Information processing device, information processing method, and computer program

Abstract

Provided are an information processing device, an information processing method, and a computer program.　This information processing device is provided with at least one processor. The processor: acquires a first data set including time-series data to be input to a system and time-series data observed from the system when the data to be input is input; generates a model describing the behavior of the system by using the acquired first data set; and outputs input data to be added to the first data set so as to improve the uncertainty in the model parameters of the generated model.

Description

Information processing device, information processing method, and computer program

[0001] The present disclosure relates to an information processing device, an information processing method, and a computer program.

[0002] Data-driven modeling of equipment states and phenomena based on observed time-series data has been a widely used approach. For example, in the field of various manufacturing processes, modeling techniques are known for describing equipment states and phenomena within a process based on time-series data observed during the process.

[0003] Aiming for highly accurate modeling and improving the quality of the input signals to the system, users must conduct repeated experiments, which takes time and effort.

[0004] International Publication No. 2021 / 106646

[0005] The present disclosure provides an information processing device, an information processing method, and a computer program that can suggest what kind of input data should be used when modeling a system from time-series data.

[0006] The information processing device disclosed herein includes at least one processor, which acquires a first dataset including time series data to be input to a system and time series data observed from the system when the data is input, generates a model that explains the behavior of the system using the acquired first dataset, and outputs input data to be added to the first dataset so as to improve uncertainty in model parameters of the generated model.

[0007] According to the present disclosure, it is possible to propose what kind of input data is best to use when modeling a system from time-series data.

[0008] FIG. 1 is an explanatory diagram illustrating a configuration of an information processing system according to an embodiment. FIG. 2 is a block diagram illustrating the internal configuration of an information processing device. FIG. 3 is a graph illustrating an example profile of a loss function. FIG. 4 is an explanatory diagram illustrating the uncertainty of model parameters. FIG. 5 is a flowchart illustrating the procedure of processing executed by an information processing device. FIG. 6 is a schematic diagram illustrating an example display of experimental conditions. FIG. 7 is a schematic diagram illustrating an example of a proposal screen in embodiment 2. FIG. 8 is a schematic diagram illustrating an example calculation of the uncertainty of model parameters in embodiment 3.

[0009] An embodiment will be described below with reference to the drawings. In the description, the same elements or elements having the same functions are designated by the same reference numerals, and redundant description will be omitted.

[0010] 1 is an explanatory diagram illustrating the configuration of an information processing system according to an embodiment of the present invention. The information processing system according to the embodiment includes a substrate processing apparatus 100 and an information processing apparatus 200.

[0011] The substrate processing apparatus 100 is an apparatus for performing required processing on a substrate (wafer). The substrate processing apparatus 100 is, for example, a semiconductor manufacturing apparatus such as an exposure apparatus, an etching apparatus, a film formation apparatus, an ion implantation apparatus, an ashing apparatus, or a sputtering apparatus. The substrate processing apparatus 100 may be a substrate processing system including one or more semiconductor manufacturing apparatuses, a transport apparatus for transporting substrates, etc., and a management apparatus for managing the entire apparatus. The substrate processing apparatus 100 may also be a display manufacturing apparatus for manufacturing flat display panels (FDPs) such as liquid crystal display panels and organic electroluminescence (EL) panels.

[0012] When a substrate is processed in the substrate processing apparatus 100, various set values ​​are set, such as the substrate temperature, the pressure and gas flow rate in the chamber, and the voltage applied from the high-frequency power supply. The set values ​​are given, for example, by a process recipe. The substrate processing apparatus 100 is provided with devices such as a heater, a gas supply source, a flow rate controller, and a high-frequency power supply, and the operation of these devices is controlled according to the set values, thereby controlling the state of the substrate processing apparatus 100 during processing. The substrate processing apparatus 100 is also provided with various sensors and measuring devices that measure the substrate temperature, the pressure and gas flow rate in the chamber, the voltages applied to the upper electrode and the lower electrode, the plasma emission intensity, and the like, and the state of the apparatus and phenomena in the chamber during processing are observed over time.

[0013] Conventionally, data-driven modeling of the state of a device or a phenomenon within the device from time series data observed about the system has been a widely used approach.

[0014] However, when there are restrictions on the experimental conditions that can be implemented, it is difficult to determine what experimental conditions should be selected to enable accurate and efficient modeling of time-series data.

[0015] For example, in the above-described substrate processing apparatus 100, a stage mechanism for holding a wafer is provided with a wafer temperature adjustment mechanism including multiple heaters for controlling the in-plane temperature distribution of the wafer. When modeling the wafer temperature adjustment mechanism, it is possible to consider from the perspective of control engineering what signals should be applied to each of the multiple heaters, provided that there is knowledge of the model object.

[0016] However, the characteristics of the object to be modeled are often unknown. When the characteristics are unknown, repeated experiments and redesign of experimental conditions are required to improve the quality of the input signal in order to achieve high-precision modeling, which requires a lot of time and effort. Furthermore, if the accuracy of the obtained model is insufficient, the input signal will have to be redesigned, but it is not clear how to improve it. When there are limitations on the experimental conditions applicable to the system, such as input constraints or operating region constraints, it is difficult to design signals commonly used in modeling experiments (such as swept sine signals and multi-sine signals).

[0017] Therefore, the information processing device 200 according to this embodiment acquires a dataset including time-series data (experimental conditions) input to a system and time-series data (observation results) observed from the system, and models the target using a modeling method capable of calculating the uncertainty of the model parameters. The information processing device 200 sequentially updates the time-series data (experimental conditions) input to the system so as to improve the uncertainty of the model parameters, thereby maximizing the degree of improvement in the uncertainty. When the information processing device 200 finds experimental conditions that maximize the degree of improvement, it suggests to the user that the experimental conditions at that time should be added to the dataset.

[0018] 2 is a block diagram showing the internal configuration of the information processing device 200. The information processing device 200 is, for example, a dedicated or general-purpose computer including a control unit 201, a storage unit 202, a communication unit 203, an operation unit 204, and a display unit 205.

[0019] The control unit 201 includes a CPU (Central Processing Unit), a ROM (Read Only Memory), a RAM (Random Access Memory), etc. The ROM included in the control unit 201 stores control programs and the like that control the operation of each hardware unit included in the information processing device 200. The CPU in the control unit 201 reads and executes the control programs stored in the ROM and computer programs (described below) stored in the storage unit 202, and controls the operation of each hardware unit, thereby causing the entire device to function as the information processing device of the present disclosure. The RAM included in the control unit 201 temporarily stores data used during execution of calculations.

[0020] In the embodiment, the control unit 201 is configured to include a CPU, a ROM, and a RAM, but the configuration of the control unit 201 is not limited to the above. The control unit 201 may be, for example, one or more processing circuits, arithmetic circuits, or circuits including a GPU (Graphics Processing Unit), an FPGA (Field Programmable Gate Array), a DSP (Digital Signal Processor), a quantum processor, volatile or non-volatile memory, etc., or may be provided as an integrated unit or partially separated. Furthermore, the control unit 201 may have functions such as a clock that outputs date and time information, a timer that measures the elapsed time from when a measurement start instruction is given to when a measurement end instruction is given, and a counter that counts numbers.

[0021] The storage unit 202 includes a storage device such as a hard disk drive (HDD), a solid state drive (SSD), an electronically erasable programmable read-only memory (EEPROM), etc. The storage unit 202 stores various computer programs executed by the control unit 201 and various data used by the control unit 201.

[0022] The computer program (program product) stored in the storage unit 202 includes a condition search program PG for causing a computer to execute a process of outputting input data to be newly added to the substrate processing apparatus 100 as experimental conditions from time-series data obtained from the substrate processing apparatus 100. The condition search program PG may be a single computer program or a program group consisting of multiple computer programs. The condition search program PG may be executed by multiple computers in cooperation. Furthermore, the condition search program PG may partially use an existing library.

[0023] A computer program including the condition search program PG is provided, for example, by a non-transitory recording medium RM on which the computer program is readably recorded. The recording medium RM is a portable memory such as a CD-ROM, USB memory, a Secure Digital (SD) card, a microSD card, or a CompactFlash (registered trademark). The control unit 201 reads various computer programs from the recording medium RM using a reading device (not shown) and stores the read computer programs in the memory unit 202. The computer programs stored in the memory unit 202 may also be provided via communication. In this case, the control unit 201 acquires the computer programs via communication via the communication unit 203 and stores the acquired computer programs in the memory unit 202.

[0024] The communication unit 203 includes a communication interface for transmitting and receiving various data to and from an external device. A communication interface conforming to a communication standard such as a local area network (LAN) can be used as the communication interface of the communication unit 203. The external device may be the substrate processing apparatus 100 described above or a user terminal (not shown). When data to be transmitted is input from the control unit 201, the communication unit 203 transmits the data to the external device as the destination, and when data transmitted from the external device is received, the communication unit 203 outputs the received data to the control unit 201.

[0025] The operation unit 204 includes operation devices such as a touch panel, a keyboard, and switches, and receives various inputs and operations from a user, etc. The control unit 201 acquires information input through the operation unit 204 and performs appropriate control based on various operation information provided by the operation unit 204.

[0026] The display unit 205 includes a display device such as a liquid crystal monitor or an organic EL (Electro-Luminescence) monitor, and displays information to be notified to the user or the like in response to an instruction from the control unit 201 .

[0027] The information processing apparatus 200 in this embodiment may be a single computer, or may be a computer system configured with multiple computers and peripheral devices. The information processing apparatus 200 may be a virtual machine whose entity is virtualized, or may be a cloud. Furthermore, although the information processing apparatus 200 and the substrate processing apparatus 100 are described as separate entities in this embodiment, the information processing apparatus 200 may be provided inside the substrate processing apparatus 100.

[0028] An outline of the processing executed by the information processing apparatus 200 will be described below. The information processing apparatus 200 acquires a data set including time-series data (experimental conditions) input to the substrate processing apparatus 100 (system) and time-series data (observation results) observed by the substrate processing apparatus 100, and models the target using a modeling method that can calculate the uncertainty of the model parameters. The target to be modeled is the substrate temperature, the plasma state in the chamber, the etching amount, the etching shape, the degree of wear of the component parts, etc., and is set appropriately by the user.

[0029] Model parameters are parameters included in a model that represents the relationship between input data (experimental conditions) and output data (observation results). For example, if a model that returns y for an argument x is described as y = θx + η, θ and η represent model parameters.

[0030] In this embodiment, in order to evaluate the uncertainty of the model parameters, a loss function (empirical loss function) that expresses the consistency between experimental data and values ​​predicted by the model is used. FIG. 3 is a graph showing an example profile of the loss function. FIG. 3 shows an example profile of the loss function when the model has two model parameters (θ and η). When the model has two model parameters θ and η, the loss function is expressed as a quadratic approximation surface whose value is determined when θ and η are specified. The graph in FIG. 3 shows a graph (contour map) in which the quadratic approximation surface is projected onto the θ-η plane.

[0031] If the model parameters θ, η are updated so that the value of the loss function is minimized from the initially set model M(θ', η'), the initially set model M(θ', η') should approach the true model M(θ, η).

[0032] However, the uncertainty of the model parameters is large in directions where the curvature of the loss function is gentle. FIG. 4 is an explanatory diagram illustrating the uncertainty of model parameters. FIG. 4 shows the cross-sectional shape of the loss function in a predetermined direction (e.g., the θ direction). The graph on the left of FIG. 4 shows the cross-sectional shape when the curvature is relatively large, and the graph on the right shows the cross-sectional shape when the curvature is relatively small. Ideally, it is possible to determine the model parameters that minimize the loss function regardless of the magnitude of the curvature. In other words, by differentiating the curve shown by the black solid line in FIG. 4 and finding the value that makes the differential value zero, the model parameters that minimize the loss function can be determined.

[0033] However, because actual observation data contains noise, the cross-sectional shape of the loss function itself contains noise. In Figure 4, the noise appearing in the cross-sectional shape is schematically shown by a thick gray solid line. As shown in the graph on the left of Figure 4, when the curvature of the cross-sectional shape is relatively large, the model parameters that minimize the loss function are easily affected by the noise appearing in the cross-sectional shape. In other words, it is difficult to find a significant difference between the magnitude of the loss function when the model parameter indicated by θa' in the graph is selected and the magnitude of the loss function when the model parameter indicated by θb' is selected, and the uncertainty of the model parameters is large.

[0034] On the other hand, when appropriate experimental data is added and the ambiguity in the model is reduced, the cross-sectional shape of the loss function becomes steeper, as shown in the graph on the right of Figure 4. In this case, the model parameters are less susceptible to noise that appears in the cross-sectional shape. In other words, there is a significant difference between the magnitude of the loss function when the model parameter indicated by θa in the graph is selected and the magnitude of the loss function when the model parameter indicated by θb is selected, and the uncertainty of the model parameters is small.

[0035] In this embodiment, the uncertainty of the model parameters is calculated by examining not only the differential value of the loss function but also the behavior near the minimum point, and experimental data that reduces the uncertainty of the model parameters is proposed.

[0036] 5 is a flowchart illustrating the procedure of processing executed by the information processing apparatus 200. Before the information processing apparatus 200 proposes experimental conditions, one or more experiments are performed under initial experimental conditions in the substrate processing apparatus 100, and the observation target is observed. The observation target and the initial experimental conditions are set appropriately by the user.

[0037] The information processing device 200 acquires a data set of initial experimental conditions and observation results from the substrate processing device 100 via the communication unit 203 (step S101). Hereinafter, the initial experimental conditions (i.e., time-series data input to the system) will be represented as u(t), and the observation results (time-series data observed from the system) will be represented as x(t). u(t) represents the experimental conditions at time t, and x(t) represents the observation results at time t. The term u(-) is used to represent all of the experimental conditions used in the initial experiment, and x(-) is used to represent all of the observation results. The data set acquired in step S101 is represented as OBS={u(-), x(-)}.

[0038] The control unit 201 uses the data set acquired in step S101 to model the target (step S102). The target to be modeled is, for example, the substrate temperature. In this case, the data set includes a time-series signal applied to the heater (initial experimental condition) and a substrate temperature measured over time in the substrate processing apparatus 100 (observation result). Based on the acquired data set, a model is generated that outputs a predicted value of the substrate temperature when a signal applied to the heater is input. The target to be modeled is not limited to the substrate temperature, but may also include the plasma state in the chamber, the etching amount, the etching shape, the degree of wear of component parts, and the like, which are set by the user as appropriate.

[0039] The function form of the model is set in advance by the user or another system depending on the target of modeling. In this flowchart, for simplicity, the model has one input / output variable and one model parameter, but the model may have two or more input / output variables and two or more model parameters.

[0040] Although this flowchart assumes that the experimental conditions change over time, the experimental conditions may also include experimental conditions that do not change over time. For example, the 0th component of u(t) may be a time-independent constant (e.g., the temperature of the experimental environment), and the 1st to 10th components of u(t) may be time-dependent variables (e.g., the magnitude of the current applied to the heater).

[0041] The control unit 201 adjusts the model parameters using the data set acquired in step S101 (step S103). The control unit 201 can adjust the model parameters using a loss function (empirical loss function) that expresses the consistency between the experimental data and the predicted values ​​by the model. By adjusting the model parameters in step S103, a model using the initial experimental conditions is generated.

[0042] Next, the control unit 201 sets an initial value y(0) and a tentative experimental condition v(-) for the generated model (step S104). If there are constraints on the experimental conditions, it is advisable to set only the experimental conditions that satisfy the constraints.

[0043] The control unit 201 obtains a prediction result by the model based on y(0) and v(-) set in step S104 (step S105). Since a model with the model parameters adjusted in step S103 is generated, the control unit 201 can use this model to calculate the time evolution y(-) of the observable when the initial value y(0), the tentative experimental condition v(-), and the model parameter θ are given as a prediction result.

[0044] In this embodiment, an initial value (predicted value at time 0) is given to the model, but a predicted value at any time (for example, the final time) may be given, or an nth-order differential coefficient at the initial time, or a combination thereof may be given. Also, a value of a function with y(-) as an argument, such as the time average of y(-), may be given.

[0045] The control unit 201 adds a dataset including tentative experimental conditions v(-) and the model prediction results y(-) to the initial dataset OBS to create a new dataset OBS' (step S106). The dataset OBS' is expressed as OBS' = OBS + {v(-), y(-)}.

[0046] The control unit 201 uses the data set OBS' created in step S106 to model the target (step S107), and calculates the uncertainty in the model parameter θ (step S108).

[0047] The modeling method can be the multi-trajectory dynamic mode decomposition (MTDMD) method disclosed in "Multi-trajectory Dynamic Mode Decomposition, Ryoji Anzaki, Shota Yamada, et al., Jxiv preprint (2024), [URL: https: / / jxiv.jst.go.jp / index.php / jxiv / preprint / view / 602]." Multi-trajectory dynamic mode decomposition is an example of a modeling method that can calculate the uncertainty of model parameters.

[0048] For example, when data sets X, Y, and U for N orbits are obtained, the optimization coefficients of the model parameters when modeled by multi-orbit dynamic mode decomposition are expressed as in Equation 1.

[0049]

[0050] Here, U represents the experimental conditions, X represents the observed results from the system, and Y represents the predicted results estimated by the model. The second brace on the right-hand side is the Hessian H (Hessian matrix H), which is the second partial derivative of the loss function (∂ 2 L / ∂θ 2 ) The control unit 201 calculates the eigenvalue λ of this Hessian H. i Since there is a relationship in which the uncertainty of the model parameter θ is small when the eigenvalue of the Hessian H is large, the control unit 201 calculates the uncertainty of the model parameter θ using, for example, Equation 2.

[0051]

[0052] The control unit 201 is not limited to the equation 2, but also uses the eigenvalue λ i The uncertainty of the model parameter θ may be calculated by the nth root of the sum of the reciprocals of the nth power of θ.

[0053] Alternatively, the modeling method may be dynamic mode decomposition (DMD), which is described in papers such as "ON DYNAMIC MODE DECOMPOSITION: THEORY AND APPLICATIONS, JH Tu, et al., Journal of Computational Dynamics (2013)" and "Dynamic Mode Decomposition with Control, JL Proctor, et al., SIAM J. APPLIED DYNAMICAL SYSTEMS, Vol. 15, No. 1, pp. 142-161."

[0054] Furthermore, as a modeling method, sparse identification of nonlinear dynamics (SINDy: Sparse Identification of Nonlinear Dynamis with Control) described in papers such as "Discovering governing equations from data by sparse identification of nonlinear dynamical systems, S.L. Brunton, et al., PNAS, April 12, 2016, vol. 113, no. 15, 3932-3937" and "Sparse Identification of Nonlinear Dynamics with Control (SINDYc), S.L. Brunton, et al., IFAC-PapersOnLine 49-18 (2016) 710-715" may be used.

[0055] Dynamic mode decomposition and sparse identification of nonlinear dynamics are also examples of modeling methods that can calculate the uncertainty of model parameters. Optimization of a loss function is used to evaluate model parameters. The loss function that represents the consistency between experimental data and a model is set to L = L(θ). The functional form of L(θ) is determined by the model and an evaluation function defined by the user. Instead of L(θ), g(L(θ)) using a monotonic function g may be used.

[0056] In the dynamic mode decomposition described above, L(θ) can be expressed as the sum of the results of applying the function described in Equation 3 to each of X and U. In general, any function such as the harmonic mean, square root of the mean square, or weighted mean of the results of each of X and U may be used.

[0057]

[0058] Here, the two matrices A and B represent the model parameter θ, and the entire equation 3 represents the loss function L(θ). Note that the model parameter θ may be mathematically expressed, such as by dynamic mode decomposition, or may be derived by numerical optimization.

[0059] The control unit 201 calculates the uncertainty of the model parameter θ by slightly changing the model parameter θ and determining how much the loss function L increases. Alternatively, the control unit 201 may calculate the uncertainty of the model parameter θ by slightly changing the model parameter θ and determining how much the reconstruction error (e.g., RMSE: Root Mean Squared Error) increases. Note that the change δθ in the model parameter θ may be determined randomly or may be generated using a unit vector in all directions.

[0060] The control unit 201 calculates the improvement amount of the uncertainty of the model parameter θ (step S109). Here, the uncertainty of the model parameter θ in the model generated using only the data set OBS obtained from the system is defined as u0. Also, the uncertainty of the model parameter θ in the model generated using the data set OBS' to which new experimental conditions have been added is defined as u1. The control unit 201 calculates the absolute value of the difference in uncertainty, |u1-u0|, to calculate the improvement amount of the model parameter.

[0061] The control unit 201 determines whether the improvement amount of the uncertainty of the model parameter θ has been maximized (step S110). The control unit 201 determines that the improvement amount has been maximized when the difference between the improvement amount calculated last time and the improvement amount calculated this time is equal to or less than a set value. The control unit 201 may determine whether the improvement amount has been maximized by determining whether the uncertainty of the model parameter θ is equal to or less than a set value, or may determine termination based on an upper limit on the number of repetitions, etc.

[0062] If the control unit 201 determines that the improvement in uncertainty has not been maximized (S110: NO), it updates the experimental conditions (step S111). If there are constraints on the experimental conditions, the control unit 201 may perform numerical optimization after imposing the constraints, and generate new experimental conditions.

[0063] Here, constraints on the experimental conditions include, for example, constraints such as the first component of v(t) must be smaller than 6.3 sin (4.2×t), avoiding similar experimental conditions (when there is little noise and the variation of input data is emphasized), and not wanting to adopt input data in a certain direction (for example, when frequency components of 300 Hz or higher are not to be included). In this case, the control unit 201 can utilize a projection operator to perform constrained optimization so that the inner product R of the input data and the function to be constrained (a function of time) becomes zero. Furthermore, the control unit 201 applies λR to the function to be minimized. 2 (λ>0) may be added for regularization.

[0064] Furthermore, v(-) may be orthogonal to the previous experimental conditions {u(-), x(-)}. The orthogonal condition can be determined by determining the condition under which the inner product is zero in the function space.

[0065] In addition to the method of the present disclosure, conventional experimental design methods may be used to determine experimental conditions that do not vary over time. In this case, it is recommended that the experimental design be designed to ensure good variability in the experimental results.

[0066] After updating the experimental conditions in step S111, the control unit 201 returns the process to step S104 and executes the processes of steps S104 to S110 again.

[0067] If the control unit 201 determines that the improvement in uncertainty has been maximized (YES in S110), it proposes to the user y(0) and v(-) set in step S104 as experimental conditions to be added (step S112). Specifically, the control unit 201 displays information about the experimental conditions to be added on the display unit 205. At this time, the control unit 201 may also display information such as a loss function profile, Hessian eigenvalues, eigenvectors, and uncertainty along with the experimental conditions. Furthermore, the control unit 201 may also display model parameters, model output data, and time-series data obtained from the system. When displaying these data, the control unit 201 may display them as two-dimensional or three-dimensional graphs, or as contour maps or heat maps. Instead of displaying them on the display unit 205, the control unit 201 may transmit them to the user's terminal device via the communication unit 203.

[0068] Fig. 6 is a schematic diagram showing an example of displaying experimental conditions. The display example in Fig. 6 shows an example in which the loss function profile, Hessian eigenvalues, eigenvectors, and uncertainty calculated from the Hessian eigenvalues ​​are displayed on the display unit 205 along with the current experimental conditions and recommended experimental conditions. In the example in Fig. 6, it can be seen that the loss function profile and the uncertainty of the model parameters are improved by adding the recommended experimental conditions.

[0069] The user who receives the proposal of additional experimental conditions from the information processing apparatus 200 performs an experiment using the experimental conditions including the additional experimental conditions in the substrate processing apparatus 100. The user does not need to adopt all of the experimental conditions proposed by the information processing apparatus 200, and may select the experimental conditions based on his or her own experience, etc. The information processing apparatus 200 may obtain the experimental results of a new experiment performed in the substrate processing apparatus 100, model the target, and verify whether the accuracy of the model was sufficient.

[0070] When the system is an automated experimental environment such as a combinatorial experiment, the information processing device 200 may perform modeling based on time series data obtained from the automated experimental environment, generate additional experimental conditions so as to improve the uncertainty of the model parameters, and instruct the automated experimental environment to conduct an additional experiment under experimental conditions that include the additional experimental conditions.

[0071] Furthermore, the information processing apparatus 200 may instruct the substrate processing apparatus 100 to conduct an additional experiment during a spare time when the information processing apparatus 200 is not normally operating. The information processing apparatus 200 can compensate for changes over time by acquiring the results of the additional experiment conducted during the spare time and creating a model based on the acquired experimental results.

[0072] Furthermore, the information processing apparatus 200 may acquire information about free time from the substrate processing apparatus 100 and select additional experimental conditions according to the free time. For example, when the information processing apparatus 200 determines that the substrate processing apparatus 100 has sufficient free time, the information processing apparatus 200 may select all recommended experimental conditions and instruct the substrate processing apparatus 100 to perform an experiment under the selected experimental conditions.

[0073] Furthermore, the information processing device 200 may set a set value or a set range for the experimental conditions and select only experimental conditions that satisfy the set value or the set range. For example, if the experimental conditions include a voltage and applying a large voltage accelerates component deterioration, the information processing device 200 may set a threshold value for the voltage and, if an experimental condition in which the voltage to be applied exceeds the threshold value is included, exclude that experimental condition from selection.

[0074] As described above, in this embodiment, when there is no specific knowledge about the dynamics of the system, or when it is difficult to design input signals that are generally used in modeling due to constraints on experimental conditions, etc., it is possible to additively (stepwise) find optimal experimental conditions using a data-driven method.

[0075] In this embodiment, if the initial experimental conditions are poor, the predictions and uncertainty calculations using the model will be inaccurate, but as calculations are repeated, the OBS will approach an optimal set of experimental conditions. For example, even if the characteristics of a component of the substrate processing apparatus 100 that uses time-series data as input and output are unknown because the target to be modeled is complex, the method disclosed herein can be used to efficiently perform experiments and generate a highly accurate model.

[0076] In the second embodiment, a configuration for accepting a user's selection of an experimental condition when proposing additional experimental conditions to the user will be described. Note that the overall configuration of the system and the internal configuration of the information processing device 200 are the same as those in the first embodiment, and therefore their description will be omitted.

[0077] FIG. 7 is a schematic diagram showing an example of a proposal screen in the second embodiment. As in the first embodiment, the proposal screen in the second embodiment shows an example in which the current experimental conditions and recommended experimental conditions are displayed on the display unit 205 together with the loss function profile, the eigenvalues ​​and eigenvectors of the Hessian, and the uncertainty calculated from the eigenvalues ​​of the Hessian. The recommended experimental conditions in this proposal screen are candidates for newly added experimental conditions and are configured to be selected by the user. The user selects preferred experimental conditions by checking checkboxes using the operation unit 204. The example in FIG. 7 shows that experimental conditions A and C have been selected.

[0078] If the system to be modeled is an automated experimental environment such as a combinatorial experiment, the control unit 201 may notify the system of the experimental conditions selected by the user and instruct the system to conduct additional experiments under those experimental conditions.

[0079] In this way, in the second embodiment, experiments can be added while checking with the user when starting up the system, when an abnormality occurs, and when modeling machine differences.

[0080] The control unit 201 may learn the user's preferences for the experimental conditions. An existing machine learning algorithm or the like is used for the learning. If the user's preferences have already been learned, the control unit 201 may select experimental conditions that match the user's preferences from the recommended experimental conditions without accepting a selection by the user, and instruct the system to conduct an additional experiment under the selected experimental conditions.

[0081] In the third embodiment, a configuration in which the object to be modeled is multidimensional will be described. Note that the overall configuration of the system and the internal configuration of the information processing device 200 are the same as those in the first embodiment, and therefore the description thereof will be omitted.

[0082] The electrostatic chuck (electrostatic adsorption stage for wafers) of the substrate processing apparatus 100 is provided with a plurality of heaters, coolers, sensors, etc., and temperature control is performed in each of a plurality of zones. The information processing apparatus 200 acquires experimental conditions and observation data for each zone using a method similar to that of the first embodiment, and generates a model for each zone that outputs a predicted temperature value for the electrostatic chuck when the experimental conditions (input signals to the heaters and coolers) are given. The information processing apparatus 200 also calculates the uncertainty of model parameters for the model in each zone. An example of the model parameter is the heat transfer coefficient.

[0083] FIG. 8 is a schematic diagram showing an example of calculation of model parameter uncertainty in embodiment 3. FIG. 8 shows an example in which the model parameter uncertainty is calculated for each zone and the level of uncertainty is displayed using shading. In the example of FIG. 8, it can be seen that the model parameter uncertainty is highest in the zone (i, j) = (3, 4) and decreases toward the periphery. In this case, the information processing device 200 proposes experimental conditions for heat transfer from the zone (3, 3) to the zone (3, 4), for example. The experimental conditions are, for example, setting the zone (3, 3) to a high temperature, the zone (3, 4) to a low temperature, and setting the others to intermediate temperatures.

[0084] Since the temperature control mechanism described above transfers heat between zones and does not control each zone independently, it is believed that improving the uncertainty of the model parameters in one zone will also improve the uncertainty of the model parameters in the surrounding zones.

[0085] Examples of multidimensional objects to be modeled are not limited to the temperature control mechanism in an electrostatic chuck, but also include temperature control mechanisms in vertical furnaces, mechanical mechanisms such as transfer robots, etc. Other examples include electrical circuits, pneumatic circuits, and other systems where values ​​at multiple parts of the system can be observed and controlled separately.

[0086] The embodiments disclosed herein are to be considered in all respects as illustrative and not restrictive. The scope of the present invention is defined by the claims, not by the above meaning, and is intended to include all modifications within the meaning and scope of the claims.

[0087] For example, in the embodiment, the substrate processing apparatus 100 is exemplified as an object (system) to be modeled. The target system is not limited to the substrate processing apparatus 100, but may be a manufacturing apparatus in which any manufacturing process is executed for electrical equipment, chemical industrial products, pharmaceuticals, food, chemical industrial products, etc. Furthermore, the target system is not limited to an apparatus or system in which any manufacturing process is executed, but may be any system that appropriately combines human living environments, economic activities, meteorological environments, etc.

[0088] Furthermore, the features described in each embodiment can be combined with each other. Independent claims and dependent claims described in the claims can be combined with each other in any combination, regardless of the reference format. Furthermore, claims may be written in a multiple claim format that references two or more other claims, or in a multiple claim format that references at least one other multiple claim (multi-multi claim format).

[0089] REFERENCE SIGNS LIST 100 Substrate processing apparatus 200 Information processing apparatus 201 Control section 202 Storage section 203 Communication section 204 Operation section 205 Display section PG Condition search program RM Recording medium

Claims

1. An information processing device comprising at least one processor, which acquires a first dataset including time series data to be input to a system and time series data observed from the system when the data is input, generates a model that explains the behavior of the system using the acquired first dataset, and outputs input data to be added to the first dataset so as to reduce uncertainty in the model parameters of the generated model.

2. The information processing device according to claim 1, wherein the information processing device calculates the uncertainty of model parameters in the model using a second dataset including new input data to the model and output data of the model obtained when the input data is input, updates the input data in the second dataset so as to improve the calculated uncertainty of the model parameters, and outputs the input data updated so as to maximize the degree of improvement in the uncertainty as input data to be added to the first dataset.

3. The information processing device according to claim 2, wherein the processor generates a model representing the behavior of the system using a dataset that is a combination of the first dataset and the second dataset, and evaluates the degree of improvement of the model parameters by comparing the uncertainty of the model parameters in the model generated using only the first dataset with the uncertainty of the model parameters in the model generated using the dataset that is a combination of the first dataset and the second dataset.

4. The information processing device according to claim 1, wherein the processor acquires time series data observed from the system when the input data is input, and generates a model that explains the behavior of the system using a first data set to which the input data and the time series data are added.

5. The information processing device according to claim 1, wherein the processor generates a model that explains the behavior of the system using multi-trajectory dynamic mode decomposition (MTDMD).

6. The information processing device according to claim 5, wherein the processor calculates the uncertainty of the model parameters using a function calculated using eigenvalues ​​of the Hessian of the multi-trajectory dynamic mode decomposition.

7. The information processing device according to claim 1, wherein the processor generates a model that explains the behavior of the system using Dynamic Mode Decomposition (DMD).

8. The information processing device according to claim 1, wherein the processor generates a model that explains the behavior of the system using Sparse Identification of Nonlinear Dynamics with Control (SINDy).

9. The information processing device according to claim 2, wherein the processor randomly determines the input data in the second data set or obtains the input data from an external source.

10. The information processing device according to claim 2, wherein the processor stops updating the input data when the uncertainty of the model parameters becomes equal to or less than a set value.

11. The information processing device according to claim 2, wherein the processor displays at least one of the model parameters of the model, the output data of the model, the time series data obtained from the system, and the uncertainty of the model parameters.

12. The information processing device according to claim 1, wherein the processor displays the model parameters using a heat map.

13. The information processing device according to claim 1, wherein the processor displays candidates for input data to be added to the first dataset, and accepts a user's selection of input data to be added to the first dataset from among the displayed candidates.

14. The information processing device according to claim 13, wherein the processor learns user preferences for the candidates, and based on the learning results, selects input data to add to the first dataset from among the candidates without accepting a user selection.

15. The information processing device according to claim 1, wherein the processor uses a constraint expressed as a function of time when outputting input data to be added to the first data set.

16. The information processing device according to claim 15, wherein the processor performs constrained optimization by using an inner product operation between the time series data input to the system and the function.

17. The information processing device according to claim 1, wherein the system includes a substrate processing apparatus, and the processor outputs input data to be added to the first data set so as to improve uncertainty in model parameters of a model that explains the behavior of the substrate processing apparatus.

18. The information processing apparatus according to claim 17, further comprising: an information processing apparatus that outputs input data to be added to the first data set to the substrate processing apparatus; and causes the substrate processing apparatus to execute processing based on the input data.

19. An information processing method in which a computer executes the following processes: acquiring a first dataset containing time-series data to be input to a system and time-series data observed from said system when said data is input; generating a model that explains the behavior of said system using the acquired first dataset; and outputting input data to be added to said first dataset so as to reduce uncertainty in the model parameters of the generated model.

20. A computer program causing a computer to execute the following processes: acquiring a first dataset including time-series data to be input to a system and time-series data observed from said system when said data is input; generating a model that explains the behavior of said system using the acquired first dataset; and outputting input data to be added to said first dataset so as to reduce uncertainty in the model parameters of the generated model.

Images