Learning system, learning method, inference system, inference method, and program

Abstract

A learning system (7) comprises an arithmetic circuit (71) capable of accessing a storage device (6) in which is saved a training data set (D1) including a plurality of data sets each constituted by a control parameter (P1) of a physical system that generates a physical phenomenon, and a measurement value (P2) of the physical phenomenon generated by the physical system. The arithmetic circuit (71) generates a plurality of trained additional parameters (unobserved prior information parameters P3) by adjusting a parameter of the machine learning model and adjusting an additional parameter for each among the plurality of data sets such that the output value of the machine learning model into which the control parameter (P1) and an additional parameter different from the control parameter (P1) have been input approaches the measurement value (P2) of the physical phenomenon.

Description

Learning system, learning method, inference system, inference method, program

[0001] The present disclosure relates to a learning system, a learning method, an inference system, an inference method, and a program.

[0002] Instead of obtaining numerical values ​​for the relationships between multiple physical quantities due to physical phenomena through actual measurements or solving governing equations through numerical calculations, a known method is to use machine learning to inductively build a model from existing data and use it as a surrogate model.

[0003] The inputs of a surrogate model are measurable information before the target physical phenomenon occurs and controllable information about the target physical phenomenon, while the output of a surrogate model is information about the target physical phenomenon during, after, or both.

[0004] Patent Document 1 focuses on the fact that the output is expressed as a distribution with probabilistic variations due to unobserved information even for a constant input, and models the standard deviation of the output distribution as an error model.

[0005] Furthermore, Non-Patent Documents 1 and 2 take advantage of the fact that there is a sufficiently large amount of data for learning, and train a model that reproduces sampling from the output distribution, rather than a representative value of the output distribution such as the standard deviation.

[0006] International Publication No. 2024 / 043337

[0007] "Learning Likelihoods with Conditional Normalizing Flows", Winkler et al., 2019"High-Resolution Image Synthesis with Latent Diffusion Models", Rombach et al., 2021

[0008] In general, the distribution of a physical quantity that can be the output of a physical phenomenon has a high degree of freedom and is not necessarily a normal distribution, for example. Therefore, a model that outputs only one representative value of the distribution, as in Patent Document 1, is limited in the physical phenomena and physical quantities that can be applied.

[0009] On the other hand, in Non-Patent Document 1 and Non-Patent Document 2, learning is performed by calculating values ​​sampled from the output distribution using a non-linear transformation conditioned by the input, using vectors sampled from a multidimensional normal distribution, so learning can be done without any restrictions on the distribution.

[0010] However, in Non-Patent Document 1, possible non-linear transformations must be learned under the strong constraint that they must be invertible. Also, in Non-Patent Document 2, when the number of training data is small, the model output is optimized with an excessively large number of variations, resulting in a phenomenon known as overconfidence, in which the probability of the trained data points is inferred to be excessively high.

[0011] The present disclosure provides a learning system, a learning method, an inference system, an inference method, and a program that enable an improvement in the degree of freedom in the distribution of predicted values ​​of measurement results of physical phenomena, while reducing the amount of data required for learning and the occurrence of overconfidence.

[0012] A learning system according to one aspect of the present disclosure includes an arithmetic circuit that can access a storage device that stores a machine learning model and a learning dataset, wherein the learning dataset includes a plurality of datasets, each of which includes control parameters of a physical system that generates a physical phenomenon and a measurement value of the measurement result of the physical phenomenon generated by the physical system to which the control parameters are applied, and the arithmetic circuit adjusts the parameters of the machine learning model for the plurality of datasets to generate learned parameters, and adjusts the additional parameters for each of the plurality of datasets to generate a plurality of learned additional parameters, so that the output value of the machine learning model when the control parameters and an additional parameter other than the control parameters are input approaches the measurement value.

[0013] A learning method according to one aspect of the present disclosure is executed by a computing circuit that can access a storage device that stores a machine learning model and a training dataset. The training dataset includes multiple datasets, each of which includes control parameters of a physical system that generates a physical phenomenon and measured values ​​of measurement results of the physical phenomenon generated by the physical system to which the control parameters are applied. The learning method generates trained parameters by adjusting the parameters of the machine learning model for the multiple datasets, and generates multiple trained additional parameters by adjusting the additional parameters for each of the multiple datasets, so that the output of the machine learning model when the control parameters and an additional parameter other than the control parameters are input approaches the measured values.

[0014] A program according to one aspect of the present disclosure is a program for causing an arithmetic circuit to execute the above learning method.

[0015] An inference system according to one aspect of the present disclosure includes an arithmetic circuit that can access a storage device that stores a learned model and a plurality of learned additional parameters, and when the learned model is executed by the arithmetic circuit, the arithmetic circuit operates to output a predicted value of the measurement result of a physical phenomenon generated by the physical system to which the control parameters have been applied in response to input of a control parameter of a physical system that generates a physical phenomenon and a learned additional parameter selected from the plurality of learned additional parameters, and when a target control parameter is input, the arithmetic circuit executes the learned model to obtain predicted values ​​corresponding to two or more of the plurality of learned additional parameters for the target control parameter.

[0016] An inference method according to one aspect of the present disclosure is executed by an arithmetic circuit that can access a storage device that stores a trained model and multiple trained additional parameters. When executed by the arithmetic circuit, the trained model causes the arithmetic circuit to operate in response to input of a control parameter of a physical system that generates a physical phenomenon and a trained additional parameter selected from the multiple trained additional parameters, such that the arithmetic circuit outputs a predicted value of a measurement result of a physical phenomenon generated by the physical system to which the control parameter is applied. When a target control parameter is input, the inference method executes the trained model to obtain predicted values ​​for the target control parameter that each correspond to two or more of the multiple trained additional parameters.

[0017] A program according to one aspect of the present disclosure is a program for causing an arithmetic circuit to execute the above-described inference method.

[0018] When executed by an arithmetic circuit, a trained model according to one aspect of the present disclosure operates the arithmetic circuit so that, in response to input of control parameters of a physical system that generates a physical phenomenon and trained additional parameters, the arithmetic circuit outputs a predicted value of the measurement result of the physical phenomenon generated by the physical system to which the control parameters are applied.

[0019] Aspects of the present disclosure enable an improvement in the degree of freedom of the distribution of predicted values ​​of measurement results of physical phenomena, while reducing the amount of data required for learning and the occurrence of overconfidence.

[0020] FIG. 1 is a diagram showing an example of the configuration of a processing system according to an embodiment; FIG. 2 is a schematic diagram of a measurement waveform in the processing system according to an embodiment; FIG. 3 is a diagram showing an example of input / output of a core model in the processing system according to an embodiment; FIG. 4 is a schematic diagram of an example of the configuration of a core model in the processing system according to an embodiment; FIG. 5 is a diagram showing an example of input / output of a sub-model in the processing system according to an embodiment;

[0021] [1. Embodiments] Hereinafter, embodiments of the present disclosure will be described, with reference to the drawings where appropriate. However, the following embodiments are merely examples for explaining the present disclosure, and are not intended to limit the present disclosure to the following content (e.g., the shape, dimensions, and arrangement of each component). Positional relationships, such as up, down, left, and right, are based on the positional relationships shown in the drawings unless otherwise specified. Each figure described in the following embodiments is a schematic diagram, and the ratios of the size and thickness of each component in each figure do not necessarily reflect the actual dimensional ratios. Furthermore, the dimensional ratios of each element are not limited to the ratios shown in the drawings.

[0022] In the following description, when it is necessary to distinguish between multiple components, prefixes such as "first" and "second" are added to the names of the components. However, when the components can be distinguished from each other by the symbols attached to them, the prefixes such as "first" and "second" may be omitted in consideration of readability of the text.

[0023] [1.1 Configuration] This embodiment relates to a surrogate model (a surrogate model for simulating a physical phenomenon) using machine learning for a physical phenomenon, and a learning method (machine learning method) and inference method thereof. In this embodiment, laser processing (laser welding) is exemplified as a physical phenomenon, but the physical phenomenon is not limited to laser processing.

[0024] FIG. 1 is a diagram illustrating an example configuration of a processing system 1 according to one embodiment. The processing system 1 is used for performing laser processing. In this embodiment, the processing system 1 irradiates workpieces placed on a processing stage 10 with laser light to perform welding (laser welding) of the workpieces 11 and 12. For example, the workpieces 11 and 12 may be made of iron, have a thickness of 0.3 mm, and have a laser light absorption rate of 40% when the laser light has a wavelength of 1070 nm and a melting point of 1700 K, or may be made of copper, have a thickness of 0.3 mm, and have a laser light absorption rate of 20% when the laser light has a wavelength of 1070 nm and a melting point of 1358 K.

[0025] The welding process may be lap welding in which a plurality of workpieces, for example, two workpieces 11 and 12, are overlapped. Note that the two workpieces 11 and 12 are welded together by laser processing with their ends offset so that they do not overlap, so that the two workpieces 11 and 12 can be individually gripped in a strength test, such as a tensile test, which will be described later.

[0026] The processing stage 10 may be movable in each of three mutually perpendicular axes (x, y, z). For example, the processing stage 10 may be an XYZ stage with strokes of 200 mm, 200 mm, and 50 mm in each direction. For example, the workpieces 11 and 12 and the processing stage 10 may be fixed in a superimposed state by a fixing member. This allows the laser light to be scanned relatively over the workpieces 11 and 12 by moving the processing stage 10.

[0027] As shown in FIG. 1, the processing system 1 includes a laser oscillator 2, an optical system 3, a processing control unit 4, inspection devices 5a, 5b, and 5c, a memory device 6, a learning system 7, an inference system 8, and an I / F unit 9.

[0028] The laser oscillator 2 is a laser processing machine for performing laser processing. The laser oscillator 2 emits a beam that forms laser light by laser oscillation. The laser light emitted by the laser oscillator 2 is a substantially parallel beam. That is, the laser oscillator 2 outputs collimated parallel light. For example, the laser oscillator 2 may be a continuous wave single-mode fiber laser capable of laser oscillation with a wavelength of 1070 nm. The wavelength of the laser light is not limited to 1070 nm and is appropriately set in consideration of the light absorption characteristics of the workpieces 11 and 12. For example, if the workpieces 11 and 12 are made of copper or gold, the wavelength of the laser light is set to a short wavelength of 405 to 450 nm. For example, if the workpieces 11 and 12 are made of aluminum, the wavelength of the laser light is set to approximately 800 nm. The laser light may be a continuous wave or a pulse wave. If the laser light is a continuous wave, the input heat can be increased, enabling high productivity and laser welding. If the laser beam is a pulsed wave, the thermal influence during laser processing can be reduced compared to when the laser beam is a continuous wave.

[0029] The optical system 3 guides the laser light from the laser oscillator 2 to the workpieces 11 and 12. The optical system 3 also guides the return light from the workpieces 11 and 12 to the inspection device 5a. In this embodiment, the optical system 3 includes first and second mirrors 3a and 3b and a lens 3c. For example, the first mirror 3a is a dichroic mirror that reflects the laser light from the laser oscillator 2 to the second mirror 3b. For example, the second mirror 3b is a folding mirror that reflects 90% or more of light with a wavelength equal to the wavelength of the laser light (e.g., 1070 nm). The lens 3c is a condensing lens. According to the optical system 3, the laser light from the laser oscillator 2 has its optical axis converted, for example, by 90° by the first mirror 3a and the second mirror 3b before entering the lens 3c. The laser light is condensed by the lens 3c and irradiated onto the workpieces 11 and 12. A molten pool is formed on the workpieces 11 and 12 by heating with the laser light. Return light is generated from the portions of the workpieces 11 and 12 that are irradiated with the laser light. The return light is received by the lens 3c. The optical axis of the return light received by the lens 3c is changed by, for example, 90° by the second mirror 3b, and then passes through the first mirror 3a and is focused on the inspection device 5a.

[0030] The machining control unit 4 controls the control parameters of a physical system that generates a physical phenomenon. In the machining system 1, the physical system is composed of a laser oscillator 2, an optical system 3, and a machining stage 10, and the physical phenomenon includes laser machining. In this embodiment, the control parameters may include, for example, the laser position, laser intensity (laser output), laser diameter, scanning speed, and profile shape. The control parameters may change over time.

[0031] In the processing system 1, a physical phenomenon occurring in the physical system is measured by the inspection devices 5a, 5b, and 5c. The inspection devices 5a, 5b, and 5c are used to obtain measurement values ​​of the measurement results of the physical phenomenon occurring in the physical system. The measurement values ​​may be values ​​obtained by measuring the physical phenomenon, such as values ​​indicating a physical quantity such as light intensity, or may be values ​​indicating a conclusion obtained by measuring the physical phenomenon, such as success or failure.

[0032] The inspection device 5a is a detection device that detects the welding condition. The inspection device 5a measures the waveform of the returned light from the optical system 3 and converts the returned light into an electrical signal corresponding to the intensity of the returned light. In this embodiment, the inspection device 5a separates the returned light into multiple types of light. Here, the multiple types of light may include visible light having a wavelength of 400 nm to 700 nm, reflected light having a wavelength of 1070 nm, and thermal radiation light having a wavelength of 1080 nm to 2000 nm. The inspection device 5a converts the visible light, reflected light, and thermal radiation light into electrical signals corresponding to the intensities of each light, and transmits the electrical signals indicating the intensities of the visible light, reflected light, and thermal radiation light to the storage device 6 as measurement values ​​of the physical phenomenon.

[0033] FIG. 2 is a schematic diagram of a measurement waveform measured by the inspection device 5a in the processing system 1 of this embodiment. (D) of FIG. 2 illustrates an example of a measurement waveform of laser light corresponding to the output (laser intensity) of the irradiated laser light, and (A) to (C) of FIG. 2 respectively illustrate measurement waveforms corresponding to the light intensity of visible light, thermal radiation light, and reflected light separated from the returned light. In (A) to (D) of FIG. 2, the horizontal axis represents time, for example, based on the number of signal samplings, and the vertical axis represents signal intensity as a signal value obtained by converting light intensity into voltage. Also, in FIG. 2, Td represents the period during which the output of the laser light becomes steady state within a period corresponding to one pulse of laser light.

[0034] The inspection device 5b is a three-dimensional shape measuring machine. The inspection device 5b measures the surface shapes of the workpieces 11 and 12 in three dimensions. The inspection device 5b measures the height of any position on the surface of the workpieces 11 and 12. The inspection device 5b includes, for example, an image sensor. The image sensor is not particularly limited, but preferably can acquire depth, and may be an RGBD camera or a stereo camera. If the image sensor is a monocular RGB camera, the inspection device 5b may be equipped with a lidar to acquire depth. The surface shape of the workpieces 11 and 12 may be, for example, the shape of a molten zone generated on the surface of the workpieces 11 and 12 by laser welding. As shown in FIG. 1, the shape of the molten zone is measured after laser processing is completed. In this embodiment, as an example, the height of the molten zone from the surface of the workpieces 11 and 12 is a maximum of approximately 400 μm, and the width of the molten zone (melt width) is approximately 130 to 330 μm. The inspection device 5b transmits numerical values ​​(height and width of the molten portion) indicating the surface shape of the workpieces 11, 12 to the storage device 6 as measurement values ​​of the measurement results of the physical phenomenon.

[0035] The inspection device 5c is a strength measuring device. The inspection device 5c measures the strength of two workpieces 11, 12 bonded together by laser welding. The strength of the workpieces 11, 12 may be the strength of the weld between the workpieces 11, 12. The strength of the workpieces 11, 12 may be measured as tensile strength by a tensile test, for example. The tensile strength is measured by gripping both ends of the two workpieces 11, 12 bonded together by laser welding. The inspection device 5c may include, for example, a pair of gripping parts that grip both ends of the workpieces 11, 12, and a drive mechanism that pulls the pair of gripping parts away from each other. In this embodiment, as an example, the tensile strength is 0 to 320 N. A tensile strength of 0 N indicates that the workpieces 11, 12 are not welded together. The inspection device 5c transmits the measured strength (tensile strength) of the workpieces 11, 12 to the storage device 6 as a measurement value of the measurement result of the physical phenomenon. The strength measurement by the inspection device 5c may be performed after the shape of the molten zone is measured by the inspection device 5b. After the strength measurement by the inspection device 5c is completed, the workpieces 11, 12 may be discharged outside the processing system 1.

[0036] The storage device 6 includes one or more storages (non-transitory storage media). The storages may be, for example, hard disk drives, optical drives, or solid-state drives (SSDs). The storages may be internal, external, or network-attached storage (NAS).

[0037] The information stored in the storage device 6 includes a training data set D1, a core model M1, a sub-model M2, and an unobserved prior information parameter P3. Fig. 1 shows a state in which the storage device 6 stores the training data set D1, the core model M1, the sub-model M2, and the unobserved prior information parameter P3. The training data set D1, the core model M1, the sub-model M2, and the unobserved prior information parameter P3 do not need to be stored in the storage device 6 at all times, but only need to be stored in the storage device 6 when needed by the learning system 7 or the inference system 8.

[0038] The training dataset D1 includes multiple datasets. Each dataset includes control parameters P1 of a physical system that generates a physical phenomenon and measurement values ​​P2 of the measurement results of the physical phenomenon generated by the physical system to which the control parameters P1 are applied. Here, the control parameters P1 are explanatory variables, and the measurement values ​​P2 of the measurement results are response variables.

[0039] In this embodiment, the control parameters P1 may include the laser position, laser intensity, laser diameter, scanning speed, and profile shape. As an example, the control parameters P1 include the laser position, laser intensity, and laser diameter from the start to the end of laser processing. Table 1 below shows an example of the control parameters P1. In Table 1 below, time 0 is the start time, and time T is the end time.

[0040]

[0041] In this embodiment, the measured value P2 may include the intensity of the return light (visible light, reflected light, and thermal radiation light) from the workpieces 11 and 12, the surface shape of the workpieces 11 and 12, and the tensile strength of the workpieces 11 and 12. As an example, the measured value P2 includes the intensity of the return light (intensity of visible light, reflected light, and thermal radiation light) from the start to the end of laser processing, and the tensile strength of the workpieces 11 and 12 after laser processing. Table 2 below shows an example of the measured value P2. In Table 2 below, time 0 is the start time, and time T is the end time.

[0042]

[0043] In this embodiment, the number of data sets of the control parameters P1 and the measurement values ​​P2 is 1000. The number of data sets may be 1000 or less. There is no particular limit to the number of data sets, but 1000 or less is preferable from the viewpoint of reducing the amount of data required for learning.

[0044] The unobserved prior information parameter P3 is a parameter separate from the control parameter P1 and is used to predict the measurement result of the physical phenomenon. The unobserved prior information parameter P3 is set independently of the control parameter P1. The unobserved prior information parameter P3 is prepared to represent the variation in the measurement value P2 for the same control parameter P1. Generally, the measurement values ​​P2 in multiple occurrences of a physical phenomenon with the same control parameter P1 do not necessarily have the same value. This means that each control parameter P1 does not have sufficient information about each measurement value P2, and some information related to each measurement value P2 (referred to as "unobserved information" in this embodiment) other than the control parameter P1 may exist. The unobserved prior information parameter P3 is a parameter for representing this unobserved information. The unobserved prior information parameter P3 is expressed, for example, as a vector. The number of parameters (the number of dimensions of the vector) of the unobserved prior information parameter P3 may be 2 or more and 20 or less. One unobserved prior information parameter P3 is prepared to correspond to each dataset included in the training dataset D1. Table 3 below shows an example of the unobserved prior information parameters P3. If the number of data sets is 1000, the number of unobserved prior information parameters P3 is also 1000.

[0045]

[0046] The information stored in the memory device 6 may further include a computer program for learning (a learning program), a computer program for inference (an inference program), temporary data generated when each computer program is executed, and first and second machine learning models.

[0047] The core model M1 is a trained model for obtaining a predicted value O1 of the measurement result of a physical phenomenon caused by a physical system from a control parameter P1 of the physical system.

[0048] FIG. 3 is a diagram illustrating an example of the input and output of the core model M1. The input of the core model M1 includes a control parameter P1 and an unobserved prior information parameter P3. The output of the core model M1 is a predicted value O1 of a measurement result. The core model M1 can be generated using a function (first machine learning model) capable of learning a predicted value O1 of a measurement result of a physical phenomenon generated by a physical system from the control parameter P1 and the unobserved prior information parameter P3 of the physical system. The first machine learning model defines an inference program into which the learned parameters are incorporated. The core model M1 is trained so that, in response to the input of the control parameter P1 and the unobserved prior information parameter P3, it outputs a predicted value O1 of a measurement result of a physical phenomenon generated by the physical system to which the control parameter P1 is applied. The core model M1 is a trained model that simulates a physical phenomenon and is known as a surrogate model.

[0049] The core model M1 can express the variability of the measurement values ​​by varying the unobserved prior information parameter P3, and makes it possible to perform estimation by sampling the predicted value of each measurement result from the distribution explained by the unobserved information, as in actual measurements.

[0050] The core model M1 is configured by a neural network. Fig. 4 is a schematic diagram of an example of the configuration of the core model M1 (an example of the structure of a neural network). In Fig. 4, the state h ０ =0.

[0051] The core model M1 includes a first model M11, a second model M12, and a third model M13.

[0052] The first model M11 constitutes a neural network (recurrent neural network) with a recursive structure. The first model M11 is a model of a state h at a time t. ｔ and each control parameter P1 (laser position P11, laser intensity P12, laser diameter P13) at time t, the state h at time t ｔ The state h at the next time point t+1 ｔ＋１ The first model M11 includes, for example, fully connected layers of an input layer and an output layer and an activation function such as ReLU between them.

[0053] The second model M12 constitutes a feedforward neural network. The second model M12 is derived from the state h at time t+1 from the first model M11. ｔ＋１ and the unobserved prior information parameter P3, the second model M12 outputs a predicted value O11 of the returned light intensity at time t+1. The second model M12 includes, for example, fully connected input and output layers and an activation function such as GELU between them.

[0054] The third model M13 constitutes a feedforward neural network. The third model M13 is a model of the state h at the time T, which is the end time. Ｔ and the unobserved prior information parameter P3, and outputs a predicted value O12 of the tensile strength. The third model M13 includes, for example, fully connected input and output layers and an activation function such as GELU between them.

[0055] In this way, the core model M1 includes a neural network with a recursive structure (recurrent neural network), defines a time series from time 0 to T, and outputs a predicted value O11 of the return light intensity from time 1 to T and a predicted value O12 of the final tensile strength (at time T) from each control parameter (laser position P11, laser intensity P12, laser diameter P13) from time 0 to T-1.

[0056] The sub-model M2 is a trained model for obtaining the control parameters P1 of the physical system from the unobserved prior information parameters P3. The sub-model M2 is defined independently of the core model M1 and is used to generate the core model M1.

[0057] FIG. 5 is a diagram showing an example of the input and output of the submodel M2. The input of the submodel M2 is an unobserved prior information parameter P3. The output of the submodel M2 is a predicted value O2 of the control parameter P1 of the physical system. The submodel M2 can be generated using a function (second machine learning model) that can learn the control parameter P1 of the physical system from the unobserved prior information parameter P3. The second machine learning model defines an inference program into which the learned parameters are incorporated. The submodel M2 is trained to output a predicted value O2 of the control parameter P1 in response to an input of the unobserved prior information parameter P3.

[0058] For example, the submodel M2 is configured by a neural network. FIG. 6 is a schematic diagram of an example configuration of the submodel M2 (an example of the structure of a neural network). The submodel M2 is constructed by a feedforward neural network. In response to input of an unobserved prior information parameter P3 and a time t, the submodel M2 outputs predicted values ​​O2 (laser position O21, laser intensity O22, laser diameter O23) of each control parameter P1 at time t. Time t can range from 0 (start time) to T-1. The feedforward neural network includes, for example, fully connected layers of an input layer and an output layer and an activation function such as GELU between them.

[0059] The learning system 7 performs machine learning to generate a core model M1 and a sub-model M2. The learning system 7 includes an arithmetic circuit 71. The arithmetic circuit 71 is communicatively connected to the storage device 6 and can access data stored in the storage device 6. The arithmetic circuit 71 may be implemented, for example, by a computer system. The computer system includes one or more processors (microprocessors) and one or more memories. The one or more processors execute programs (stored in one or more memories or the storage device 6) to realize various functions of the learning system 7. The programs may be pre-recorded in the memory or the storage device 6, or may be provided via a telecommunications line such as the Internet, or recorded on a non-transitory recording medium such as a memory card.

[0060] When generating the core model M1, the calculation circuit 71 refers to the learning dataset D1 and adjusts the parameters of the machine learning model for multiple datasets to generate learned parameters so that the output value of the machine learning model when a control parameter P1 and an additional parameter other than the control parameter P1 are input approaches the measurement value P2, and also adjusts the additional parameters for each of the multiple datasets to generate multiple learned additional parameters.

[0061] The core model M1 is obtained by incorporating the learned parameters thus obtained into a machine learning model (first machine learning model) for the core model M1. The learned additional parameters for each data set thus obtained are used as unobserved prior information parameters P3. The number of learned additional parameters obtained is equal to the number of data sets.

[0062] When generating the core model M1, the arithmetic circuit 71 also generates a sub-model M2. By using the sub-model M2, the independence of the unobserved prior information parameter P3 from the control parameter P1 can be ensured. Specifically, the arithmetic circuit 71 adjusts the parameters of the second machine learning model so as to reduce a second difference between the output value of the second machine learning model when the additional parameter is input and the control parameter P1 input to the first machine learning model together with the additional parameter, and adjusts the additional parameter so as to reduce a first difference between the output of the first machine learning model and the measurement value P2 and increase the second difference.

[0063] The arithmetic circuitry 71 can adjust the parameters for the core model M1 (parameters of the first machine learning model), the parameters for the sub-model M2 (parameters of the second machine learning model), and the additional parameters (unobserved prior information parameters P3) using the loss function L. More specifically, the arithmetic circuitry 71 adjusts the parameters of the first machine learning model, the parameters of the second machine learning model, and the additional parameters so as to minimize the value of the loss function L.

[0064] The loss function L may be expressed as L1-L2.

[0065] L1 relates to the core model M1. L1 is a term (first term) representing a first difference. For example, L1 is a term that decreases as the output value of the core model M1, to which each control parameter P1 is input, approaches each measurement value P2 corresponding to the control parameter P1. L1 may be expressed, for example, by a mean square error function.

[0066] L2 relates to the submodel M2. L2 is a term (second term) representing the second difference. For example, L2 is a term of a loss function that is minimized as the submodel M2 is optimized. L2 is the loss function that is minimized as the submodel M2 is optimized, and is expressed as a function (e.g., a mean square error function) that decreases as the output value of the submodel M2 approaches each control parameter P1 corresponding to the input unobserved prior information parameter P3 when the unobserved prior information parameter P3 is used as an input to the submodel M2.

[0067] In this way, the loss function L minimized as a result of optimizing the unobserved prior information parameter P3 and the core model M1 is represented by a positively weighted sum of a first term (e.g., a mean square error function) L1 that decreases as the output value of the core model M1, which uses each control parameter P1 as input, approaches each measurement value P2 corresponding to the control parameter P1, and a second term (e.g., −1 times the loss function minimized as a result of optimizing the sub-model) that monotonically decreases with respect to the value L2 of the loss function minimized as a result of optimizing the sub-model.

[0068] The optimization in the learning system 7 may be performed by, for example, a gradient method or evolutionary computation. The optimization in the learning system 7 is performed so as to simultaneously minimize different loss functions for the core model M1 and the sub-model M2.

[0069] The first term L1, which represents the loss function for the core model M1, is minimized to estimate each measurement value P2 from each control parameter P1. The core model M1 can represent the variability of actual measurements by varying the unobserved prior information parameter P3, and can perform estimation by sampling predicted values ​​O1 of each measurement result from a distribution explained by unobserved information, just like actual measurements.

[0070] Minimizing the second term L2, which represents the loss function for the submodel M2, is adversarial learning for optimizing the submodel M2. More specifically, the submodel M2 attempts to extract as much information about each control parameter P1 as possible from the unobserved prior information parameter P3, but the unobserved prior information parameter P3 itself changes its value so that it does not include information about each control parameter P1 in order to reduce the accuracy of the submodel M2. Through this adversarial learning, the unobserved prior information parameter P3 is learned as a vector independent of each control parameter P1.

[0071] In this way, the learning system 7 optimizes unobserved prior information parameters P3 and learnable functions (parameters of the first machine learning model) from a learning dataset D1 including multiple datasets of control parameters P1 and measurement values ​​P2 stored in the storage device 6.

[0072] FIG. 7 is a flowchart showing an example of the operation of the learning system 7.

[0073] The arithmetic circuit 71 determines initial parameters (S1). More specifically, the arithmetic circuit 71 determines initial parameters of a machine learning model (first machine learning model) used to generate the core model M1, initial parameters of a machine learning model (second machine learning model) used to generate the sub-model M2, and initial parameters (initial values) of additional parameters that define the unobserved prior information parameter P3. Each initial parameter may be determined randomly.

[0074] The arithmetic circuit 71 calculates the value of the loss function L of the initial parameters using the selected data set, and sets the calculated value of the loss function L to the minimum value (S2).

[0075] The arithmetic circuit 71 changes all or part of the parameters of the first machine learning model, the parameters of the second machine learning model, and the additional parameters (S3). The method for changing the parameters is not particularly limited, but known optimization methods such as the gradient method can be used.

[0076] The arithmetic circuit 71 calculates the value of the loss function L of the changed parameters using the selected data set (S4).

[0077] The arithmetic circuit 71 determines whether the value of the loss function L of the changed parameters is smaller than the minimum value (S5).

[0078] If the value of the loss function L of the changed parameters is smaller than the minimum value (S5: YES), the arithmetic circuit 71 updates the minimum value to the value of the loss function L of the changed parameters (S6). If the value of the loss function L of the changed parameters is not smaller than the minimum value (S5: NO), the arithmetic circuit 71 does not update the minimum value and proceeds to the next step S7.

[0079] The arithmetic circuit 71 determines the minimum number of updates (S7). The minimum number of updates is used as a criterion for whether or not to terminate parameter adjustment. The minimum number of updates is determined based on whether or not the value of the loss function L has updated to the minimum value. If the value of the loss function L has updated to the minimum value, the minimum number of updates is decreased by a first specified value (e.g., 2), and if the value of the loss function L has not updated to the minimum value, the minimum number of updates is increased by a second specified value (e.g., 1). The initial value of the minimum number of updates is determined appropriately based on the extent to which the parameters are to be adjusted.

[0080] The arithmetic circuit 71 determines whether the minimum number of updates is equal to or less than the upper limit (S8). The upper limit is determined appropriately based on the extent to which the parameters are to be adjusted.

[0081] If the minimum number of updates is equal to or less than the upper limit (S8: YES), the calculation circuit 71 adopts the parameter corresponding to the minimum value.

[0082] The calculation circuit 71 repeats the same process for other data sets, but the unobserved prior information parameter P3 is set to a value that is individual to each data set, thereby providing an unobserved prior information parameter P3 for each data set, as shown in Table 3.

[0083] The learning system 7 described above defines a surrogate model as the core model M1, and defines an unobserved prior information parameter P3, a learnable vector linked to a dataset, as the input of the core model M1 to model sampling from a free distribution. The submodel M2 evaluates the dependency between the unobserved prior information parameter P3 and each control parameter P1 that serves as other input to the core model M1, while the core model M1 reduces the dependency and makes it independent, thereby constructing an unobserved prior information parameter P3 that expresses unobserved information regardless of each control parameter P1. This can avoid overconfidence with a small amount of data. In this embodiment, the number of variations in the inputs to be learned is the same as the number of datasets, so overconfidence is unlikely to occur even with a small amount of data. The machine learning model used to construct the core model M1 may be, for example, a neural network, in which case the output distribution can be expressed without constraints. In the case of other machine learning models, the constraints on the distribution output are determined only by constraints on the input and output of the machine learning model and are not limited by the learning method.

[0084] The I / F unit 9 functions as an input device for inputting information from a user and as an output device for outputting information to a user. The I / F unit 9 includes one or more human-machine interfaces. Examples of human-machine interfaces include input devices such as a keyboard, a pointing device (a mouse, a trackball, etc.), and a touchpad, output devices such as a display and a speaker, and input / output devices such as a touch panel.

[0085] The inference system 8 includes an arithmetic circuit 81. The arithmetic circuit 81 is communicatively connected to the storage device 6 and can access data stored in the storage device 6. The arithmetic circuit 81 can be realized, for example, by a computer system. The computer system includes one or more processors (microprocessors) and one or more memories. The one or more processors execute programs (stored in one or more memories or the storage device 6) to realize various functions of the inference system 8. The programs may be pre-recorded in the memory or the storage device 6, or may be provided via a telecommunications line such as the Internet, or recorded on a non-transitory recording medium such as a memory card.

[0086] The inference system 8 executes inference using the core model M1. FIG. 8 is a flowchart showing an example of the operation of the inference system 8.

[0087] The arithmetic circuit 81 receives the target control parameters (S11). As an example, the arithmetic circuit 81 uses the I / F unit 9 to display a screen for inputting the target control parameters.

[0088] The calculation circuit 81 selects an unobserved prior information parameter P3 to be used together with the target control parameter (S12). In Table 3, the unobserved prior information parameter P3 is v １ ~v １０００ There are 1000 unobserved prior information parameters P3, and one (for example, v １ ) is selected.

[0089] The arithmetic circuit 81 executes the core model M1 using the target control parameter and the selected unobserved prior information parameter P3 (S13). The core model M1 operates the arithmetic circuit 81 in response to the input of the target control parameter and the unobserved prior information parameter P3 so as to output a predicted value O1 of the measurement result of a physical phenomenon that will be generated by a physical system to which the target control parameter is applied.

[0090] The arithmetic circuit 81 determines whether predicted values ​​O1 of the measurement results have been obtained for a specified number of unobserved prior information parameters P3 (S14). The specified number can be arbitrarily selected from the range of 2 or more and the number of unobserved prior information parameters P3 or less. In this embodiment, the specified number may be 1000, which is the same as the number of unobserved prior information parameters P3. The specified number being the same as the number of unobserved prior information parameters P3 means that it is determined whether predicted values ​​O1 of the measurement results have been obtained for all unobserved prior information parameters P3.

[0091] In step S14, if the predicted value O1 of the measurement result has not been obtained for the specified number of unobserved prior information parameters P3, for example, if the number of predicted values ​​O1 of the measurement result does not reach the specified number (S14: NO), the calculation circuit 81 returns to step S12 and selects an unselected one from the multiple unobserved prior information parameters P3.

[0092] In step S14, when predicted values ​​O1 of the measurement results have been obtained for a predetermined number of unobserved prior information parameters P3, for example, when the number of predicted values ​​O1 of the measurement results has reached a predetermined number (S14: YES), the calculation circuit 81 presents a distribution of the predicted values ​​O1 of the measurement results (S15). That is, at the stage when step S15 is reached, a predetermined number of predicted values ​​O1 have been obtained from the core model M1 by using the same target control parameter P1 and a predetermined number of different unobserved prior information parameters P3. The calculation circuit 81 presents the distribution of the predicted values ​​O1 using this predetermined number of predicted values ​​O1 via the I / F unit 9.

[0093] In this way, when a target control parameter is input, the arithmetic circuit 81 executes the trained model (core model M1) to obtain predicted values ​​O1 corresponding to two or more of the trained additional parameters (unobserved prior information parameters P3) for the target control parameter. Then, the arithmetic circuit 81 presents a distribution of the predicted values ​​O1.

[0094] 9 is a diagram showing an example of the output of the inference system 8, i.e., the distribution of the predicted value O1. In FIG. 9, the predicted value O1 is the tensile strength O12. In FIG. 9, the distribution of the predicted value O1, i.e., the distribution of the tensile strength O12, is shown in a graph. Based on the distribution of the predicted value O1, it is possible to understand what kind of measurement results can be obtained when the target control parameter P1 is used.

[0095] As described above, the inference system 8 uses the core model M1 to input each control parameter P1 and estimate the distribution of predicted values ​​O1 of each measurement result when processing is performed using each control parameter P1. The distribution of predicted values ​​O1 shown in FIG. 9 is obtained by sampling a sufficient number of times (e.g., 1,000 times) with each calculation by the core model M1 considered as one sampling, with the maximum number of samplings being the number of data (number of data sets) used in training. In the learning system 7, the unobserved prior information parameter P3 is trained to be a vector independent of each control parameter P1, so that the unobserved prior information parameter P3 corresponding to a certain control parameter P1 can be used to infer a different control parameter P1. In other words, regardless of the value of each control parameter P1, all unobserved prior information parameters P3 can be used, making it possible to perform a large number of samplings with the maximum number of training data.

[0096] 1.2 Effects, etc. The learning system 7 described above includes an arithmetic circuit 71 that can access a storage device 6 that stores a machine learning model and a learning dataset D1. The learning dataset D1 includes multiple datasets, each of which includes a control parameter P1 of a physical system that generates a physical phenomenon and a measurement value P2 of a measurement result of the physical phenomenon generated by the physical system to which the control parameter P1 is applied. The arithmetic circuit 71 adjusts the parameters of the machine learning model with respect to the multiple datasets to generate learned parameters, and adjusts the additional parameters with respect to the multiple datasets to generate multiple learned additional parameters (unobserved prior information parameters P3) so that an output value of the machine learning model when the control parameter P1 and an additional parameter other than the control parameter P1 are input approaches the measurement value P2. This configuration enables an improvement in the degree of freedom of the distribution of a predicted value O1 of the measurement result of the physical phenomenon, while reducing the amount of data required for learning and the occurrence of overconfidence.

[0097] In the learning system 7, the additional parameter is set independently of the control parameter P1 and represents the variability of the measurement value P2 for the same control parameter P1. This configuration enables an improvement in the degree of freedom of the distribution of the predicted value O1 of the measurement result of the physical phenomenon, while reducing the amount of data required for learning and the occurrence of overconfidence.

[0098] In the learning system 7, the machine learning model is a first machine learning model, the storage device 6 stores a second machine learning model separate from the first machine learning model, the first difference is the difference between the output of the first machine learning model and a measurement value P2, the second difference is the difference between the output value of the second machine learning model when an additional parameter is input and a control parameter P1 input to the first machine learning model together with the additional parameter, and the arithmetic circuit 71 adjusts the parameters of the second machine learning model so as to reduce the second difference, and adjusts the additional parameter so as to reduce the first difference and increase the second difference. This configuration enables an improvement in the degree of freedom of the distribution of a predicted value O1 of a measurement result of a physical phenomenon, while reducing the amount of data required for learning and the occurrence of overconfidence.

[0099] In the learning system 7, the arithmetic circuit 71 adjusts the parameters of the first machine learning model, the parameters of the second machine learning model, and the additional parameters so as to minimize the value of a loss function L, where the loss function L is expressed as L1-L2, where L1 is a term representing the first difference and L2 is a term representing the second difference. This configuration enables an improvement in the degree of freedom of the distribution of the predicted value O1 of the measurement result of a physical phenomenon, while reducing the amount of data required for learning and the occurrence of overconfidence.

[0100] In the learning system 7, the number of the multiple data sets is 1000 or less, and the number of additional parameters is 2 or more and 20 or less. This configuration enables an improvement in the degree of freedom of the distribution of the predicted value O1 of the measurement result of the physical phenomenon, while reducing the amount of data required for learning and the occurrence of overconfidence.

[0101] The learning system 7 described above can be said to execute the following learning method. The learning method is executed in the learning system 7 by arithmetic circuits 71 and 81 that can access a storage device 6 that stores a machine learning model and a learning dataset D1. The learning dataset D1 includes multiple datasets, each of which includes a control parameter P1 of a physical system that generates a physical phenomenon and a measurement value P2 of the measurement result of the physical phenomenon generated by the physical system to which the control parameter P1 is applied. The learning method adjusts the parameters of the machine learning model for the multiple datasets to generate learned parameters, and adjusts the additional parameter for each of the multiple datasets to generate multiple learned additional parameters (unobserved prior information parameters P3) so that the output of the machine learning model approaches the measurement value P2 when the control parameter P1 and an additional parameter other than the control parameter P1 are input. This configuration enables an improvement in the degree of freedom of the distribution of a predicted value O1 of the measurement result of the physical phenomenon, while reducing the amount of data required for learning and the occurrence of overconfidence.

[0102] The learning system 7 is implemented using an arithmetic circuit 71. That is, the learning method can be implemented by the arithmetic circuit 71 executing a program. This program is a program for causing the arithmetic circuit 71 to execute the above-described learning method. This configuration enables an improvement in the degree of freedom of the distribution of the predicted value O1 of the measurement result of a physical phenomenon, while also reducing the amount of data required for learning and the occurrence of overconfidence.

[0103] The above-described inference system 8 includes an arithmetic circuit 81 that can access a storage device 6 that stores a trained model (core model M1) and multiple trained additional parameters (unobserved prior information parameters P3). When executed by the arithmetic circuit 81, the trained model (core model M1) operates the arithmetic circuit 71 to output a predicted value O1 of a measurement result of a physical phenomenon generated by the physical system to which the control parameter P1 is applied in response to input of a control parameter P1 of a physical system that generates a physical phenomenon and a trained additional parameter (unobserved prior information parameter P3) selected from the multiple trained additional parameters (unobserved prior information parameters P3). When a target control parameter P1 is input, the arithmetic circuit 81 executes the trained model (core model M1) to obtain predicted values ​​O2 corresponding to two or more of the multiple trained additional parameters (unobserved prior information parameters P3) for the target control parameter P1. This configuration enables an improvement in the degree of freedom of the distribution of the predicted value O1 of the measurement result of the physical phenomenon, while reducing the amount of data required for training and the occurrence of overconfidence.

[0104] In the inference system 8, the calculation circuit 81 presents the distribution of predicted values. This configuration makes it possible to present the distribution of predicted values ​​O1 of the measurement results of a physical phenomenon.

[0105] In the inference system 8, the trained model (core model M1) is obtained by training a machine learning model using a training dataset D1 including multiple datasets each including a control parameter P1 and measurement values ​​P2 of the measurement results, and the number of predicted values ​​O1 of the measurement results is equal to or less than the number of the multiple datasets. This configuration enables multiple samplings with the number of datasets in the training dataset as the maximum number.

[0106] In the inference system 8, the trained model (core model M1) is obtained by training a machine learning model using a training dataset D1 including multiple datasets each including a control parameter P1 and a measurement value P2 of the measurement result, and the target control parameter P1 is different from the control parameter P1 included in the training dataset D1. This configuration allows all trained additional parameters (unobserved prior information parameters P3) to be used regardless of the value of each control parameter P1.

[0107] In the inference system 8, the trained model (core model M1) is obtained by training a machine learning model using a training dataset D1 including multiple datasets each including a control parameter P1 and a measurement value P2 of a measurement result, and the multiple trained additional parameters (unobserved prior information parameters P3) are generated by adjusting the additional parameters for each of the multiple datasets so that the output of the machine learning model when the control parameter P1 and an additional parameter other than the control parameter P1 are input approaches the measurement value P2. This configuration enables an improvement in the degree of freedom of the distribution of the predicted value O1 of the measurement result of a physical phenomenon, while reducing the amount of data required for training and the occurrence of overconfidence.

[0108] The inference system 8 described above can be said to execute the following inference method. The inference method is executed by an arithmetic circuit 81 that can access a storage device 6 that stores a trained model (core model M1) and multiple trained additional parameters (unobserved prior information parameters P3). When executed by the arithmetic circuit 81, the trained model (core model M1) operates the arithmetic circuit 81 to output a predicted value O1 of a measurement result of a physical phenomenon generated by the physical system to which the control parameter P1 is applied in response to input of a control parameter P1 of a physical system that generates a physical phenomenon and a trained additional parameter selected from the multiple trained additional parameters. The inference method executes the trained model (core model M1) when a target control parameter P1 is input, and obtains predicted values ​​O1 corresponding to two or more of the multiple trained additional parameters for the target control parameter P1. This configuration enables an improvement in the degree of freedom of the distribution of the predicted value O1 of the measurement result of the physical phenomenon, while reducing the amount of data required for training and the occurrence of overconfidence.

[0109] The inference system 8 is realized by using an arithmetic circuit 81. That is, the inference method can be realized by the arithmetic circuit 81 executing a program. This program is a program for causing the arithmetic circuit 81 to execute the above-described inference method. This configuration enables an improvement in the degree of freedom of the distribution of the predicted value O1 of the measurement result of a physical phenomenon, while also enabling a reduction in the amount of data required for learning and the occurrence of overconfidence.

[0110] When the trained model (core model M1) described above is executed by the calculation circuit 71, it operates the calculation circuit 71 so that, in response to input of a control parameter P1 of a physical system that generates a physical phenomenon and a trained additional parameter, it outputs a predicted value O1 of the measurement result of the physical phenomenon generated by the physical system to which the control parameter P1 is applied.

[0111] [2. Modifications] The embodiments of the present disclosure are not limited to the above-described embodiments. The above-described embodiments can be modified in various ways depending on the design, etc., as long as the object of the present disclosure can be achieved. Modifications of the above-described embodiments are listed below. The modifications described below can be applied in appropriate combinations.

[0112] In one variation, the physical system may include a galvanometer mirror and an fθ lens disposed between the total reflection mirror and the lens, and the laser light may be scanned over the workpieces 11 and 12 by the galvanometer mirror and the fθ lens.

[0113] In one modified example, the configurations of the core model M1 shown in FIG. 4 and the sub-model M2 shown in FIG. 6 are merely examples, and the three-dimensional shape may also be estimated by, for example, including a convolutional neural network in the core model M1.

[0114] In one variation, the operation circuitry 71 may not necessarily perform the optimization itself, but may instead have an external device perform the optimization. For example, the operation circuitry 71 may have a quantum computer (e.g., a quantum annealing machine) perform the optimization. In this case, the operation circuitry 71 may be accessible to the quantum computer.

[0115] In one variant, learning system 7 or inference system 8 may be realized by two or more computers capable of communicating with each other, such as multiple servers. It is not necessary for multiple functions (components) of learning system 7 or inference system 8 to be concentrated in a single housing; the components of learning system 7 or inference system 8 may be distributed across multiple housings. Furthermore, at least some of the functions of learning system 7 or inference system 8, for example, some functions of arithmetic circuits 71, 81, may be realized by the cloud (cloud computing) or the like.

[0116] In one modification, the physical phenomenon is not limited to laser processing (laser welding) as described in the above embodiment. Below, examples of physical phenomena other than laser welding to which the learning system, learning method, inference system, inference method, and program of the present disclosure can be applied are listed.

[0117] In one example, the physical phenomenon may be powder film formation using a flat plate. In this example, the physical system may be a powder film formation device. The control parameters P1 may include the surface roughness of the flat plate, the pressure (gap), the area of ​​the film to be formed, film pre-processing (film thickness uniformization, primary molding, heating), etc. The measured values ​​P2 of the measurement results may include film thickness, film density, transferability, etc. Causes of variation in the measurement results are thought to include stress distribution due to local deformation of the flat plate and film non-uniformity, as well as temperature distribution of the flat plate and film, etc.

[0118] In one example, the physical phenomenon may be die coating. In this example, the physical system may be a die coating device. The control parameters P1 may include slurry viscosity, temperature, die tip shape, gap within the die, pressure (discharge rate), and gap between the die and the workpiece. The measurement values ​​P2 of the measurement results may include film thickness, film density, and abnormalities (bubbles). Causes of variation in the measurement results are thought to include variation in slurry viscosity and variation in the gap between the die and the workpiece.

[0119] In one example, the physical phenomenon may be powder milling. In this example, the physical system may be a ball mill. The control parameters P1 may include the powder input amount, temperature, blade shape, number of blades, blade rotation speed, grinding ball hardness, grinding ball size, and number of grinding balls, etc. The measurement values ​​P2 of the measurement results may include particle size distribution and power consumption, etc. Causes of variation in the measurement results are thought to include variation in powder input density and variation in the flow behavior of the powder or balls, etc.

[0120] In one example, the physical phenomenon may be press cutting. In this example, the physical system may be a press cutting machine. The control parameters P1 may include the blade shape, blade hardness, clearance between the die and punch, and processing speed, etc. The measurement values ​​P2 of the measurement results may include the cutting surface shape and blade life, etc. Causes of variation in the measurement results are thought to include changes in the blade shape and variations in clearance, etc.

[0121] In one example, the physical phenomenon may be laser removal processing. In this example, the physical system may be a laser oscillator. The control parameters P1 may include the laser wavelength, laser intensity, laser shape, laser pulse width, repetition frequency, etc. The measurement values ​​P2 of the measurement results may include the processed cross-sectional shape, energy saving, and processing volume per unit time, etc. Causes of variation in the measurement results are thought to include changes in laser intensity, etc.

[0122] In one example, the physical phenomenon may be ultrasonic bonding. In this example, the physical system may be an ultrasonic bonding machine. The control parameters P1 may include a pressing load, a shape of the horn / anvil, ultrasonic output (frequency, amplitude, output time), temperature, etc. The measured values ​​P2 of the measurement results may include a bonding strength, energy saving, processing volume per unit time, etc. Causes of variation in the measurement results are thought to include variation in the shape of the horn / anvil, changes in the horn / anvil, changes in the relative angle of the horn / anvil, etc.

[0123] In one example, the physical phenomenon may be the movement of a robot arm. In this example, the physical system may be a pneumatic actuator of the robot arm. That is, the present disclosure may be applied to the control of a pneumatic actuator of a robot arm. The control parameter P1 may include a valve opening, etc. The measurement value P2 of the measurement result may include a tip position of the robot arm, etc. Causes of variation in the measurement result are thought to include fluctuations in air pressure, air leaks, etc.

[0124] In one example, the physical phenomenon may be the temperature distribution in a given space or location. Here, the physical system can be considered to be the surrounding environment of the given space or location. In this case, the control parameter P1 may include a time series of the temperature up to the present in the surrounding environment, a time series of the humidity distribution up to the present, etc. The measurement value P2 of the measurement result may include the temperature 24 hours from now, the humidity distribution 24 hours from now, etc. Causes of the variation in the measurement results are thought to include the coarseness of the distribution of observation points, errors in the observation values, etc. This example makes it possible to predict the future temperature distribution.

[0125] Needless to say, the present disclosure can be applied to physical phenomena other than the above examples. In addition to the above examples, the present disclosure can also be applied to, for example, pulverization using various mills (such as ball mills), spray granulation, opposed granulation, rotary kneading, extrusion kneading, powder sintering, firing, ultrasonic bonding, pressure welding, thermal diffusion bonding, friction bonding, gas welding, arc welding, resistance welding, brazing, adhesive bonding using paste, fastening, casting, and injection molding. The above examples list factors that are thought to cause variability in measurement results. However, according to the present disclosure, such factors can be obtained as unobserved prior information parameters P3 without having to measure them in advance. Therefore, the present disclosure enables an improvement in the degree of freedom in the distribution of predicted values ​​of measurement results of physical phenomena, while eliminating the need to identify or measure in advance factors that are thought to cause variability in measurement results.

[0126] [3. Aspects] As is clear from the above-described embodiment and modifications, the present disclosure includes the following aspects.

[0127] [Aspect 1] A learning system comprising: an arithmetic circuit that can access a storage device that stores a machine learning model and a training dataset; wherein the training dataset includes a plurality of datasets, each of which includes control parameters of a physical system that generates a physical phenomenon and a measurement value of a measurement result of the physical phenomenon generated by the physical system to which the control parameters are applied; and wherein the arithmetic circuit adjusts parameters of the machine learning model for the plurality of datasets to generate trained parameters, and adjusts the additional parameters for each of the plurality of datasets to generate a plurality of trained additional parameters, so that an output value of the machine learning model when the control parameters and an additional parameter different from the control parameters are inputted approaches the measurement value.

[0128] [Aspect 2] The learning system according to aspect 1, wherein the additional parameter is set independently of the control parameter and represents the variability of the measurement values ​​for the same control parameter.

[0129] [Aspect 3] The learning system of Aspect 1 or 2, wherein the machine learning model is a first machine learning model, the storage device stores a second machine learning model separate from the first machine learning model, the first difference is a difference between an output of the first machine learning model and the measurement value, and the second difference is a difference between an output value of the second machine learning model when the additional parameter is input and the control parameter input to the first machine learning model together with the additional parameter, and the arithmetic circuit adjusts the parameter of the second machine learning model so that the second difference becomes smaller, and adjusts the additional parameter so that the first difference becomes smaller and the second difference becomes larger.

[0130] [Aspect 4] The learning system of Aspect 3, wherein the arithmetic circuit adjusts the parameters of the first machine learning model, the parameters of the second machine learning model, and the additional parameters so as to minimize a value of a loss function, the loss function being expressed as L1-L2, where L1 is a term representing the first difference, and L2 is a term representing the second difference.

[0131] [Aspect 5] The learning system according to any one of Aspects 1 to 4, wherein the number of the plurality of data sets is 1000 or less, and the number of the additional parameters is 2 or more and 20 or less.

[0132] [Aspect 6] A learning method executed by an arithmetic circuit that can access a storage device that stores a machine learning model and a learning dataset, wherein the learning dataset includes a plurality of datasets, each of which includes control parameters of a physical system that generates a physical phenomenon and a measurement value of a measurement result of the physical phenomenon generated by the physical system to which the control parameters are applied, and the learning method includes: adjusting parameters of the machine learning model for the plurality of datasets to generate learned parameters, and adjusting the additional parameters for each of the plurality of datasets to generate a plurality of learned additional parameters, so that an output of the machine learning model when the control parameters and an additional parameter other than the control parameters are inputted approaches the measurement value.

[0133] [Aspect 7] A program for causing the arithmetic circuit to execute the learning method of aspect 6.

[0134] [Aspect 8] An inference system comprising an arithmetic circuit that can access a storage device that stores a trained model and a plurality of trained additional parameters, wherein the trained model, when executed by the arithmetic circuit, operates the arithmetic circuit so that, in response to input of a control parameter of a physical system that generates a physical phenomenon and a trained additional parameter selected from the plurality of trained additional parameters, it outputs a predicted value of a measurement result of the physical phenomenon that will be generated by the physical system to which the control parameter is applied, and when a target control parameter is input, the arithmetic circuit executes the trained model to obtain the predicted value corresponding to two or more of the plurality of trained additional parameters for the target control parameter.

[0135] [Aspect 9] The inference system of aspect 8, wherein the arithmetic circuitry presents a distribution of the predicted values.

[0136] [Aspect 10] The inference system of aspect 8 or 9, wherein the trained model is obtained by training a machine learning model using a training dataset including a plurality of datasets each including the control parameter and measurement values ​​of the measurement results, and the number of predictions of the measurement results is equal to or less than the number of datasets.

[0137] [Aspect 11] The inference system of any one of Aspects 8 to 10, wherein the trained model is obtained by training a machine learning model using a training dataset including a plurality of datasets each including the control parameter and a measurement value of the measurement result, and the target control parameter is different from the control parameter included in the training dataset.

[0138] [Aspect 12] The inference system of any one of Aspects 8 to 11, wherein the trained model is obtained by training a machine learning model using a training dataset including a plurality of datasets each including the control parameter and a measurement value of the measurement result, and the plurality of trained additional parameters are generated by adjusting the additional parameters for each of the plurality of datasets so that an output of the machine learning model when the control parameter and an additional parameter other than the control parameter are inputted approaches the measurement value.

[0139] [Aspect 13] An inference method executed by an arithmetic circuit that can access a storage device that stores a trained model and a plurality of trained additional parameters, wherein the trained model, when executed by the arithmetic circuit, operates the arithmetic circuit so as to, in response to input of a control parameter of a physical system that generates a physical phenomenon and a trained additional parameter selected from the plurality of trained additional parameters, output a predicted value of a measurement result of the physical phenomenon that will be generated by the physical system to which the control parameter is applied, and wherein, when a target control parameter is input, the inference method executes the trained model to obtain the predicted values ​​that respectively correspond to two or more of the plurality of trained additional parameters for the target control parameter.

[0140] [Aspect 14] A program for causing the arithmetic circuit to execute the inference method of aspect 13.

[0141] [Aspect 15] A trained model that, when executed by an arithmetic circuit, operates the arithmetic circuit in response to input of control parameters of a physical system that generates a physical phenomenon and trained additional parameters, to output a predicted value of a measurement result of the physical phenomenon that the physical system generates to which the control parameters have been applied.

[0142] Aspects 2 to 5 and 9 to 12 are optional elements and are not essential.

[0143] [4. Terminology] In this disclosure, machine learning-related terms are defined and used as follows.

[0144] A "trained model" refers to an "inference program" that incorporates "trained parameters."

[0145] "Trained parameters" refer to parameters (coefficients) obtained as a result of learning using a training dataset. Trained parameters are generated by inputting the training dataset into a training program and mechanically adjusting them for a specific purpose. Although trained parameters are adjusted to suit the purpose of learning, they are simply parameters (numerical information, etc.) on their own, and only function as a trained model when incorporated into an inference program. For example, in the case of deep learning, the main trained parameters are parameters used to weight the links between each node.

[0146] An "inference program" is a program that can output a certain result for an input by applying built-in trained parameters. For example, it is a program that specifies a series of calculation procedures for applying trained parameters acquired as a result of training to an image given as input and outputting a result (authentication or judgment) for that image.

[0147] A "learning dataset," also known as a training dataset, refers to secondary processed data that is generated to facilitate analysis using the target learning method by converting and processing raw data through preprocessing such as removing missing values ​​and outliers, adding separate data such as label information (ground truth data), or a combination of these. A learning dataset may also include data that has been "padded" by applying certain transformations to the raw data.

[0148] "Raw data" refers to data that is primarily acquired by users, vendors, other businesses, research institutions, etc., and that has been converted and processed so that it can be loaded into a database.

[0149] A "learning program" is a program that executes an algorithm to find certain rules from a training dataset and generate a model that expresses those rules. Specifically, this refers to a program that specifies the procedures to be executed by a computer in order to realize learning using the adopted learning method.

[0150] The present disclosure is applicable to a learning system, a learning method, an inference system, an inference method, and a program. Specifically, the present disclosure is applicable to a learning system, a learning method, an inference system, an inference method, and a program related to a surrogate model for simulating a physical phenomenon.

[0151] 6 Storage device 7 Learning system 71 Arithmetic circuit 8 Inference system 81 Arithmetic circuit D1 Learning dataset P1 Control parameter P2 Measurement value P3 Unobserved prior information parameter (learned additional parameter) M1 Core model (learned model) M2 Submodel O1 Predicted value (predicted value of measurement result) O2 Predicted value (predicted value of control parameter)

Claims

1. A learning system comprising: an arithmetic circuit that can access a storage device that stores a machine learning model and a training dataset; wherein the training dataset includes a plurality of datasets, each of which includes control parameters of a physical system that generates a physical phenomenon and a measurement value of a measurement result of the physical phenomenon generated by the physical system to which the control parameters are applied; and wherein the arithmetic circuit adjusts the parameters of the machine learning model for the plurality of datasets to generate trained parameters, and adjusts the additional parameters for each of the plurality of datasets to generate a plurality of trained additional parameters, so that an output value of the machine learning model when the control parameters and an additional parameter other than the control parameters are inputted approaches the measurement value.

2. The learning system according to claim 1, wherein the additional parameter is set independently of the control parameter and represents the variability of the measurement values ​​for the same control parameter.

3. The learning system of claim 1, wherein the machine learning model is a first machine learning model, and a first difference is the difference between the output of the first machine learning model and the measurement value, and the storage device stores a second machine learning model separate from the first machine learning model, and the first difference is the difference between the output of the first machine learning model and the measurement value, and the second difference is the difference between the output value of the second machine learning model when the additional parameter is input and the control parameter input to the first machine learning model together with the additional parameter, and the arithmetic circuit adjusts the parameters of the second machine learning model so that the second difference becomes smaller, and adjusts the additional parameter so that the first difference becomes smaller and the second difference becomes larger.

4. The learning system of claim 3, wherein the arithmetic circuit adjusts the parameters of the first machine learning model, the parameters of the second machine learning model, and the additional parameters so as to minimize the value of a loss function, the loss function being represented by L1-L2, L1 being a term representing the first difference, and L2 being a term representing the second difference.

5. The learning system of claim 1, wherein the number of the plurality of data sets is 1,000 or less, and the number of the additional parameters is 2 or more and 20 or less.

6. A learning method executed by an arithmetic circuit that can access a storage device that stores a machine learning model and a learning dataset, wherein the learning dataset includes a plurality of datasets, each of which includes control parameters of a physical system that generates a physical phenomenon and a measurement value of a measurement result of the physical phenomenon generated by the physical system to which the control parameters are applied, and the learning method comprises: adjusting the parameters of the machine learning model for the plurality of datasets to generate learned parameters, and adjusting the additional parameters for each of the plurality of datasets to generate a plurality of learned additional parameters, so that when the control parameters and an additional parameter different from the control parameters are input, the output of the machine learning model approaches the measurement value.

7. A program for causing the arithmetic circuit to execute the learning method of claim 6.

8. An inference system comprising an arithmetic circuit capable of accessing a storage device that stores a trained model and a plurality of trained additional parameters, wherein the trained model, when executed by the arithmetic circuit, operates the arithmetic circuit so that, in response to input of a control parameter of a physical system that generates a physical phenomenon and a trained additional parameter selected from the plurality of trained additional parameters, it outputs a predicted value of the measurement result of the physical phenomenon generated by the physical system to which the control parameter is applied, and when a target control parameter is input, the arithmetic circuit executes the trained model to obtain the predicted value corresponding to two or more of the plurality of trained additional parameters for the target control parameter.

9. The inference system of claim 8, wherein the calculation circuitry provides a distribution of the predicted values.

10. The inference system of claim 8, wherein the trained model is obtained by training a machine learning model using a training dataset including a plurality of datasets including the control parameters and measurement values ​​of the measurement results, and the number of predictions of the measurement results is less than or equal to the number of the plurality of datasets.

11. The inference system of claim 8, wherein the trained model is obtained by training a machine learning model using a training dataset including multiple datasets each including the control parameter and a measurement value of the measurement result, and the target control parameter is different from the control parameter included in the training dataset.

12. The inference system of claim 8, wherein the trained model is obtained by training a machine learning model using a training dataset including multiple datasets each including the control parameter and a measurement value of the measurement result, and the multiple trained additional parameters are generated by adjusting the additional parameters for each of the multiple datasets so that the output of the machine learning model when the control parameter and an additional parameter other than the control parameter are input approaches the measurement value.

13. An inference method executed by an arithmetic circuit that can access a storage device that stores a trained model and a plurality of trained additional parameters, wherein the trained model, when executed by the arithmetic circuit, operates the arithmetic circuit so that, in response to input of a control parameter of a physical system that generates a physical phenomenon and a trained additional parameter selected from the plurality of trained additional parameters, it outputs a predicted value of the measurement result of the physical phenomenon generated by the physical system to which the control parameter is applied, and when a target control parameter is input, the inference method executes the trained model to obtain the predicted value corresponding to two or more of the plurality of trained additional parameters for the target control parameter.

14. A program for causing the arithmetic circuit to execute the inference method of claim 13.

15. A trained model that, when executed by an arithmetic circuit, operates the arithmetic circuit to output, in response to input of control parameters of a physical system that generates a physical phenomenon and trained additional parameters, a predicted value of the measurement result of the physical phenomenon that the physical system generates when the control parameters are applied.

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