussian processes; it is important to understand that effective formulas representing the limits of an infinite number of such Gaussian processes can be evaluated. These effective formulas can be evaluated, for example, when the hyperparameters of a second posterior model are optimized again based on new measurement points.

[0076] The process of determining a new second measurement point and adapting the second post-hoc model can be explained according to algorithm 3.

[0077] Algorithm 3: Bayesian optimization of the second posterior model 214 for i←1,2,…do: 1. Optimization of the acquisition function x via a second posterior model i =argmax x α(f t |x,D t ) using the input parameter value x i To find. 2. Input parameter value x i Output value y belonging to i =y i (x i ) 3. Known second measurement point D t A new measurement point (x i ,y i Add ).

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[0078] Figure 2D shows the control of the second apparatus 208 by an adapted second post-model 234 according to various embodiments. This can be done similarly to the control of the second apparatus 208 described in relation to Figure 2B. The second control device 206 may be supplied with a desired output value 222 of at least one output variable, and the control device 206 can determine an input parameter value 246 of at least one input variable, which is assigned according to the adapted second post-model 234. The control device 206 can control the second apparatus 208 according to the determined input parameter value 246 of at least one input variable in order to perform a physical or chemical process.

[0079] According to various embodiments, the training of the second post-hoc model can be performed sequentially based on multiple other models. Specifically, the first post-hoc model can be trained based on yet another post-hoc model (hereinafter referred to as the third post-hoc model) before using the first post-hoc model to train the second post-hoc model. This yet another post-hoc model may similarly be trained based on yet another post-hoc model.

[0080] For example, the third post-post model can represent the relationship between at least one input variable and at least one output variable of yet another process related to a physical or chemical process. The first post-post model can be obtained by incorporating the third post-post model, as described above, by incorporating the first post-post model according to algorithm 1 or algorithm 2 to obtain the second post-post model. The third post-post model is obtained at a known third measurement point D s(1) It can be determined based on, or the third post-model is a known third measurement point D s(1) It may be assumed that these are determined based on the above. As described herein, known measurement points, such as a known third measurement point, can also be determined using simulation.

[0081] As concrete examples of such transfer learning, a known third measurement point can be obtained from simulation, and the third posterior model can represent this relationship; a known first measurement point can be measured in the laboratory using an experimental apparatus similar to the production system, and the first posterior model can represent this relationship; a known second measurement point can be measured in the production system, and the second posterior model can represent the relationship between the input and output variables of the production system.

[0082] According to various embodiments, multiple other n s For each model, the training of the second posterior model 214 may be performed sequentially. Here, each other model can be obtained by incorporating each preceding model, as described in this specification for the training of the second posterior model incorporating the first posterior model. Specifically, the second posterior model 214 is obtained by n s It can be considered as a stack of interconnected Gaussian processes.

[0083] Regarding the first concept, a common kernel function for all models can be expressed according to equation (9).

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[0084] A second posterior model 214 can be obtained using algorithm 4 according to the first concept (for example, it can be trained).

[0085] Algorithm 4: Training the second posterior model 214 according to the first concept. Input: Each known measurement point (D s1 ,D s2 ,…,D t ) and each kernel function (k s1 ,k s2 ,…,k t ) Output: p(f t |D t ) 1. (Known measurement point D to which it belongs) s1 If it has been normalized beforehand, for example,

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[0086] Regarding the second concept, all other n s To have the covariance of the n models, the covariance function of the second posterior model 214 can be extended. In this case, the common kernel function of all models can be expressed according to equation (10).

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[0087] Specifically, the extended covariance function is calculated for all other n in the block diagonal. s It may include the covariances of the individual models. An additional covariance term may be added selectively to predict each other model except for the first model. This results in a size (2n s -1)*(2n s -1) The kernel function matrix is ​​obtained. In this case, the expression in equation (6)

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[0088] A second posterior model 214 can be obtained using algorithm 5 according to the second concept (for example, it can be trained).

[0089] Algorithm 5: Training the second posterior model according to the second concept Input: Each known measurement point (D s1 ,D s2,…,D t ) and each kernel function (k s1 ,k s2 ,…,k t ) Output: p(f t |D t ) 1. (Known measurement point D to which it belongs) s1 If it has been normalized beforehand, for example,

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[0090] Other n s The training of a second posterior model 214 based on individual models (e.g., by Algorithm 1, Algorithm 2, Algorithm 3, or Algorithm 4), as described herein, reduces the overall computational complexity for obtaining the second posterior model 214 compared to conventional Bayesian kernel methods that consider model uncertainty. The overall computational complexity can be divided into (i) the computational complexity for training another model, (ii) the computational complexity for training the posterior model (e.g., the second posterior model 214) assuming all other models are trained, and (iii) the computational complexity for predictions by the trained models. Table 1 shows a comparison of the computational complexes (i), (ii), and (iii) of conventional Bayesian kernel methods, hierarchical Gaussian processes according to reference [1], sequential hierarchical Gaussian processes according to the first concept, and enhanced hierarchical Gaussian processes according to the second concept. In Table 1, N s v = 1, 2, ..., n s Assuming that is the case,

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[0091] [Table 1]

[0092] Other models can be trained at the start of Bayesian optimization and do not require further training during Bayesian optimization. Therefore, the computational complexity (i) of training other models has a relatively small impact on the overall computational complexity. Post-hoc model training may be performed once at each iteration of Bayesian optimization, thereby adapting the post-hoc model to the newly detected measurement points at each iteration (see, for example, 4. in Algorithm 3). As shown in Table 1, post-hoc model training using conventional Bayesian kernel methods is performed for a total of N known measurement points. t +N s It is scaled by the cube (i.e., by powers of 3), and therefore this can be a restrictive factor in Bayesian optimization. Typically, N is the number of known measurement points of the target model to be learned. t is, all others are n s Number of known measurement points for each model: N s It can be considered to be significantly smaller than (i.e., N t < <N s In such general cases, the learning of the posterior model by the first concept and the learning of the posterior model by the second concept scale computationally from N by a cube. sThis can be reduced to a squared relationship. Furthermore, during the training of the posterior model using the first concept and the posterior model using the second concept, only the optimization of the hyperparameters of the model to be trained is required, so fewer hyperparameters are optimized compared to the conventional Bayesian kernel method where all models are optimized together, thereby further reducing computational complexity. The prediction of the trained model may be performed multiple times in each iteration of the Bayesian optimization during the optimization of the acquisition function (see, for example, 1 in Algorithm 3). Thus, the computational complexity (iii) for the prediction of the trained model is also relevant to the overall computational complexity. As shown in Table 1, the computational complexity (iii) of the first and second concepts corresponds to the computational complexity (iii) of the conventional Bayesian kernel method. Reference [1] reduces such computational complexity (iii), but reference [1] is different from other n s It does not present a well-founded method for considering the uncertainty of individual models. Essentially, it is not possible to map the covariances between individual measurements of other models. Within the framework of statistical models, other n s By correctly considering the uncertainty of each model, the efficiency of Bayesian optimization can be improved.

[0093] For illustrative purposes, Figure 3A illustrates the hierarchical Gaussian process 316 from reference [1], a sequential hierarchical Gaussian process 320 from the first concept, and an enhanced hierarchical Gaussian process 318 from the second concept, with β=1. Figure 3A shows the source function 308 modeled by the exemplary first post-post model and the objective function 314 modeled by the exemplary second post-post model, which represent the relationship between the input parameter value 302 and the output value 304, respectively. The first post-post model representing the source function 308 is based on a known first measurement point D s It may be determined based on 306, or the first post-model representing the source function 308 is a known first measurement point D sBased on 306, it can be determined. For the objective function 314 represented by the second posterior model, the known second measurement point D t , 312 may exist. Illustration a) shows the known first measurement point D s , in the right-hand region where 306 is absent, the first posterior model has a relatively high uncertainty of 310. Illustration (b) shows that the posterior model trained using the hierarchical Gaussian process 316 according to reference [1], with β=1, underestimates the uncertainty in this right-hand region. In contrast, illustrations (b) and (c) show that both the posterior model trained using the sequential hierarchical Gaussian process 320 according to the first concept and the posterior model trained using the enhanced hierarchical Gaussian process 318 according to the second concept take into account the uncertainty in this right-hand region.

[0094] Figure 3B shows a comparison between the conventional Bayesian kernel method 360 (without transfer learning), the conventional Gaussian process 316 from reference [1] with β=1, the sequential hierarchical Gaussian process 320 based on the first concept, and the enhanced hierarchical Gaussian process 318 based on the second concept. Illustration 332 shows another model (n s This shows Bayesian optimization for (=1), which is illustrated with a simple regret 334 as a function of optimization iterations 336 for the 1D Forrester function 338, the 2D Brain function 340, the 3D Hartmann 3 function 342, and the 6D Hartmann 6 function 344. Illustration 352 shows Bayesian optimization for several other models, which is illustrated with three other models (n s Hartmann 6 function 354 including =3, 5 other models (n sFor the Alpine function 356, which includes (=5), a simple regret 334 is used as a function of the optimization iterations 336. The smaller the simple regret value, the better the optimization found, and the fewer the optimization iterations 336 for which a small simple regret value is found, the more efficient the Bayesian optimization becomes. Specifically, Figure 3B shows that the improvement in the efficiency of Bayesian optimization by the first and second concepts improves as the number of dimensions increases compared to other methods (see Illustration 332, e.g., the 6-dimensional Hartmann 6 function 344). Multiple other models (n s >1) Significant improvements in efficiency have also been shown in this case (Illustration 352, for example, n s (See Alpine function 356, where = 5)

[0095] Specifically, Bayesian optimization is facilitated by the transfer learning concept described herein, in which all uncertainties of the aforementioned models are transmitted (i.e., uncertainty propagation). Transfer learning described herein can significantly increase learning efficiency based on uncertainty transmission, for example, when only a few measurement points exist or can be detected to obtain a model (for example, due to relatively high costs (e.g., time costs, energy consumption, expenses, etc.)). Conventional Bayesian optimization methods increase computational costs by fully considering uncertainty, or introduce defects in the trained model by not considering uncertainty at all, and can introduce significant inaccuracies in the model when only a few measurement points exist. The concept described herein can achieve both uncertainty consideration and relatively high learning efficiency. Transfer learning described herein provides relatively high data efficiency and optimization efficiency by transmitting uncertainty.

[0096] Figure 4 shows flowcharts of Method 400 for controlling a physical or chemical process according to various embodiments.

[0097] Method 400 may include taking a first posterior model to obtain a second posterior model (in 402). The second posterior model may represent a relationship between at least one input variable and at least one output variable of a physical or chemical process. The first posterior model may represent a relationship between at least one input variable and at least one output variable of a process related to a physical or chemical process.

[0098] (In 402) Obtaining a second posterior model by incorporating the first posterior model may involve obtaining multiple Gaussian processes using a common covariance function (in 402A). Each of the multiple Gaussian processes can be obtained by deriving the function from the first posterior model and forming the expectation value of each Gaussian process.

[0099] According to various embodiments, a second posterior model can be obtained using at least one of two concepts (also called an approach). According to the first concept, multiple Gaussian processes can be first averaged using a common covariance function, and then the averaged Gaussian processes can be adjusted to known measurement points. According to the second concept, multiple Gaussian processes can be individually adjusted to known measurement points, and then the adjusted multiple Gaussian processes can be averaged.

[0100] According to the first concept, (in 402) obtaining a second post-post model by incorporating the first post-post model may further include obtaining a second pre-post model as the average of multiple Gaussian processes, and then obtaining the second post-post model using adjustments to the pre-post model to match known measurement points (in 402B). For example, (in 402) obtaining a second post-post model by incorporating the first post-post model may involve a known second measurement point D tThe hyperparameters of the second posterior model are optimized so that the probability of being represented by the second prior model is increased (e.g., maximized), and the optimized hyperparameters are used to determine the known second measurement point D t In conjunction with this, the second pre-model f t This may include adjusting the following:

[0101] According to various embodiments, the hyperparameters of the covariance function of the first model can remain unchanged during the training or learning (e.g., hyperparameter optimization) of the second model.

[0102] According to the second concept, (in 402) obtaining the second posterior model by incorporating the first posterior model may further include adjusting each of the multiple Gaussian processes to match known measurement points and obtaining the second posterior model as the average of the adjusted multiple Gaussian processes (in 402B). The second concept also has the advantage that the hyperparameters of the first model do not need to be newly optimized during the training of the second model.

[0103] Method 400 may further include controlling a physical or chemical process using a second post-hoc model (in 404).

Claims

1. A method (400) for controlling a physical or chemical process, Each known measurement point has an input parameter value of at least one input variable of the physical or chemical process, and an output value of at least one output variable of the physical or chemical process that is assigned to the input parameter value. The first post-process model represents the relationship between at least one input variable and at least one output variable of another process related to the physical or chemical process, The aforementioned method, - This includes obtaining a second post-post model by incorporating the first post-post model (402), wherein the second post-post model represents the relationship between the at least one input variable and the at least one output variable of the physical or chemical process, and obtaining the second post-post model by incorporating the first post-post model (402) is, - The function is derived from the first posterior model, and each Gaussian process is found by forming the expectation value of the Gaussian process, and multiple Gaussian processes are found using a common covariance function (402A), - Obtain a pre-model as the average of the multiple Gaussian processes, and using the known measurement points, obtain a second post-model by optimizing the hyperparameters of the model such that at least one hyperparameter of the covariance function of the first post-model remains unchanged, and then adjust the model to match the known measurement points (402B), or - Adjusting each of the multiple Gaussian processes to match the known measurement points, and obtaining the second post-hoc model as the average value of the adjusted multiple Gaussian processes (402B), Includes, The above method further, - Controlling the physical or chemical process using the second post-process model (404), Method (400).

2. The above method further, - Based on the second post-hoc model, the process includes selecting a new input parameter value for at least one input variable of the physical or chemical process using an acquisition function. - Includes measuring the output value of the at least one output variable that is assigned to the new input parameter value, wherein the selected new input parameter value and the measured new output value form a new measurement point. - This includes adapting the second post-process model using the new measurement points, wherein the adapted second post-process model represents the physical or chemical process for the known measurement points and the new measurement points. - Using the second post-process model that has been adapted, control the physical or chemical process. The method according to claim 1 (400).

3. A third post-hoc model represents a relationship between at least one input variable and at least one output variable of yet another process related to the physical or chemical process, where each other measurement point of the other known measurement points includes the input parameter value of at least one input variable of the other process and the output value of at least one output variable of the other process that is assigned to the input parameter value. The aforementioned method, - This includes obtaining the first post-event model by incorporating the third post-event model, and obtaining the first post-event model by incorporating the third post-event model is - The function is derived from the third posterior model to form the expectation value of the Gaussian process, thereby finding each individual Gaussian process, and multiple other Gaussian processes are found using another common covariance function. - Obtaining another pre-model as the average value of the multiple other Gaussian processes, and then obtaining the first post-model by adjusting the other pre-model to match the other known measurement points, or - Adjusting each of the multiple other Gaussian processes to match the other known measurement points, and obtaining the first post-hoc model as the average value of the adjusted multiple other Gaussian processes, including, The method according to claim 1 (400).

4. Controlling the physical or chemical process using the second post-process model (404) - To determine the input parameter value of the at least one input variable that is assigned to a desired output value of the at least one output variable of the physical or chemical process, according to the second post-process model described above. - To control the physical or chemical process according to the obtained input parameter values, including, The method according to claim 1 (400).

5. An apparatus (208) configured to carry out the method (400) according to any one of claims 1 to 4.

6. - Apparatus (208) configured to perform a physical or chemical process, A control device (206) configured to use a second post-model (214, 234) obtained according to the method (400) of any one of claims 1 to 4 to determine input parameter values ​​(226, 246) assigned to a desired output value (222) of at least one output variable of the physical process or the chemical process, and to control the apparatus (208) to execute the physical process or the chemical process according to the determined input parameter values ​​(226, 246), A system including (200).

7. The aforementioned physical process or chemical process is - Processing of workpieces, - Adjustment of the device, - Manufacturing of products, or - Movement of the robot arm That is, The system (200) according to claim 6.

8. A computer program that includes instructions for causing a processor to perform the method (400) according to any one of claims 1 to 4 when executed by the processor.

9. A computer-readable medium storing instructions for causing the processor to perform the method (400) according to any one of claims 1 to 4 when the processor is running.

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