Support method, recording medium, support program, and support system

Abstract

To provide a support method capable of easily controlling a trade-off between an expected value and a variance of an objective variable.SOLUTION: A support method includes: a coefficient setting process (step S3) of receiving setting of a value of a risk aversion coefficient α included in a heteroscedasticity acquisition function AF; and a process (step S4) of executing heteroscedasticity Bayesian optimization on the basis of a first predictive distribution f that is a predictive distribution of an expected value of an objective variable, a second predictive distribution g that is a predictive distribution of variance of the objective variable, the heteroscedasticity acquisition function AF, and an exploration range, to acquire, from within the exploration range, a recommended value of an explanatory variable that maximizes the heteroscedasticity acquisition function AF. The heteroscedasticity acquisition function AF indicates a function in which the larger the value of the risk aversion coefficient α becomes, the higher the proportion of acquiring the recommended value from a region with a smaller variance of the objective variable. The coefficient setting process (step S3) includes a process of setting the value of the risk aversion coefficient α on the basis of a position of a slider 201 operable by an operator.SELECTED DRAWING: Figure 3

Description

[Technical Field]

[0001] The present invention relates to an assistance method, a recording medium, an assistance program, and an assistance system. [Background technology]

[0002] A technique is known in which Bayesian optimization is performed on a data set in which explanatory variables and objective variables are associated, and the value of the explanatory variable that optimizes (minimizes or maximizes) the value of the objective variable is estimated (see, for example, Patent Document 1). Specifically, a machine learning model is made to learn the data set (machine learning), and a predictive distribution (posterior distribution) of the objective variable is output from the machine learning model. Then, based on the predictive distribution of the objective variable, an acquisition function, and a search range, values ​​(recommended values) of the explanatory variables that maximize the acquisition function are searched for within the search range as candidates for the optimal solution.

[0003] Incidentally, the values ​​of the objective variable (observed values) obtained through an experiment may differ from experiment to experiment, even when the same values ​​of the explanatory variables (same experimental conditions) are used. In other words, the values ​​of the objective variable (observed values) obtained through an experiment contain observation noise. The variance of the observation noise added to the values ​​of the objective variable (observed values) may differ depending on the values ​​of the explanatory variables. In other words, the values ​​of the objective variable (observed values) obtained through an experiment may exhibit heteroscedasticity. In this case, it is necessary to perform Bayesian optimization that takes into account the heteroscedasticity of the values ​​of the objective variable (observed values) contained in the dataset. This type of Bayesian optimization is called heteroscedastic Bayesian optimization.

[0004] When the values ​​(observed values) of the objective variable show heteroscedasticity, a trade-off may exist between the expected value (predicted value) of the objective variable and the predicted variance of the objective variable. For example, when performing Bayesian optimization with the goal of minimizing the objective variable, recommended values ​​of explanatory variables that minimize the expected value (predicted value) of the objective variable may increase the variance of the objective variable, while recommended values ​​of explanatory variables that reduce the variance of the objective variable may increase the expected value (predicted value) of the objective variable.

[0005] Therefore, heteroscedastic Bayesian optimization uses an acquisition function that includes a risk aversion coefficient to search for optimal solution candidates while avoiding areas where variance is predicted to be large. The larger the value of the risk aversion coefficient, the more aggressively areas where variance is predicted to be large are avoided when searching for optimal solution candidates. The smaller the value of the risk aversion coefficient, the more aggressively areas where variance is predicted to be large are avoided when searching for optimal solution candidates. The operator sets the value of the risk aversion coefficient when performing heteroscedastic Bayesian optimization. [Prior art documents] [Patent documents]

[0006] [Patent Document 1] Japanese Patent Application Publication No. 2023-174450 Summary of the Invention [Problem to be solved by the invention]

[0007] However, it is not possible to unequivocally determine how large the value of the risk aversion coefficient should be to actively avoid areas where variance is predicted to be large. In addition, the scale of the objective variable and variance differs for each object to be optimized. Therefore, a constant value cannot be used for the risk aversion coefficient. Therefore, it is not easy to control the tradeoff between the expected value and variance of the objective variable.

[0008] The present invention has been made in view of the above-mentioned problems, and an object of the present invention is to provide an assistance method, a recording medium, an assistance program, and an assistance system that can easily control the trade-off between the expected value and the variance of a response variable. [Means for solving the problem]

[0009] According to one aspect of the present invention, a support method is a method for supporting a search for explanatory variable values ​​that maximize or minimize the expected value of a dependent variable. The support method includes the steps of: causing a first machine learning model capable of outputting a predictive distribution to output a first predictive distribution, which is a predictive distribution of the expected value of the dependent variable; causing a second machine learning model capable of outputting a predictive distribution to output a second predictive distribution, which is a predictive distribution of the variance of the dependent variable; a coefficient setting step of accepting a value of a risk aversion coefficient included in a heteroscedastic acquisition function; and performing heteroscedastic Bayesian optimization based on the first predictive distribution, the second predictive distribution, the heteroscedastic acquisition function for which the risk aversion coefficient value has been set in the coefficient setting step, and a search range to obtain recommended values ​​of the explanatory variables within the search range that maximize the heteroscedastic acquisition function. The heteroscedastic acquisition function indicates a function in which the larger the value of the risk aversion coefficient, the more likely the recommended value is obtained from a region with a smaller variance of the dependent variable. The coefficient setting step includes a step of setting the value of the risk aversion coefficient based on the position of a slider that can be operated by an operator.

[0010] In one embodiment, when setting the value of the risk aversion coefficient, a truncated normal distribution corresponding to the position of the slider is created, and the value of the risk aversion coefficient is set based on values ​​randomly sampled from the truncated normal distribution.

[0011] In one embodiment, the slider is movable between a first position where a value on the first scale is greater than 0 and a second position where a value on the first scale is less than 1. When setting the value of the risk aversion coefficient, the closer the position of the slider is to the second position, the greater the value to which the risk aversion coefficient is set.

[0012] In one embodiment, when assisting in a search for a value of the explanatory variable that minimizes the expected value of the dependent variable, the coefficient setting step includes the steps of: displaying the slider, the first scale, a first object indicating a virtual range corresponding to a range of possible values ​​of the dependent variable, a second scale indicating a virtual expected value corresponding to the expected value, and a second object indicating one of the values ​​included on the second scale; shortening a length of the first object as the slider approaches the second position and moving the second object to a position corresponding to a larger value among the positions corresponding to the values ​​included on the second scale; and when assisting in a search for a value of the explanatory variable that maximizes the expected value of the dependent variable, the coefficient setting step includes the steps of displaying the slider, the first scale, the first object, the second scale, and the second object; and shortening a length of the first object as the slider approaches the second position and moving the second object to a position corresponding to a smaller value among the positions corresponding to the values ​​included on the second scale.

[0013] According to another aspect of the present invention, a recording medium is a computer-readable medium, and stores an assistance program that defines the above-described assistance method.

[0014] According to yet another aspect of the present invention, an assistance program is a computer program executable by a computer, and defines the assistance method described above.

[0015] According to yet another aspect of the present invention, an assistance system is a system for assisting in the search for explanatory variable values ​​that maximize or minimize the expected value of a dependent variable. The assistance system includes a storage unit, a display unit, an operation unit, and a processing unit. The storage unit stores a first machine learning model capable of outputting a predictive distribution, a second machine learning model capable of outputting a predictive distribution, and a heteroscedastic acquisition function. The display unit displays a slider. The operation unit accepts operation of the slider by an operator. The processing unit causes the first machine learning model to output a first predictive distribution, which is a predictive distribution of the expected value of the dependent variable, and causes the second machine learning model to output a second predictive distribution, which is a predictive distribution of the variance of the dependent variable. Furthermore, the processing unit sets a value of a risk aversion coefficient included in the heteroscedastic acquisition function based on the position of the slider. Furthermore, the processing unit performs heteroscedastic Bayesian optimization based on the first predictive distribution, the second predictive distribution, the heteroscedastic acquisition function in which the value of the risk aversion coefficient is set based on the position of the slider, and a search range to obtain recommended values ​​of the explanatory variables that maximize the heteroscedastic acquisition function from within the search range. The heteroscedastic acquisition function indicates a function in which the larger the value of the risk aversion coefficient, the higher the rate at which the recommended values ​​are obtained from an area with smaller variances.

[0016] In one embodiment, when setting the value of the risk aversion coefficient, the processing unit creates a truncated normal distribution corresponding to the position of the slider, and sets the value of the risk aversion coefficient based on values ​​randomly sampled from the truncated normal distribution.

[0017] In one embodiment, the display unit further displays a first scale, and the slider moves, in response to operation of the operation unit by the worker, between a first position where the first scale indicates a value greater than 0 and a second position where the first scale indicates a value less than 1. When setting the value of the risk aversion coefficient, the processing unit sets the risk aversion coefficient to a larger value the closer the position of the slider is to the second position.

[0018] In one embodiment, the display unit further displays a first object indicating a virtual range corresponding to a range of possible values ​​of the objective variable, a second scale indicating a virtual expected value corresponding to the expected value, and a second object indicating one of the values ​​included on the second scale. When assisting in a search for a value of the explanatory variable that minimizes the expected value of the objective variable, the processing unit shortens the length of the first object and moves the second object to a position corresponding to a larger value among the positions corresponding to the values ​​included on the second scale as the slider position is closer to the second position. When assisting in a search for a value of the explanatory variable that maximizes the expected value of the objective variable, the processing unit shortens the length of the first object and moves the second object to a position corresponding to a smaller value among the positions corresponding to the values ​​included on the second scale as the slider position is closer to the second position. [Effects of the Invention]

[0019] According to the assistance method, recording medium, assistance program, and assistance system of the present invention, it is possible to easily control the trade-off between the expected value and variance of the response variable. [Brief explanation of the drawings]

[0020] [Figure 1] 1 is a block diagram showing a configuration of a support system according to a first embodiment of the present invention. [Figure 2] FIG. 10 is a diagram illustrating an example of a predicted distribution of an expected value and a variance of a dependent variable. [Figure 3] 1 is a flowchart showing a support method according to the first embodiment of the present invention. [Figure 4] 1 is a diagram showing the procedure of an experiment using the assistance method, recording medium, assistance program, and assistance system according to the first embodiment of the present invention. [Figure 5] 10(a) to 10(c) are diagrams showing an example of a coefficient setting screen displayed on a display unit. [Figure 6]FIG. 10 is a block diagram showing the configuration of a support system according to a second embodiment of the present invention. [Figure 7] FIG. 10 is a schematic diagram of a substrate processing system including a support system according to a third embodiment of the present invention. [Figure 8] FIG. 10 is a block diagram showing the configuration of a support system according to a third embodiment of the present invention. [Figure 9] FIG. 10 is a block diagram showing the configuration of a support system according to a fourth embodiment of the present invention. [Figure 10] 1(a) to 1(c) are diagrams showing an example of a truncated normal distribution. [Figure 11] 10 is a flowchart showing a coefficient setting process included in a support method according to a fourth embodiment of the present invention. [Figure 12] 10 is a flowchart showing an example of a coefficient setting step included in a support method according to a fourth embodiment of the present invention. DETAILED DESCRIPTION OF THE INVENTION

[0021] Hereinafter, embodiments of the recording medium, assistance program, and assistance system of the present invention will be described with reference to the drawings (FIGS. 1 to 12). However, the present invention is not limited to the following embodiments, and can be implemented in various forms without departing from the spirit of the present invention. Note that duplicated explanations may be omitted as appropriate. In addition, the same or equivalent parts in the drawings will be designated by the same reference numerals, and explanations will not be repeated.

[0022] [Embodiment 1] First, referring to FIG. 1, a recording medium 200, an assistance program SP, and an assistance system 100A according to this embodiment will be described. FIG. 1 is a block diagram showing the configuration of the assistance system 100A according to this embodiment. The assistance system 100A is a system that assists in the search for explanatory variable values ​​(recommended or candidate values) that optimize (maximize or minimize) the expected value (predicted value) of a target variable. As shown in FIG. 1, the assistance system 100A according to this embodiment includes a terminal device 101A. The assistance program SP is installed in the terminal device 101A from the recording medium 200. The terminal device 101A executes the assistance program SP installed from the recording medium 200 to search for explanatory variable values ​​that optimize the expected value of the target variable. The terminal device 101A is an example of an "assistance device." The terminal device 101A may be, for example, a general-purpose computer or a dedicated computer.

[0023] Specifically, the recording medium 200 is a medium that can be read by a computer. A program (computer program) to be executed by a computer is non-temporarily recorded on the recording medium 200. The recording medium 200 records an assistance program SP. In other words, the recording medium 200 stores the assistance program SP. The assistance program SP is a computer program that can be executed by a computer.

[0024] The recording medium 200 may be, for example, a medium including a semiconductor memory such as an SD memory card or a USB (Universal Serial Bus) memory, or a medium including a magnetic disk such as a hard disk drive. Alternatively, the recording medium 200 may be an optical disk such as a CD (Compact Disk), a DVD (Digital Versatile Disk), or a Blu-ray disk, or may be a main memory device or an auxiliary memory device installed in another computer system.

[0025] The assistance program SP includes a first machine learning model ML1, a second machine learning model ML2, and a heteroscedastic Bayesian optimization program BP. In this embodiment, the assistance program SP further includes a preprocessing program FP.

[0026] The first machine learning model ML1 includes a model capable of outputting a predictive distribution. The first machine learning model ML1 learns (machine learns) a data set (learning data) in which a dependent variable and an explanatory variable are associated with each other, and outputs a predictive distribution of the expected value of the dependent variable.

[0027] The second machine learning model ML2 includes a model capable of outputting a predictive distribution. The second machine learning model ML2 learns (machine learns) a dataset (learning data) in which the variance of the dependent variable and the explanatory variables are associated, and outputs a predictive distribution of the variance of the dependent variable.

[0028] The algorithm of the first machine learning model ML1 is not particularly limited as long as it includes an algorithm capable of outputting a predictive distribution. The first machine learning model ML1 may include, for example, a Gaussian process regression model. Similarly, the algorithm of the second machine learning model ML2 is not particularly limited as long as it includes a model capable of outputting a predictive distribution. The second machine learning model ML2 may include, for example, a Gaussian process regression model.

[0029] The heteroscedastic Bayesian optimization program BP includes a computer program that performs heteroscedastic Bayesian optimization based on the predictive distribution output from the first machine learning model ML1, the predictive distribution output from the second machine learning model ML2, the heteroscedastic acquisition function AF, and a search range, and outputs values ​​(recommended values ​​or candidate values) of explanatory variables that maximize the heteroscedastic acquisition function AF.

[0030] The preprocessing program FP includes a computer program that performs preprocessing on a dataset (training data). In this embodiment, the dataset (training data) preprocessed by the preprocessing program FP is input to a first machine learning model ML1. Similarly, the dataset (training data) preprocessed by the preprocessing program FP is input to a second machine learning model ML2.

[0031] The terminal device 101A includes an operation unit 102, a display unit 103, an interface unit 104, a storage unit 105, and a processing unit .

[0032] The operation unit 102 includes a user interface device operated by the worker. The operation unit 102 inputs a signal according to the operation of the worker to the processing unit 106. The operation unit 102 may include, for example, a keyboard, a mouse, and a touch sensor. The touch sensor may be superimposed on the display surface of the display unit 103. A graphical user interface may be configured by superimposing the touch sensor on the display surface of the display unit 103. For example, the worker can operate the operation unit 102 to instruct the installation of the assistance program SP. The worker can also operate the operation unit 102 to instruct the execution of the assistance program SP.

[0033] The display unit 103 is controlled by the processing unit 106 to display various screens. For example, the display unit 103 may display the source code of the assistance program SP. For example, while the source code of the assistance program SP is displayed on the display unit 103, the operator can operate the operation unit 102 to set a dataset to be learned by the first machine learning model ML1. The display unit 103 includes a display device such as a liquid crystal display device or an organic electroluminescence (EL) display device.

[0034] The interface unit 104 exchanges information, data, or signals with the recording medium 200. Specifically, the interface unit 104 reads out the assistance program SP from the recording medium 200. The assistance program SP read out from the recording medium 200 is stored in the memory unit 105 by the processing unit 106. As a result, the assistance program SP is installed in the terminal device 101A.

[0035] For example, the interface unit 104 may be electrically connected to the recording medium 200 to input and output information, data, or signals to and from the recording medium 200. Specifically, the interface unit 104 may include a slot or a USB terminal. A card-shaped information carrier such as an SD memory card may be inserted into the slot. A USB memory may be inserted into the USB terminal, or the other end of a USB cable, one end of which is electrically connected to a hard disk drive, may be inserted into the USB terminal. Alternatively, the interface unit 104 may include an optical disc drive. The optical disc drive reads information (data) from a CD, DVD, or Blu-ray disc.

[0036] The storage unit 105 has a main storage device. The main storage device includes, for example, a semiconductor memory. The storage unit 105 may further include an auxiliary storage device. The auxiliary storage device includes, for example, at least one of a semiconductor memory and a hard disk drive. The storage unit 105 stores various computer programs and various data. Specifically, the storage unit 105 stores first learning data LD1 and second learning data LD2. The storage unit 105 also stores an assistance program SP installed from the recording medium 200. In other words, the assistance program SP is non-temporarily recorded in the storage unit 105. The storage unit 105 is a recording medium that non-temporarily records the assistance program SP.

[0037] The first training data LD1 is a data set used for training the first machine learning model ML1. Specifically, the first training data LD1 includes a data set that associates a response variable with an explanatory variable.

[0038] For example, when using the assistance program SP to find an optimal solution for at least one of various parameters that define the operation of a substrate processing apparatus, the objective variable may be the particle count or an evaluation index value of the etching profile. In this case, the operator repeats an experiment in which the substrate processing apparatus processes multiple substrates multiple times while changing the parameter values ​​(experimental conditions) that are explanatory variables, and obtains the particle count or etching profile evaluation index value that is the objective variable for each substrate. Then, a data set (first learning data LD1) is created that associates the particle count or etching profile evaluation index value for each substrate with the corresponding parameter value (corresponding experimental condition).

[0039] The second training data LD2 is a data set used for training the second machine learning model ML2. Specifically, the second training data LD2 includes a data set that associates the variance of a dependent variable with an explanatory variable. Specifically, each value of the explanatory variable is associated with a corresponding value of one or more dependent variables.

[0040] For example, when the objective variable is the particle count or the evaluation index value of the etching profile, even if a substrate processing apparatus processes multiple substrates using a certain parameter value, the particle count or the evaluation index value of the etching profile will differ for each substrate. That is, the particle count or the evaluation index value of the etching profile will be dispersed. Furthermore, the degree of variation in the particle count or the evaluation index value of the etching profile will differ for each parameter value. That is, the particle count or the evaluation index value of the etching profile will exhibit heteroscedasticity. The operator creates a data set (second learning data LD2) that associates each parameter value with the corresponding particle count dispersion or etching profile evaluation index value dispersion.

[0041] The processing unit 106 includes a processor. The processing unit 106 may include, for example, a central processing unit (CPU), a graphics processing unit (GPU), a neural network processing unit (NPU), or a quantum computer. Alternatively, the processing unit 106 may include a general-purpose computing device or a dedicated computing device. For example, the processing unit 106 may include a field-programmable gate array (FPGA) or an application-specific integrated circuit (ASIC).

[0042] The processing unit 106 performs various processes such as numerical calculations, information processing, and device control by executing computer programs stored in the storage unit 105 based on instructions from an operator input via the operation unit 102. For example, the processing unit 106 reads out an assistance program SP from the recording medium 200 via the interface unit 104 and stores the assistance program SP in the storage unit 105. The processing unit 106 also executes the assistance program SP.

[0043] Next, heteroscedasticity of a dependent variable will be described with reference to FIG. 2. FIG. 2 is a diagram illustrating an example of a predictive distribution of the expected value and variance of a dependent variable. In FIG. 2, the horizontal axis represents the dependent variable. The vertical axis represents the dependent variable. The variance of the dependent variable illustrated in FIG. 2 indicates heteroscedasticity. Specifically, the variance of the dependent variable includes variance expressed by standard deviation (episodic uncertainty) and variance expressed by noise (aleatoric uncertainty). The magnitude of variance expressed by standard deviation is constant for each value of the dependent variable. In contrast, noise occurs for some values ​​of the dependent variable. Furthermore, the magnitude of noise differs between certain values ​​of the dependent variable and other values. As a result, for example, when minimizing a dependent variable, a value of the dependent variable that minimizes the expected value of the dependent variable may increase the variance of the dependent variable, while a value of the dependent variable that reduces the variance of the dependent variable may increase the expected value of the dependent variable.

[0044] Next, the assistance method, recording medium 200, assistance program SP, and assistance system 100A of this embodiment will be described with reference to Figures 1 to 3. Figure 3 is a flowchart showing the assistance method of this embodiment. Here, the assistance method refers to a method for assisting in the search for values ​​(recommended values ​​or candidate values) of explanatory variables that optimize (maximize or minimize) the expected value of a target variable. As shown in Figure 3, the assistance method of this embodiment includes steps S1 to S5.

[0045] The assistance method of this embodiment is executed, for example, by the terminal device 101A included in the assistance system 100A described with reference to Fig. 1. More specifically, the assistance method shown in Fig. 3 is executed by the terminal device 101A executing the assistance program SP read from the recording medium 200. In this case, the flowchart shown in Fig. 3 corresponds to the flow of processing executed by the processing unit 106 included in the terminal device 101A. In other words, Fig. 3 shows the processing executed by the processing unit 106 included in the assistance system 100A of this embodiment.

[0046] The process (assistance method) shown in Fig. 3 starts when the operator operates the operation unit 102 to instruct execution of the assistance program SP. When the process shown in Fig. 3 starts, the processing unit 106 causes the first machine learning model ML1 to learn (machine learn) the first learning data LD1 and outputs a predictive distribution of the expected value of the dependent variable from the first machine learning model ML1 (step S1). The predictive distribution output from the first machine learning model ML1 indicates the predictive distribution of the expected value and standard deviation of the dependent variable described with reference to Fig. 2. Hereinafter, the predictive distribution output from the first machine learning model ML1 may be referred to as the "first predictive distribution f."

[0047] Specifically, the operator operates the operation unit 102 to specify (set) the first training data LD1 as a data set to be trained by the first machine learning model ML1. Then, the operator operates the operation unit 102 to instruct training of the first training data LD1. The processing unit 106 executes the preprocessing program FP in response to the operator's instruction. As a result, preprocessing is performed on the first training data LD1. Specifically, the values ​​of the explanatory variables included in the first training data LD1 are normalized so that they fall within the range of 0 to 1. In addition, the objective variable is standardized. The processing unit 106 trains (machines learns) the preprocessed first training data LD1 in the first machine learning model ML1. As a result, the first predictive distribution f is output from the first machine learning model ML1 and stored in the storage unit 105.

[0048] Furthermore, the processing unit 106 causes the second machine learning model ML2 to learn (machine learn) the second learning data LD2, and causes the second machine learning model ML2 to output a predictive distribution of the variance of the dependent variable (step S2). The predictive distribution output from the second machine learning model ML2 represents the predictive distribution of the standard deviation and noise of the dependent variable described with reference to FIG. 2. Hereinafter, the predictive distribution output from the second machine learning model ML2 may be referred to as the "second predictive distribution g."

[0049] Specifically, the operator operates the operation unit 102 to specify (set) the second training data LD2 as a data set to be trained by the second machine learning model ML2. Then, the operator operates the operation unit 102 to instruct training of the second training data LD2. The processing unit 106 executes the preprocessing program FP in response to the operator's instruction. As a result, preprocessing is performed on the second training data LD2. Specifically, the values ​​of the explanatory variables included in the second training data LD2 are normalized so that they fall within the range of 0 to 1. In addition, the objective variable is standardized. The processing unit 106 trains (machines trains) the preprocessed second training data LD2 in the second machine learning model ML2. As a result, the second predictive distribution g is output from the second machine learning model ML2 and stored in the storage unit 105.

[0050] The order of execution of the first learning process (step S1) in which the first machine learning model ML1 learns the first training data LD1 and the second learning process (step S2) in which the second machine learning model ML2 learns the second training data LD2 can be reversed. Alternatively, the first learning process (step S1) and the second learning process (step S2) may be executed in parallel. In this case, the operator operates the operation unit 102 to instruct learning of the first training data LD1 and the second training data LD2.

[0051] After acquiring the first predictive distribution f and the second predictive distribution g, the processing unit 106 accepts a setting of the value of the risk aversion coefficient α included in the heteroscedastic acquisition function AF, and sets the accepted value to the risk aversion coefficient α (step S3). Specifically, as will be described later with reference to FIGS. 5(a) to 5(c), the processing unit 106 sets the value of the risk aversion coefficient α based on the position of the slider 201. Note that the order of executing the coefficient setting step (step S3) is not limited to after acquiring the first predictive distribution f and the second predictive distribution g. The value of the risk aversion coefficient α may be set before executing heteroscedastic Bayesian optimization.

[0052] Here, the heteroscedastic acquisition function AF and the risk aversion coefficient α will be described. The risk aversion coefficient α is a parameter that controls the trade-off between the expected value and variance of the dependent variable. Specifically, the heteroscedastic acquisition function AF indicates a function in which the larger the value of the risk aversion coefficient α, the higher the rate at which recommended values ​​(or candidate values) of the dependent variables are obtained from areas where the variance of the dependent variable is smaller. Therefore, the larger the value of the risk aversion coefficient α, the more actively regions where variance is predicted to be large are avoided, and values ​​(recommended values ​​or candidate values) of the dependent variables that optimize the dependent variable are searched for. Furthermore, the smaller the value of the risk aversion coefficient α, the more passively regions where variance is predicted to be large are avoided, and values ​​(recommended values ​​or candidate values) of the dependent variables that optimize the dependent variable are searched for.

[0053] For example, the assistance program SP (heterogeneous Bayesian optimization program BP) may include a heterogeneous acquisition function AF defined by the following formula (1). Formula (1) shows the heterogeneous acquisition function AF defined based on an upper confidence bound (UCB) and a lower confidence bound (LCB). In the heterogeneous acquisition function AF in formula (1), the first term UCB shows the acquisition function for the first predictive distribution f. The second term LCB shows the acquisition function for the second predictive distribution g. In formula (1), the risk aversion coefficient α is used as the coefficient of the second term.

number

[0054] Alternatively, the support program SP (heterogeneous Bayesian optimization program BP) may include a heterogeneous acquisition function AF defined by the following formula (2). Formula (2) shows the heterogeneous acquisition function AF defined based on the expected improvement (EI). In the heterogeneous acquisition function AF of formula (2), the first term EI shows the acquisition function for the first predictive distribution f. The following formula (3) included in the second term shows the expected value of the second predictive distribution g. In formula (2), the risk aversion coefficient α is used as the coefficient of the second term.

number

number

[0055] The assistance program SP may include one heteroscedasticity acquisition function AF or multiple types of heteroscedasticity acquisition functions AF. If the assistance program SP includes multiple types of heteroscedasticity acquisition functions AF, the operator operates the operation unit 102 to set the type of heteroscedasticity acquisition function AF to be used this time in the source code of the assistance program SP before performing heteroscedasticity Bayesian optimization.

[0056] After setting the value of the risk aversion coefficient α, the processing unit 106 executes the heteroscedastic Bayesian optimization program BP (step S4). Specifically, the processing unit 106 executes heteroscedastic Bayesian optimization based on the first predictive distribution f, the second predictive distribution g, the heteroscedastic acquisition function AF for which the value of the risk aversion coefficient α was set in the coefficient setting step (step S3), and the search range, and acquires values ​​(recommended values ​​or candidate values) of the explanatory variables that maximize the heteroscedastic acquisition function AF from within the search range. Note that, before executing the heteroscedastic Bayesian optimization, the operator operates the operation unit 102 to set values ​​of the search range in the source code of the assistance program SP.

[0057] Finally, the processing unit 106 causes the display unit 103 to display the recommended values ​​(or candidate values) of the explanatory variables obtained by performing the heteroscedastic Bayesian optimization (step S5), and ends the processing (assistance method) shown in Fig. 3. More specifically, the processing unit 106 may cause the display unit 103 to display a graph of the first predictive distribution f and a graph of the second predictive distribution g, together with the recommended values ​​of the explanatory variables. Alternatively, the processing unit 106 may cause the display unit 103 to display each of the graphs of the first predictive distribution f, the second predictive distribution g, and the heteroscedastic acquisition function A F, together with the recommended values ​​of the explanatory variables.

[0058] By displaying the graph of the first predictive distribution f and the graph of the second predictive distribution g on the display unit 103, the operator can more easily determine the value of the risk aversion coefficient α to be set when heteroscedastic Bayesian optimization is next performed. Specifically, the outlines of the graphs of the first predictive distribution f and the second predictive distribution g change as the experiment is repeated. Therefore, the operator can visually confirm the magnitude of the variance of the objective variable by repeating the experiment. Therefore, by checking the graph of the first predictive distribution f and the graph of the second predictive distribution g, the operator can determine whether to more aggressively avoid areas where variance is predicted to be large when heteroscedastic Bayesian optimization is next performed.

[0059] Next, the procedure of an experiment using the assistance method, recording medium 200, assistance program SP, and assistance system 100A of this embodiment will be described with reference to Fig. 4. Fig. 4 is a diagram showing the procedure of an experiment using the assistance method, recording medium 200, assistance program SP, and assistance system 100A of this embodiment.

[0060] The experimental procedure shown in Fig. 4 is started after executing the support method shown in Fig. 3. As shown in Fig. 4, the operator performs an experiment using recommended values ​​(currently recommended values) of explanatory variables obtained by executing the support method shown in Fig. 3 (step S11), and obtains the experimental results (values ​​of the objective variables) (step S12). Then, the operator determines whether the experimental results (values ​​of the objective variables) are optimal values ​​(maximum or minimum values) (step S13).

[0061] If the operator determines that the experimental results are not optimal (No in step S13), he or she updates the first learning data LD1 and the second learning data LD2 using the values ​​of the explanatory variables used in the current experiment (current recommended values) and the current experimental results (values ​​of the objective variables) (step S14), and re-executes the support method described with reference to Fig. 3. Then, the operator repeats updating the first learning data LD1 and the second learning data LD2 (step S14), the support method described with reference to Fig. 3, and the experiment (steps S11 and S12) until he or she determines that the experimental results are optimal.

[0062] If the operator determines that the experimental result is an optimal value (Yes in step S13), the operator ends the experiment. For example, the operator may end the experiment when the operator determines that the experimental result has converged to a value within the target range.

[0063] Next, the coefficient setting step (step S3) shown in Fig. 3 will be described with reference to Fig. 1, Fig. 3, and Fig. 5(a) to Fig. 5(c). Fig. 5(a) to Fig. 5(c) are diagrams showing an example of a coefficient setting screen GA displayed on the display unit 103. In detail, Fig. 5(a) to Fig. 5(c) show the coefficient setting screen GA displayed on the display unit 103 when supporting a search for values ​​of explanatory variables that minimize the expected value of a target variable.

[0064] 5(a), in the coefficient setting step (step S3), the processing unit 106 displays a coefficient setting screen GA on the display unit 103. A slider 201 is displayed on the coefficient setting screen GA. In other words, the display unit 103 displays the slider 201.

[0065] The operation unit 102 described with reference to FIG. 1 further receives an operation of the slider 201. The worker can operate the slider 201 via the operation unit 102. Specifically, the operation unit 102 receives a slide operation of the slider 201. The worker can slide the slider 201 by operating the operation unit 102. In other words, the worker can change the position of the slider 201 by operating the operation unit 102. The processing unit 106 sets the value of the risk aversion coefficient α based on the position of the slider 201.

[0066] For example, the processing unit 106 may set the value of the risk aversion coefficient α based on the position of the slider 201 and the following formula (4). In formula (4), β is a parameter indicating the ratio of consideration of the variance of the objective variable to the expected value of the objective variable. In other words, β is a parameter indicating which of the expected value and the variance is to be emphasized. Hereinafter, β may be referred to as a "ratio parameter β." Note that, because the ratio parameter β is a parameter indicating a ratio, it indicates a value greater than 0 and less than 1 (0<β<1). Risk aversion coefficient α=β / (1-β) (4)

[0067] More specifically, the position of the slider 201 and the value of the ratio parameter β are associated with each other, and the processing unit 106 changes the value of the ratio parameter β in accordance with changes in the position of the slider 201. The processing unit 106 acquires the value of the ratio parameter β from the position of the slider 201, and sets the value of the risk aversion coefficient α based on the acquired value of the ratio parameter β and equation (4). More specifically, a confirm button (soft button) (not shown) is further displayed on the coefficient setting screen GA. When the operator operates the operation unit 102 to press the confirm button, the processing unit 106 acquires the value of the ratio parameter β from the position of the slider 201 at the time the confirm button was pressed.

[0068] More specifically, the slider 201 is slidable (movable) between a first position P1 and a second position P2. The closer the position of the slider 201 is to the second position P2, the larger the value of the ratio parameter β becomes. As a result, the larger the value of the risk aversion coefficient α becomes. Therefore, the closer the slider 201 is to the second position P2, the more aggressively regions where variance is predicted to be large are avoided, and explanatory variable values ​​that optimize the dependent variable are searched for. On the other hand, the closer the slider 201 is to the first position P1, the more aggressively regions where variance is predicted to be large are avoided, and explanatory variable values ​​that optimize the dependent variable are searched for.

[0069] In this embodiment, the display unit 103 further displays a first scale 202, a first indicator 203, a second scale 204, and a second indicator 205. In detail, the first scale 202, the first indicator 203, the second scale 204, and the second indicator 205 are further displayed on the coefficient setting screen GA.

[0070] The slider 201 moves on the first scale 202. Each value included in the first scale 202 indicates the value of the ratio parameter β. Therefore, the position of the slider 201 on the first scale 202 indicates the value of the ratio parameter β. As already explained, the ratio parameter β indicates a value greater than 0 and less than 1 (0<β<1). Therefore, the first scale 202 indicates each value in the range greater than 0 and less than 1.

[0071] In this embodiment, the slider 201 moves in increments of 0.1. For example, the slider 201 may be movable from a position where the first scale 202 indicates a value of 0.1 to a position where the first scale 202 indicates a value of 0.9. In this case, the first position P1 indicates the position where the first scale 202 indicates a value of 0.1. The second position P2 indicates the position where the first scale 202 indicates a value of 0.9.

[0072] The first indicator 203 indicates a virtual range corresponding to the range of possible values ​​of the objective variable. In other words, the first indicator 203 shows an image of the range of possible values ​​of the objective variable. The first indicator 203 is an example of a "first object."

[0073] The second scale 204 indicates a virtual expected value corresponding to the expected value of the objective variable. The second indicator 205 indicates one of the values ​​included in the second scale 204. In other words, the second indicator 205 indicates the virtual expected value of the objective variable. The second indicator 205 is an example of a "second object." Note that the second scale 204 may also indicate the expected value of the objective variable.

[0074] Fig. 5(a) shows the coefficient setting screen GA when the slider 201 is positioned at a position where the value on the first scale 202 indicates 0.1. Fig. 5(b) shows the coefficient setting screen GA when the slider 201 is positioned at a position where the value on the first scale 202 indicates 0.6. Fig. 5(c) shows the coefficient setting screen GA when the slider 201 is positioned at a position where the value on the first scale 202 indicates 0.9.

[0075] As shown in FIGS. 5(a) to 5(c), the processing unit 106 displays, among the values ​​included in the first scale 202, the value at which the slider 201 is positioned on the coefficient setting screen GA (display unit 103). That is, the processing unit 106 displays the value of the ratio parameter β on the display unit 103. As a result, the operator can visually recognize (confirm) the value of the ratio parameter β. This can assist the operator in determining whether to more actively or more passively avoid areas where variance is predicted to be large. This allows the operator to more easily control the trade-off between the expected value and variance of the response variable.

[0076] 5(a) to 5(c), the processing unit 106 shortens the length of the first indicator 203 as the position of the slider 201 approaches the second position P2 (β=0.9). The processing unit 106 also lengthens the length of the first indicator 203 as the position of the slider 201 approaches the first position P1 (β=0.1).

[0077] Since the length of the first indicator 203 corresponds to the range of possible values ​​of the dependent variable, a shorter length of the first indicator 203 indicates a narrower range of possible values ​​of the dependent variable. In other words, it indicates that areas where variance is predicted to be large will be avoided more aggressively. A longer length of the first indicator 203 indicates a wider range of possible values ​​of the dependent variable. In other words, it indicates that areas where variance is predicted to be large will be avoided more aggressively. Therefore, based on the length of the first indicator 203, the operator can intuitively determine whether the value of the risk aversion coefficient α should be set to a value that more aggressively avoids areas where variance is predicted to be large, or to a value that more aggressively avoids areas where variance is predicted to be large. This allows the operator to more easily control the trade-off between the expected value and variance of the dependent variable.

[0078] 5(a) to 5(c), the closer the position of the slider 201 is to the second position P2 (β=0.9), the more the processing unit 106 moves the second indicator 205 to a position corresponding to a larger value (larger expected value) among the values ​​included in the second scale 204. Furthermore, the closer the position of the slider 201 is to the first position P1 (β=0.1), the more the processing unit 106 moves the second indicator 205 to a position corresponding to a smaller value (smaller expected value) among the values ​​included in the second scale 204.

[0079] Therefore, when minimizing the dependent variable, the operator can visually recognize that the closer the position of the slider 201 is to the second position P2 (β=0.9), the larger the expected value of the dependent variable while more actively avoiding areas where variance is predicted to be large, and the closer the position of the slider 201 is to the first position P1 (β=0.1), the smaller the expected value of the dependent variable while more passively avoiding areas where variance is predicted to be large. In other words, the operator can visually recognize the proportion of the dependent variable's expected value that takes into account the variance. Therefore, the operator can more easily control the trade-off between the expected value and variance of the dependent variable.

[0080] The coefficient setting screen GA displayed on the display unit 103 when supporting a search for explanatory variable values ​​that maximize the expected value of the dependent variable differs from that when minimizing the dependent variable only in the position of the second indicator 205. Specifically, when maximizing the dependent variable, the processing unit 106 moves the second indicator 205 to a position corresponding to a smaller value (smaller expected value) among the values ​​included on the second scale 204 as the position of the slider 201 is closer to the second position P2 (β=0.9). Furthermore, the processing unit 106 moves the second indicator 205 to a position corresponding to a larger value (larger expected value) among the values ​​included on the second scale 204 as the position of the slider 201 is closer to the first position P1 (β=0.1).

[0081] The first embodiment of the present invention has been described above with reference to Figures 1 to 4 and 5(a) to 5(c). According to the first embodiment, the operator can set the value of the risk aversion coefficient α by operating the slider 201. Therefore, the operator can operate the slider 201 to more easily control the trade-off between the expected value and variance of the response variable.

[0082] Furthermore, according to the first embodiment, the value of the ratio parameter β corresponding to the position of the slider 201 is displayed, so that the operator can operate the slider 201 to more easily control the trade-off between the expected value and the variance of the response variable.

[0083] Furthermore, according to the first embodiment, the ratio parameter β is a parameter indicating a ratio, and indicates a value greater than 0 and less than 1 (0<β<1). Therefore, the operator can easily recognize the size of the ratio of the variance of the response variable to the expected value of the response variable. As a result, the operator can more easily control the trade-off between the expected value and variance of the response variable by operating the slider 201.

[0084] Furthermore, according to the first embodiment, the operator can visually recognize the relationship (trade-off relationship) between the range of possible values ​​of the dependent variable and the expected value of the dependent variable, based on the length of the first indicator 203 and the position of the second indicator 205. Therefore, the operator can operate the slider 201 to more easily control the trade-off between the expected value and variance of the dependent variable.

[0085] In the embodiment described with reference to FIGS. 1 to 4 and 5(a) to 5(c), the assistance system 100A (terminal device 101A) acquires the assistance program SP from the recording medium 200. However, the assistance system 100A (terminal device 101A) may acquire the assistance program SP from another computer system. For example, the terminal device 101A may be communicatively connected to the other computer system via a cable and acquire the assistance program SP from the other computer system. Alternatively, the terminal device 101A may be communicatively connected to the other computer system via a line network such as the Internet and acquire the assistance program SP from the other computer system. The other computer system may be a general-purpose computer or a dedicated computer. The other computer system may be a server.

[0086] 1 to 4 and 5(a) to 5(c), the assistance program SP is installed in the terminal device 101A, but the assistance program SP does not have to be installed in the terminal device 101A. The terminal device 101A may execute the assistance program SP stored in the recording medium 200.

[0087] [Embodiment 2] Next, a second embodiment of the present invention will be described with reference to Figures 3, 5(a) to 5(c), and 6. However, only differences from the first embodiment will be described, and explanations of the same aspects as in the first embodiment will be omitted. The second embodiment differs from the first embodiment in that the server 300 outputs recommended values ​​(candidate values) of explanatory variables based on the assistance program SP.

[0088] 6 is a block diagram showing the configuration of a support system 100B of embodiment 2. As shown in FIG.

[0089] In the second embodiment, the terminal device 101B includes an operation unit 102, a display unit 103, a storage unit 105, a communication unit 107, and a processing unit .

[0090] The communication unit 107 is connected to a network and performs communication with the server 300. The network includes, for example, the Internet, a local area network (LAN), a public telephone network, and a short-range wireless network. The communication unit 107 includes a communication device. The communication unit 107 is, for example, a network interface controller.

[0091] The communication unit 107 is controlled by the processing unit 106 to exchange information, data, or signals with the server 300. For example, the communication unit 107 transmits the first learning data LD1, the second learning data LD2, and information indicating the value of the search range to the server 300.

[0092] The server 300 includes a communication unit 301 , a storage unit 302 , and a processing unit 303 .

[0093] The communication unit 301 is connected to a network and communicates with the terminal device 101B. The communication unit 301 includes a communication device. The communication unit 301 is, for example, a network interface controller. The communication unit 301 is controlled by the processing unit 303 and exchanges information, data, or signals with the terminal device 101B. For example, the communication unit 301 receives the first learning data LD1, the second learning data LD2, and information indicating the value of the search range from the terminal device 101B.

[0094] The storage unit 302 has a main storage device and an auxiliary storage device. The main storage device includes, for example, a semiconductor memory. The auxiliary storage device includes, for example, a hard disk drive. The storage unit 302 stores the assistance program SP. The storage unit 302 also stores the first learning data LD1 and the second learning data LD2 received from the terminal device 101B, and information indicating the value of the search range.

[0095] The processing unit 303 includes a processor. The processing unit 303 may include, for example, a CPU, a GPU, an NPU, or a quantum computer. Alternatively, the processing unit 303 may include a general-purpose computing device or a dedicated computing device. For example, the processing unit 303 may include an FPGA or an ASIC. The processing unit 303 executes the assistance program SP based on an instruction from the terminal device 101B.

[0096] Next, the support method, support program SP, and support system 100B of the second embodiment will be described with reference to Fig. 6 and Fig. 3. The processing unit 303 starts the process shown in Fig. 3 based on a command from the terminal device 101B.

[0097] 3 starts, the processing unit 303 causes the first machine learning model ML1 to learn (machine learn) the first training data LD1 received from the terminal device 101B, and causes the first machine learning model ML1 to output a predictive distribution of the expected value of the dependent variable (first predictive distribution f) (step S1). The processing unit 303 also causes the second machine learning model ML2 to learn (machine learn) the second training data LD2 received from the terminal device 101B, and causes the second machine learning model ML2 to output a predictive distribution of the variance of the dependent variable (second predictive distribution g) (step S2).

[0098] After acquiring the first predictive distribution f and the second predictive distribution g, the processing unit 303 receives a setting of the value of the risk aversion coefficient α included in the unequal variance acquisition function AF, and sets the received value to the risk aversion coefficient α (step S3).

[0099] Specifically, the processing unit 303 transmits the coefficient setting screen GA described with reference to Figures 5(a) to 5(c) to the terminal device 101B, and causes the display unit 103 of the terminal device 101B to display the coefficient setting screen GA.

[0100] 5(a) to 5(c), the operator slides the slider 201 and presses the confirm button (not shown). As a result, the processing unit 303 acquires the value of the ratio parameter β, and sets the value of the risk aversion coefficient α based on the acquired value of the ratio parameter β and the above equation (4).

[0101] Specifically, operation information indicating the operation content of the operation unit 102 by the worker is transmitted from the terminal device 101B to the server 300. For example, if the operation content indicates an operation to change the position of the slider 201 (slide operation), the processing unit 303 transmits the coefficient setting screen GA in which the position of the slider 201 has been changed to the terminal device 101B based on the operation information received from the terminal device 101B, and transitions the coefficient setting screen GA to be displayed on the display unit 103. Furthermore, if the operation content indicates an operation to press a confirm button (not shown) on the coefficient setting screen GA, the processing unit 303 acquires the value of the ratio parameter β from the position of the slider 201 when the confirm button was pressed, based on the operation information received from the terminal device 101B.

[0102] After setting the value of the risk aversion coefficient α, the processing unit 303 executes the heteroscedastic Bayesian optimization program BP to obtain values ​​(recommended values ​​or candidate values) of the explanatory variables that maximize the heteroscedastic acquisition function AF (step S4). Then, the processing unit 303 transmits information indicating the recommended values ​​(or candidate values) of the explanatory variables to the terminal device 101B, and causes the display unit 103 to display the recommended values ​​of the explanatory variables (step S5). As a result, the process (support method) shown in FIG. 3 ends.

[0103] More specifically, the processing unit 303 may transmit information indicating a graph of the first predictive distribution f and information indicating a graph of the second predictive distribution g, together with information indicating the recommended values ​​of the explanatory variables, to the terminal device 101B, and cause the graph of the first predictive distribution f and the graph of the second predictive distribution g to be further displayed on the display unit 103. Alternatively, the processing unit 303 may transmit information indicating respective graphs of the first predictive distribution f, the second predictive distribution g, and the heteroscedastic acquisition function A F, together with information indicating the recommended values ​​of the explanatory variables, to the terminal device 101B, and cause the display unit 103 to further display respective graphs of the first predictive distribution f, the second predictive distribution g, and the heteroscedastic acquisition function A F.

[0104] The second embodiment of the present invention has been described above with reference to Fig. 3, Fig. 5(a) to Fig. 5(c), and Fig. 6. According to the second embodiment, similar to the first embodiment, the operator can operate the slider 201 to more easily control the trade-off between the expected value and variance of the response variable.

[0105] [Embodiment 3] Next, a third embodiment of the present invention will be described with reference to Figures 7 and 8. However, only differences from the first and second embodiments will be described, and a description of the same aspects as the first and second embodiments will be omitted. The third embodiment differs from the first and second embodiments in that the control device 10 included in the substrate processing system 1000 also functions as the support system 100C.

[0106] 7 is a schematic diagram of a substrate processing system 1000 including a support system 100C of this embodiment. In detail, FIG. 7 is a schematic plan view of a substrate processing apparatus 400 included in the substrate processing system 1000.

[0107] As shown in Fig. 7, the substrate processing system 1000 includes a substrate processing apparatus 400 and a control device 10. The substrate processing apparatus 400 processes a substrate W. The control device 10 controls the substrate processing apparatus 400. In this embodiment, the substrate W is a disk-shaped semiconductor wafer. The substrate processing apparatus 400 is a single-wafer processing apparatus, and processes the substrates W one by one.

[0108] In detail, the substrate processing apparatus 400 includes a plurality of substrate processing units 2, a fluid cabinet 401, a plurality of fluid boxes 402, a plurality of load ports LP, an indexer robot IR, and a center robot CR.

[0109] A cassette CA is placed on each of the load ports LP. The cassette CA accommodates a stack of substrates W. The cassette CA is, for example, a FOUP (Front Opening Unified Pod), a SMIF (Standard Mechanical Interface) pod, or an OC (Open Cassette).

[0110] The indexer robot IR transports substrates W between the cassette CA and the center robot CR. The center robot CR transports substrates W between the indexer robot IR and a plurality of substrate processing units 2. Note that a placement stage (path) on which the substrate W is temporarily placed may be provided between the indexer robot IR and the center robot CR, and the device may be configured so that the substrate W is transferred indirectly between the indexer robot IR and the center robot CR via the placement stage.

[0111] The substrate processing units 2 form a plurality of towers TW (four towers TW in FIG. 7). The towers TW are arranged to surround the center robot CR in a plan view. Each tower TW includes a plurality of substrate processing units 2 (three substrate processing units 2 in FIG. 7) stacked one above the other.

[0112] The fluid cabinet 401 contains a fluid. Specifically, the fluid cabinet 401 contains a processing liquid. Alternatively, the fluid cabinet 401 may contain a processing liquid and a gas.

[0113] The processing liquid is not particularly limited as long as it is a liquid that comes into contact with the substrate W. The processing liquid may include, for example, dilute hydrofluoric acid (DHF), hydrofluoric acid (HF), hydrofluoric nitric acid (a mixture of hydrofluoric acid and nitric acid (HNO3)), buffered hydrofluoric acid (BHF), ammonium fluoride, HFEG (a mixture of hydrofluoric acid and ethylene glycol), phosphoric acid (H3PO4), sulfuric acid, acetic acid, nitric acid, hydrochloric acid, ammonia water, hydrogen peroxide water, organic acids (e.g., citric acid, oxalic acid), organic alkalis (e.g., tetramethylammonium hydroxide (TMAH)), sulfuric acid / hydrogen peroxide water mixture (SPM), ammonia / hydrogen peroxide water mixture (SC1), hydrochloric acid / hydrogen peroxide water mixture (SC2), isopropyl alcohol (IPA), surfactants, corrosion inhibitors, pure water (e.g., deionized water), carbonated water, electrolytic ionized water, hydrogen water, ozone water, or hydrochloric acid water at a dilute concentration (e.g., about 0.001% by weight to about 0.01% by weight). The gas may include, for example, an inert gas. The inert gas is, for example, nitrogen gas.

[0114] Each fluid box 402 corresponds to one of the multiple towers TW. The fluid in the fluid cabinet 401 is supplied to all of the substrate processing units 2 included in the corresponding tower TW via one of the fluid boxes 402.

[0115] Each of the substrate processing units 2 processes one substrate W at a time. Specifically, each of the substrate processing units 2 processes the substrate W by supplying a processing liquid to the substrate W. For example, each of the substrate processing units 2 performs a cleaning process or an etching process on the substrate W.

[0116] The control device 10 controls the operation of each part of the substrate processing apparatus 400. For example, the control device 10 controls the substrate processing unit 2, the fluid cabinet 401, the fluid box 402, the load port LP, the indexer robot IR, and the center robot CR. The control device 10 includes a control unit 11 and a memory unit 12.

[0117] The control unit 11 controls the operation of each unit of the substrate processing apparatus 400 based on various information stored in the storage unit 12. The control unit 11 includes a processor. The control unit 11 may include, for example, a CPU, a GPU, an NPU, or a quantum computer. Alternatively, the control unit 11 may include a general-purpose computing device or a dedicated computing device. For example, the control unit 11 may include an FPGA or an ASIC.

[0118] The memory unit 12 stores various types of information for controlling the operation of the substrate processing apparatus 400. For example, the memory unit 12 stores various types of data and various computer programs. The various types of data include recipe data. The recipe data indicates a recipe that defines the processing content, processing conditions, and processing procedure for the substrate W. In the recipe, various setting values ​​(recipe parameter values) are set as processing conditions.

[0119] The storage unit 12 includes a main storage device. The main storage device includes, for example, a semiconductor memory. The storage unit 12 may further include an auxiliary storage device. The auxiliary storage device includes, for example, at least one of a semiconductor memory and a hard disk drive.

[0120] 8 is a block diagram showing the configuration of a support system 100C of this embodiment. In detail, FIG. 8 is a block diagram showing the configuration of a control device 10.

[0121] As shown in Figures 7 and 8, the control device 10 also functions as an assistance system 100C. More specifically, as shown in Figure 8, an assistance program SP is installed in the control device 10 from a recording medium 200. Similar to the terminal device 101A described with reference to Figures 1 to 4 and Figures 5(a) to 5(c), the control device 10 executes the assistance program SP installed from the recording medium 200 and searches for values ​​(recommended values ​​or candidate values) of explanatory variables that optimize the expected value of the objective variable. The control device 10 is an example of an "assistance device."

[0122] Specifically, as shown in Fig. 8, the control device 10 further includes an operation unit 13, a display unit 14, and an interface unit 15. The configurations of the operation unit 13, the display unit 14, and the interface unit 15 are similar to those of the operation unit 102, the display unit 103, and the interface unit 104 described with reference to Fig. 1, and therefore a description thereof will be omitted.

[0123] 1, the storage unit 12 stores the first learning data LD1, the second learning data LD2, and the assistance program SP read from the recording medium 200 by the interface unit 15. In the substrate processing system 1000, the explanatory variables may include, for example, at least one of various setting values ​​(recipe parameter values) defined by a recipe and various setting values ​​(apparatus parameter values) set for the substrate processing apparatus 400. When the substrate processing unit 2 performs a cleaning process, the objective variable may be, for example, the number of particles. When the substrate processing unit 2 performs an etching process, the objective variable may be, for example, an evaluation index value of an etching profile.

[0124] The control unit 11 executes the assistance program SP in the same manner as the processing unit 106 described with reference to Figures 1 to 4 and Figures 5(a) to 5(c), and outputs values ​​(recommended values ​​or candidate values) of the explanatory variables that optimize the expected value of the objective variable.

[0125] The third embodiment of the present invention has been described above with reference to Fig. 7 and Fig. 8. According to the third embodiment, similarly to the first and second embodiments, the operator can operate the slider 201 to more easily control the trade-off between the expected value and the variance of the response variable.

[0126] In the third embodiment, the substrate processing apparatus 400 performs a cleaning process or an etching process on the substrate W, but the substrate processing apparatus 400 is not particularly limited as long as it is an apparatus for processing a substrate. For example, the substrate processing apparatus 400 may be a coating apparatus, a developing apparatus, an exposure apparatus, a baking apparatus, or a film forming apparatus.

[0127] Furthermore, in the third embodiment, the substrate processing apparatus 400 is of a single wafer type, but the substrate processing apparatus 400 may be of a batch type.

[0128] In addition, in the third embodiment, the substrate processing apparatus 400 processes a disk-shaped semiconductor wafer, but the substrate to be processed is not limited to a semiconductor wafer. The substrate to be processed may be a glass substrate for a photomask, a glass substrate for a liquid crystal display, a glass substrate for a plasma display, a substrate for an FED (Field Emission Display), a substrate for an optical disk, a substrate for a magnetic disk, or a substrate for a magneto-optical disk. The shape of the substrate to be processed is also not limited to a disk shape.

[0129] [Embodiment 4] Next, a fourth embodiment of the present invention will be described with reference to Figures 9 to 12. However, differences from the first to third embodiments will be described, and a description of the same aspects as the first to third embodiments will be omitted. The fourth embodiment differs from the first to third embodiments in step S3 (coefficient setting step) shown in Figure 3. That is, the fourth embodiment differs from the first to third embodiments in the method of setting the risk aversion coefficient α.

[0130] Fig. 9 is a block diagram showing the configuration of a support system 100D of this embodiment. As shown in Fig. 9, the support system 100D includes a terminal device 101A, similar to the support system 100A described with reference to Figs. 1 to 4 and 5(a) to 5(c). A support program SP read from a recording medium 200 is stored in the storage unit 105 of the terminal device 101A. The support system 100D differs from the support system 100A in that the support program SP further includes a truncated normal distribution sampling program NP.

[0131] The truncated normal distribution sampling program NP includes each expected value corresponding to each value of the ratio parameter β that can be set by the operator operating the slider 201 (see FIGS. 5(a) to 5(c)). In other words, the truncated normal distribution sampling program NP includes each expected value corresponding to each position to which the slider 201 can be moved. The truncated normal distribution sampling program NP also includes a predetermined standard deviation value.

[0132] The processing unit 106 executes the truncated normal distribution sampling program NP when setting the value of the risk aversion coefficient α. Specifically, the processing unit 106 acquires the value of the ratio parameter β set by the operator by operating the slider 201 when setting the value of the risk aversion coefficient α. Then, the processing unit 106 creates a truncated normal distribution ND based on the expected value corresponding to the acquired value of the ratio parameter β and a predetermined standard deviation value. In other words, the processing unit 106 creates a truncated normal distribution ND corresponding to the position of the slider 201.

[0133] For example, when the slider 201 moves in increments of 0.1 within a range of 0.1 to 0.9, the values ​​of the ratio parameter β that the operator can set by operating the slider 201 include nine values: "0.1," "0.2," ..., "0.8," and "0.9." Therefore, the truncated normal distribution sampling program NP includes nine values: "0.1," "0.2," ..., "0.8," and "0.9" as expected values ​​used to create the truncated normal distribution ND.

[0134] Furthermore, the truncated normal distribution ND indicates a probability distribution in which the domain of the random variable is finite. In this embodiment, the domain of the random variable is set to the range in which the slider 201 can move. For example, if the slider 201 moves within the range of 0.1 to 0.9, the domain of the random variable is set to the range of 0.1 to 0.9.

[0135] 10(a) to 10(c) are diagrams showing an example of a truncated normal distribution ND generated by the processing unit 106 executing the truncated normal distribution sampling program NP.

[0136] Specifically, FIG. 10(a) shows a truncated normal distribution ND1 with an expected value of "0.1". FIG. 10(b) shows a truncated normal distribution ND2 with an expected value of "0.5". FIG. 10(c) shows a truncated normal distribution ND3 with an expected value of "0.9". As shown in FIGS. 10(a) to 10(c), truncated normal distributions ND with different shapes are created for each expected value. For example, when the value of the ratio parameter β set by the operator by operating the slider 201 is "0.1", the processing unit 106 creates the truncated normal distribution ND1 shown in FIG. 10(a).

[0137] The truncated normal distribution sampling program NP may include predetermined standard deviation values ​​for each value of the ratio parameter β that can be set by the operator operating the slider 201.

[0138] Fig. 11 is a flowchart showing the coefficient setting step (step S3 in Fig. 3) included in the support method of embodiment 4. In other words, Fig. 11 shows the flow of the process executed by the processing unit 106 included in the terminal device 101A.

[0139] When the processing unit 106 starts the coefficient setting process, it causes the display unit 103 to display the coefficient setting screen GA as described with reference to FIGS. 5(a) to 5(c). Then, the processing unit 106 creates a truncated normal distribution ND corresponding to the position of the slider 201 when the confirm button (not shown) is pressed, and acquires a value randomly sampled from the created truncated normal distribution ND (step S31). Then, the processing unit 106 sets the risk aversion coefficient α based on the value acquired from the truncated normal distribution ND (step S32). As a result, the process shown in FIG. 11 ends. In detail, the processing unit 106 sets the value acquired from the truncated normal distribution ND as the value of the ratio parameter β in the above equation (4). As a result, the value of the risk aversion coefficient α is set based on the above equation (4).

[0140] Fig. 12 is a flowchart showing an example of the coefficient setting step (step S3 in Fig. 3) included in the support method of embodiment 4. In other words, Fig. 12 shows an example of the flow of processing executed by the processing unit 106 included in the terminal device 101A. As shown in Fig. 12, step S31 in Fig. 11 may include steps S311 to S313.

[0141] Specifically, the processing unit 106 acquires the value of the ratio parameter β as described with reference to Figures 5(a) to 5(c) based on the position of the slider 201 when the confirm button (not shown) is pressed (step S311). In other words, the processing unit 106 acquires the value on the first scale 202 where the slider 201 is located.

[0142] Next, the processing unit 106 creates a truncated normal distribution ND (step S312) in which the value of the ratio parameter β acquired based on the position of the slider 201 is the expected value. For example, if the value of the acquired ratio parameter β is 0.9, the processing unit 106 creates a truncated normal distribution ND3 shown in FIG. 10(c).

[0143] Next, the processing unit 106 acquires a value randomly sampled from the created truncated normal distribution ND (step S313). Then, the processing unit 106 sets the value acquired by random sampling as the value of the ratio parameter β in the above formula (4). As a result, the value of the risk aversion coefficient α is set based on the above formula (4). For example, when the truncated normal distribution ND3 shown in FIG. 10(c) is created, the processing unit 106 sets the value acquired from the truncated normal distribution ND3 shown in FIG. 10(c) as the value of the ratio parameter β in the above formula (4).

[0144] The fourth embodiment of the present invention has been described above with reference to Fig. 9 to Fig. 12. According to the fourth embodiment, similarly to the first to third embodiments, the operator can operate the slider 201 to more easily control the trade-off between the expected value and the variance of the response variable.

[0145] Furthermore, Bayesian optimization tends to be more efficient when the behavior of the acquisition function differs for each search. According to the fourth embodiment, the value of the risk aversion coefficient α can be set randomly. As a result, the behavior of the acquisition function becomes random for each search. This may improve the efficiency of searching for the values ​​of explanatory variables that optimize (maximize or minimize) the objective variable.

[0146] In the fourth embodiment, the terminal device 101A executes the assistance program SP as in the first embodiment, but the server 300 may execute the assistance program SP as in the second embodiment, or the control device 10 of the substrate processing system 1000 may execute the assistance program SP as in the third embodiment.

[0147] The embodiments of the present invention have been described above with reference to the drawings (FIGS. 1 to 12). However, the present invention is not limited to the above embodiments and can be embodied in various forms without departing from the spirit of the present invention. Furthermore, the components disclosed in the above embodiments can be modified as appropriate. For example, some of the components shown in one embodiment may be added to the components of another embodiment, or some of the components shown in one embodiment may be deleted from the embodiment.

[0148] The drawings mainly show each component in a schematic manner to facilitate understanding of the invention, and the thickness, length, number, spacing, etc. of each component shown in the drawings may differ from the actual ones due to the convenience of creating the drawings. Furthermore, the configuration of each component shown in the above embodiment is merely an example and is not particularly limited, and it goes without saying that various modifications are possible within a range that does not substantially deviate from the effects of the present invention.

[0149] For example, in the embodiment described with reference to Figures 1 to 12, the assistance program SP includes the unequal variance acquisition function AF, but the assistance program SP may include multiple types of acquisition functions. In this case, the assistance program SP may create the unequal variance acquisition function AF based on the acquisition function set by the operator operating the operation unit 102. Alternatively, the operator may operate the operation unit 102 to set the formula of the unequal variance acquisition function AF in the source code of the assistance program SP.

[0150] 1 to 12, the assistance program SP includes the preprocessing program FP, but the assistance program SP does not have to include the preprocessing program FP. For example, a preprocessing program created by an operator may be stored in the storage units 105 and 12. [Industrial Applicability]

[0151] The present invention is useful in methods and systems for performing heteroscedastic Bayesian optimization. [Explanation of symbols]

[0152] 10: Control device 11: Control section 12: Storage section 13:Operation section 14:Display section 100A: Support System 100B: Support System 100C: Support System 100D: Support System 101A: Terminal device 101B: Terminal device 102:Operation unit 103:Display section 105: Storage section 106: Processing section 200: Recording medium 201: Slider 202: 1st scale 203: First indicator 204: Second scale 205: Second indicator 300: Server 302: Storage section 303: Processing section AF: Heteroscedastic Acquisition Function ML1: First machine learning model ML2: Second machine learning model ND, ND1~ND3: Truncated normal distribution P1: 1st position P2: 2nd position SP: Support Program

Claims

1. A method for assisting in searching for values ​​of explanatory variables that maximize or minimize an expected value of a target variable, comprising: outputting a first predictive distribution, which is a predictive distribution of an expected value of the dependent variable, from a first machine learning model capable of outputting a predictive distribution; outputting a second predictive distribution, which is a predictive distribution of the variance of the dependent variable, from a second machine learning model capable of outputting a predictive distribution; a coefficient setting step of receiving a setting of a value of a risk aversion coefficient included in a heteroscedastic acquisition function; a step of performing heteroscedastic Bayesian optimization based on the first predictive distribution, the second predictive distribution, the heteroscedastic acquisition function for which the value of the risk aversion coefficient has been set in the coefficient setting step, and a search range, and acquiring, from within the search range, recommended values ​​of the explanatory variables that maximize the heteroscedastic acquisition function; Including, the heteroscedastic acquisition function indicates a function in which the larger the value of the risk aversion coefficient, the higher the rate at which the recommended value is acquired from an area in which the variance of the objective variable is smaller; The coefficient setting step includes a step of setting a value of the risk aversion coefficient based on a position of a slider that can be operated by a worker.

2. The support method according to claim 1 , wherein, when setting the value of the risk aversion coefficient, a truncated normal distribution corresponding to the position of the slider is created, and the value of the risk aversion coefficient is set based on values ​​randomly sampled from the truncated normal distribution.

3. the slider is movable between a first position where a value on the first scale is greater than 0 and a second position where a value on the first scale is less than 1; The support method according to claim 1 , wherein, when setting the value of the risk aversion coefficient, the risk aversion coefficient is set to a larger value as the position of the slider is closer to the second position.

4. In the case of supporting a search for values ​​of the explanatory variables that minimize the expected value of the objective variable, the coefficient setting step includes: displaying the slider, the first scale, a first object indicating a virtual range corresponding to a range of possible values ​​of the objective variable, a second scale indicating a virtual expected value corresponding to the expected value, and a second object indicating one of the values ​​included in the second scale; a step of shortening a length of the first object as the position of the slider approaches the second position, and moving the second object to a position corresponding to a larger value among positions corresponding to the values ​​included in the second scale; Including, In the case of supporting a search for values ​​of the explanatory variables that maximize the expected value of the objective variable, the coefficient setting step includes: displaying the slider, the first scale, the first object, the second scale, and the second object; a step of shortening a length of the first object as the position of the slider approaches the second position, and moving the second object to a position corresponding to a smaller value among positions corresponding to the values ​​included in the second scale; The method of claim 3 , comprising:

5. A computer-readable recording medium having a support program that defines the support method according to any one of claims 1 to 4 recorded thereon.

6. A support program executable by a computer and defining the support method according to any one of claims 1 to 4.

7. A support system for supporting a search for values ​​of explanatory variables that maximize or minimize an expected value of a target variable, a storage unit that stores a first machine learning model capable of outputting a predictive distribution, a second machine learning model capable of outputting a predictive distribution, and a heteroscedastic acquisition function; a display unit that displays a slider; an operation unit that accepts operation of the slider by an operator; a processing unit that causes the first machine learning model to output a first predictive distribution, which is a predictive distribution of an expected value of the dependent variable, and causes the second machine learning model to output a second predictive distribution, which is a predictive distribution of a variance of the dependent variable; Equipped with The processing unit setting a value of a risk aversion coefficient included in the heteroscedastic earnings function based on the position of the slider; performing heteroscedastic Bayesian optimization based on the first predictive distribution, the second predictive distribution, the heteroscedastic acquisition function in which the value of the risk aversion coefficient is set based on the position of the slider, and a search range, to obtain recommended values ​​of the explanatory variables within the search range that maximize the heteroscedastic acquisition function; The heteroscedastic acquisition function indicates a function in which the larger the value of the risk aversion coefficient, the higher the proportion of the recommended value obtained from an area with smaller variance.

8. 8. The assistance system according to claim 7, wherein, when setting the value of the risk aversion coefficient, the processing unit creates a truncated normal distribution corresponding to the position of the slider, and sets the value of the risk aversion coefficient based on values ​​randomly sampled from the truncated normal distribution.

9. the display unit further displays a first scale; the slider moves between a first position where the first scale indicates a value greater than 0 and a second position where the first scale indicates a value less than 1 in response to an operation of the operation unit by the operator; The assistance system according to claim 7 , wherein, when setting the value of the risk aversion coefficient, the processing unit sets the risk aversion coefficient to a larger value as the position of the slider is closer to the second position.

10. the display unit further displays a first object indicating a virtual range corresponding to a range of possible values ​​of the objective variable, a second scale indicating a virtual expected value corresponding to the expected value, and a second object indicating one of the values ​​included in the second scale; When assisting in a search for a value of the explanatory variable that minimizes the expected value of the objective variable, the processing unit shortens a length of the first object as the position of the slider approaches the second position, and moves the second object to a position corresponding to a larger value among positions corresponding to the values ​​included in the second scale; 10. The assistance system according to claim 9, wherein, when assisting in a search for a value of the explanatory variable that maximizes the expected value of the target variable, the processing unit shortens a length of the first object as the position of the slider approaches the second position, and moves the second object to a position corresponding to a smaller value among positions corresponding to the values ​​included in the second scale.

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