Information processing method, computer program, and information processing device

Abstract

The invention provides an information processing method, a computer program, and an information processing apparatus for optimizing a physical system. In this information processing method, an information processing device performs: a process in which a system model is stored in a storage unit in advance, said system model being obtained by modeling a physical system by connecting a plurality of constituent element models obtained by modeling each of a plurality of physical constituent elements included in the physical system; receiving a setting of an objective function that is calculated on the basis of an output value of the system model; determining an allowable region of an input value in which an output value of the objective function satisfies a predetermined condition; determining an allowable region of the input value of the constituent element model in which the output value of the constituent element model falls within the allowable region for the constituent element model that outputs the input value; and determining the permissible region for the input value of the system model by determining the permissible region for a plurality of constituent element models constituting the system model.

Description

TECHNICAL FIELD

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

[0002] A model construction method is proposed in Patent Literature 1, which receives a hierarchical tree structure defining nodes associated with hardware of a physical system, collects data including a timestamp associated with a hardware constituent element and observation data, derives a node state of the nodes based on the collected data, constructs a finite state machine (FSM) model defining a sequence of states associated with the nodes based on the timestamp, and creates a model of the physical system as a part of a global finite state machine of the physical system.

[0003] Patent Literature 1: Japanese Patent Application Laid-Open No. 2021-536626 SUMMARY

[0004] The present disclosure provides an information processing method, a computer program, and an information processing apparatus for optimizing a physical system.

[0005] In an information processing method of one embodiment, the following processing is performed by an information processing apparatus: a system model is pre-stored in a storage section, the system model being obtained by linking a plurality of constituent element models respectively modeling a plurality of physical constituent elements included in a physical system and modeling the physical system; a setting of an objective function that performs an operation based on an output value of the system model is accepted; a permissible region of an input value in which an output value of the objective function satisfies a prescribed condition is decided; for the constituent element models outputting the input value, a permissible region of an input value of the constituent element model in which an output value of the constituent element model falls within the permissible region is decided; and the decision of the permissible region is performed for the plurality of constituent element models constituting the system model, thereby deciding a permissible region of an input value of the system model.

[0006] According to the present disclosure, it is possible to expect optimization of a physical system. BRIEF DESCRIPTION OF DRAWINGS

[0007] Figure 1 is a schematic diagram for explaining one example of an outline of an information processing system of the present embodiment.

[0008] Figure 2 is a block diagram showing one configuration example of an information processing apparatus provided by the information processing system of the present embodiment.

[0009] Figure 3 is a flowchart showing one example of steps of an optimization process performed by the information processing apparatus of the present embodiment.

[0010] Figure 4 is a schematic diagram for explaining one example of a method for determining an allowable region.

[0011] Figure 5 is a schematic diagram showing one display example of an optimization result.

[0012] Figure 6 is a schematic diagram showing one configuration example of a system model of a modification example.

[0013] Figure 7 is a schematic diagram for explaining an outline of the information processing system of Embodiment 2.

[0014] Figure 8 is a flowchart showing one example of steps of an optimization process performed by the information processing apparatus of Embodiment 2. DETAILED DESCRIPTION

[0015] Hereinafter, specific examples of the information processing system of the embodiments of the present disclosure will be described with reference to the drawings. Furthermore, the present disclosure is not limited to these examples, and is intended to include the meaning equivalent to the claims and all modifications within the scope.

[0016] [Embodiment 1]

[0017] <Outline of System>

[0018] Figure 1 is a schematic diagram for explaining one example of an outline of the information processing system of the present embodiment. The information processing system of the present embodiment is a system that reproduces a physical system existing in a real space (physical space) in a virtual space (digital space or network space), and performs management and control of the physical system, and the like. This is a technology that can be called so-called digital twinning. In the present embodiment, the information processing system performs digital twinning that reproduces a substrate processing system 3 that performs substrate processing such as manufacturing of semiconductor wafers in a virtual space, as one example of a physical system.

[0019] In the technology of digital twinning, a system model that models the substrate processing system 3 based on various data collected in the substrate processing system 3 is created. In the present embodiment, a constituent element model that individually models a plurality of constituent elements such as a cooler, a heater, and a time measurement that constitute the substrate processing system 3 is included in the system model. In the present drawing, the constituent element model is represented by a circular symbol, the constituent element model A corresponds to the cooler of the substrate processing system 3, the constituent element model B corresponds to the heater, and the constituent element model C corresponds to the time measurement.

[0020] Further, in the present embodiment, the system model is a structure in which a plurality of component models are connected in a hierarchy. In the illustrated system model, there is a layer including the above-described component models A, B, and C, and a layer including component models E, U, and T as a higher layer of the layer. Hereinafter, the layer including the component models E, U, and T is referred to as a first layer, and the layer including the component models A, B, and C is referred to as a second layer. The component models E, U, and T of the first layer perform various predictions related to the processing of the substrate processing system 3 on the basis of data obtained from the component models A, B, and C of the second layer. The component models A, B, and C of the second layer predict the processing results of the functions of the cooler, the heater, and the time measurement of the substrate processing system 3 on the basis of the input data to the substrate processing system 3.

[0021] These component models are created in advance as follows: the input data to the component and the output data from the component are extracted from the data collected with respect to the substrate processing system 3, and the parameters and the like of the model are adjusted on the basis of the extracted data to reproduce the correspondence of the input and the output. The component model can be represented by, for example, an operation formula based on the physical properties of the component, and can be, for example, a machine learning model such as a neural network, or a model of a structure other than these.

[0022] For example, the component model A of the second layer is a model that acquires the cooler set temperature as input data 1 and predicts the cooler temperature of the substrate processing system 3. The component model B is a model that acquires the heater set temperature as input data 2 and acquires the set of the on / off of the heater as input data 3, and predicts the heater temperature of the substrate processing system 3. The component model C is a model that measures the processing time of the substrate processing system 3 in a virtual space. Further, in the present drawing, the input data to the component model C is not illustrated, but, for example, data such as the on / off of the power supply of the substrate processing system 3, the start / stop of the substrate processing, and the like can be input to the component model C.

[0023] Further, for example, the structure model E of the first layer is a model that predicts the environmental load such as the electricity fee or the amount of carbon dioxide discharged accompanying the operation of the substrate processing system. Further, in the present drawing, the illustration of the component model of the second layer to which the component model E is connected is omitted. The component model U is a model that predicts the temperature of the substrate processed by the substrate processing system 3 on the basis of the cooler temperature output from the component model A of the second layer and the heater temperature output from the component model B. The component model T is a model that estimates the required time of the substrate processing performed by the substrate processing system 3 on the basis of the result of the time measurement output from the component model C.

[0024] That is, the illustrated system model includes three constituent element models E, U, T in the first layer, and three constituent element models A, B, C in the second layer. The constituent element models A, B of the second layer are linked to the constituent element model U of the first layer, and the constituent element model C of the second layer is linked to the constituent element model T of the first layer. In addition, the illustrated system model is one example and is not limited thereto. The illustrated system model is a simplified model, and an actual system model can be constituted by linking more constituent element models divided into more layers. That is, the system model handled by the information processing system can be a model having a hierarchical structure of three or more layers. In addition, the system model can also be a model in which a plurality of constituent element models do not form a hierarchical structure, in other words, a model of only one layer.

[0025] For example, the information processing system acquires various data measured by a sensor or the like from the substrate processing system 3 that performs substrate processing, inputs the acquired data to the system model, and acquires various prediction values and the like output by the system model in accordance with the input of the data. The information processing system can perform monitoring of the operation state of the substrate processing system 3, prediction of the characteristics of a substrate processed by the substrate processing system 3, or control of the substrate processing system 3 that has fed back the acquired data, on the basis of the acquired data.

[0026] In addition, the information processing system of the present embodiment can perform processing of determining conditions of input data that cause the substrate processing system 3 to optimally operate in a target and a constraint or the like set by a user, that is, optimization processing, using a system model of the substrate processing system 3 generated in advance. In this case, the user sets a target function G that targets optimization of the substrate processing system 3, and a constraint condition for each constituent element model or a combination thereof.

[0027] The target function G is a function linked to one or a plurality of constituent element models of the highest layer (the first layer) of the system model. The target function G is a function that accepts one or a plurality of data output by the linked constituent element models as input, and outputs a result of performing a prescribed operation on the input data, and the prescribed operation performed by the user setting the function and a condition for the output value of the function. In a case where the output data of the constituent element model E is set to e, the output data of the constituent element model U is set to u, and the output data of the constituent element model T is set to t, the illustrated target function G can be set as, for example, the following formula (1). In addition, in formula (1), w1, w2, w3 are weights, and Z is an arbitrary numerical value.

[0028] Target function G: w1 x e + w2 x u + w3 x t ≤ Z... (1)

[0029] By setting this formula (1), the user can, for example, set a target function that targets the substrate processing system 3 to be operated in a state where the output of the constituent element model E is equal to or less than a certain value, the output of the constituent element model U is equal to or less than a certain value, and the output of the constituent element model T is equal to or less than a certain value. Figure 1The substrate processing system 3 shown is set as an optimization target to minimize the electricity cost as much as possible, to minimize the difference between the substrate temperature and the target value as much as possible, and to shorten the required time as much as possible. In addition, the user can set which of these three optimizations to focus on by appropriately setting the weights w1, w2, w3 to optimize.

[0030] Further, the method of setting the objective function is not limited to the method of the above-described equation (1), and various methods can be employed. In addition, the objective function can be automatically set by a device such as an information processing device, rather than manually set by a user or the like. For example, a device such as an information processing device can determine the objective function based on one or more conditions or the like appropriately set for the substrate processing system 3. In addition, a device such as an information processing device can determine the objective function by machine learning using various data obtained from the substrate processing system 3. In addition, for example, the objective function set in another information processing system of the same or similar type that has already been operated can be acquired and used as the objective function of the present information processing system.

[0031] Regarding the constraint condition set by the user for each component model, for example, as a range of values acceptable for the output data of the component model, it can be set to the following equation (2). Further, in equation (2), e1 and e2 are threshold values for the output data e of the component model E, u1 and u2 are threshold values for the output data u of the component model U, and t1 and t2 are threshold values for the output data t of the component model T.

[0032] e1 < e < e2

[0033] u1 < u < u2 … (2)

[0034] t1 < t < t2

[0035] Further, the method of setting the constraint condition is not limited to the method of the above-described equation (2), and various methods can be employed. In addition, the constraint condition can be set in advance by, for example, a designer or manager of the substrate processing system 3, or a creator of the system model and the component models, or the like, rather than being set by the user. The user can make modifications or additions to the constraint condition set in advance by these designers or the like.

[0036] In addition, the above-described constraint condition is one example of a condition set individually for each component model. The constraint condition can be set for a combination of a plurality of component models. For example, in a combination of the two component models of the cooler and the heater of the system model shown, to prevent excessive heating, a constraint condition can be set in advance so that the heater cannot be turned on if the cooler is not operating. Figure 1

[0037] As described above, the user can set the constraint condition for each component model, and the system model can be optimized while taking into account the constraint condition set by the user. In addition, the user can set the constraint condition for each component model, and the system model can be optimized while taking into account the constraint condition set by the user. Figure 1 ​As shown, the system model linking the user-created objective function G becomes a so-called tree-structured model in which the objective function G is taken as a root node, one or more component models of the first layer are linked to the root node, one or more component models of the second layer are linked to each component model of the first layer, and one or more input data to each component model of the second layer are taken as leaf nodes. Further, the system model not linking the objective function and the input data is a model including a plurality of tree structures with the component models of the first layer as root nodes.

[0038] Further, in the present embodiment, the objective function and the system model become a tree structure, but are not limited thereto. The objective function and the system model can include a structure different from the tree structure, such as one component model of the second layer being linked to a plurality of component models of the first layer.

[0039] The information processing system of the present embodiment determines the range (allowable region) of the values acceptable to each input data to the objective function based on the user-set objective function and the constraint condition. The information processing system determines the range (allowable region) of the values acceptable to each input data to each component model of the next layer based on the allowable region of each input data to the objective function. In this way, the information processing system determines the allowable region of the input data to the component model of the next layer in order from the uppermost objective function by recursively repeating the determination, and thus can finally determine the allowable region of the input data to the lowermost component model. That is, in the present embodiment, the information processing system determines the range (allowable region) of the values acceptable to each input data to each component model of the next layer based on the range (allowable region) of the values acceptable to each input data to the objective function. Figure 1 In the example shown, the allowable region can be determined for each of the input data 1, 2, 3 as a result of the optimization processing based on the objective function G. By setting each input data to the substrate processing system 3 in such a manner as to become within the determined allowable region, the substrate processing system 3 can be caused to perform processing satisfying the objective function and the constraint condition.

[0040] <Device Structure>

[0041] Figure 2is a block diagram showing one configuration example of the information processing apparatus 1 that the information processing system of the present embodiment is provided with. The information processing apparatus 1 of the present embodiment is an apparatus that monitors and controls, and the like, the operation of the substrate processing system 3, by being connected to the substrate processing system 3 via a communication cable or the like. In addition, the information processing system of the present embodiment performs the above-described monitoring and control, and the like, using a system model (digital twin of the substrate processing system 3) that is modeled on the substrate processing system 3, and performs processing for optimizing the operation of the substrate processing system 3 using the system model. The information processing apparatus 1 of the present embodiment can be realized, for example, by installing the computer program of the present embodiment in a general-purpose information processing apparatus such as a personal computer or a server computer. The information processing apparatus 1 of the present embodiment is configured with a processing section 11, a storage section 12, a communication section 13, a display section 14, an operation section 15, and the like. In the present embodiment, the processing by the information processing apparatus 1 is described as being performed by one information processing apparatus 1, but the processing by the information processing apparatus 1 can be performed by a plurality of apparatuses in a distributed manner.

[0042] The processing section 11 is configured with a computing processing apparatus such as a CPU (Central Processing Unit), an MPU (Micro-Processing Unit), a GPU (Graphics Processing Unit), or a quantum processor, a ROM (Read Only Memory), and a RAM (Random Access Memory), and the like. The processing section 11 performs various processing such as processing for monitoring and controlling the operation of the substrate processing system 3, and optimization processing using the system model, by reading out and executing the program 12a stored in the storage section 12.

[0043] The storage section 12 is configured with a large-capacity storage apparatus such as a hard disk, for example. The storage section 12 stores various programs executed by the processing section 11, and various data required for the processing by the processing section 11. In the present embodiment, the storage section 12 stores the program 12a executed by the processing section 11. In addition, a model information storage section 12b that stores information related to the system model of the substrate processing system 3 is provided in the storage section 12.

[0044] In the present embodiment, the program (computer program, program product) 12a is provided in a form in which it is recorded on a recording medium 99 such as a memory card or an optical disc, and the information processing apparatus 1 reads out the program 12a from the recording medium 99 and stores it in the storage section 12. However, the program 12a may, for example, also be written to the storage section 12 at the manufacturing stage of the information processing apparatus 1. Also, for example, the program 12a can be acquired by the information processing apparatus 1 through communication from a remote server device or the like that distributes content. For example, the program 12a can be read out by a writing device from content recorded on the recording medium 99 and written to the storage section 12 of the information processing apparatus 1. The program 12a can be provided in a form in which it is distributed via a network, or in a form in which it is recorded on the recording medium 99.

[0045] The model information storage section 12b of the storage section 12 stores information related to a system model of the substrate processing system 3 that is created in advance. The information related to the system model may, for example, include information of a plurality of component model included in the system model, and information related to which component model is linked to which component model, and the like. Also, in the information of the component model, for example, information indicating the structure of the model, and information of internal parameters of the model determined by machine learning or the like can be included. The information processing apparatus 1 can constitute the system model by reading out the information stored in the model information storage section 12b in advance, and use it for processing such as control and optimization of the substrate processing system 3.

[0046] Further, the method of generating the system model of the substrate processing system 3 (digital twin of the substrate processing system 3) is a prior art, and therefore detailed explanation is omitted in the present embodiment. The system model and the component model can be generated, for example, by a process of machine learning using various data obtained from the substrate processing system 3. The generation of these models can be performed by the information processing apparatus 1, or the information processing apparatus 1 can acquire information of a model generated by a device different from the information processing apparatus 1 and store it in the model information storage section 12b. In any case, in the information processing system of the present embodiment, the system model of the substrate processing system 3 as shown in the drawing is generated in advance by an appropriate method. Figure 1 The system model stores its information in the model information storage section 12b in advance so as to be available when the information processing apparatus 1 performs control and optimization of the substrate processing system 3 or the like.

[0047] The communication section 13 is connected to the substrate processing system 3 via a cable such as a communication line or a signal line, and performs transmission and reception of data between the substrate processing system 3 via the cable. In the present embodiment, the communication section 13 transmits the control input data provided from the processing section 11 to the substrate processing system 3. Also, the communication section 13 receives data transmitted from the substrate processing system 3 and provides the received data to the processing section 11.

[0048] The display section 14 is configured using a liquid crystal display or the like, and displays various images, characters, and the like based on the processing by the processing section 11. In the present embodiment, the display section 14 displays various information such as the operation status of the substrate processing system 3, and information related to the result of the optimization processing, and the like. The operation section 15 accepts operations by a user, and notifies the processing section 11 of the accepted operations. For example, the operation section 15 accepts operations by a user through a mechanical button or a touch panel provided on the surface of the display section 14, or the like. Alternatively, the operation section 15 can be an input device such as a mouse or a keyboard, and these input devices can also be configured to be detachable from the information processing apparatus 1.

[0049] Further, the storage section 12 can be an external storage device connected to the information processing apparatus 1. Alternatively, the information processing apparatus 1 can be a multi-computer configured to include a plurality of computers, or a virtual machine configured by software. Further, the information processing apparatus 1 is not limited to the above-described configuration, and can not include the display section 14, the operation section 15, and the like, for example.

[0050] Further, in the information processing apparatus 1 of the present embodiment, the processing section 11 reads and executes the program 12a stored in the storage section 12, whereby the functions of the control processing section 11a, the setting accepting section 11b, the optimization processing section 11c, the display processing section 11d, and the like are realized by the processing section 11 as software.

[0051] The control processing section 11a controls the operation of the substrate processing system 3 in accordance with a predetermined step of substrate processing (manufacturing step of a semiconductor, recipe), for example. Further, the control processing section 11a monitors the operation of the substrate processing system 3 based on data obtained from the substrate processing system 3 in association with the execution of substrate processing. In the present embodiment, the control processing section 11a predicts the merit or precision, or the like, with respect to the processing performed by the substrate processing system 3 using the system model stored in the model information storage section 12b, and adjusts the control of the substrate processing system 3 by feeding back the prediction result.

[0052] Further, in the information processing system of the present embodiment, both the control of the substrate processing system 3 and the optimization using the system model are performed by the information processing apparatus 1, but are not limited thereto. For example, an information processing apparatus that performs the control of the substrate processing system 3 and an information processing apparatus that performs the optimization using the system model can be separately provided. In this case, for example, the result of the optimization processing performed by one information processing apparatus can be provided to the other information processing apparatus, and the other information processing apparatus performs the control of the substrate processing system 3 using the result. Further, the processing performed by the information processing system of the present embodiment can be performed by three or more information processing apparatuses appropriately distributed.

[0053] The setting accepting section 11b accepts settings such as a target function and a constraint condition from the user. The setting accepting section 11b displays a hierarchical structure (tree structure) of the system model shown in FIG. 6 on the display section 14, accepts an operation of connecting the target function G to an arbitrary component model of the first layer of the system model, and an operation of inputting a specific function of the target function G, and accepts the target function G for optimization from the user. Further, the setting accepting section 11b accepts a constraint condition for each component model from the user by accepting an operation of selecting a component model from the displayed hierarchical structure of the system model, and an operation of inputting a specific constraint condition for the selected component model. Note that the method of input accepting the target function and the constraint condition is one example, and is not limited thereto. The setting accepting section 11b can accept settings by any method. Figure 1 The setting accepting section 11b accepts settings such as a target function and a constraint condition from the user. The setting accepting section 11b displays a hierarchical structure (tree structure) of the system model shown in FIG. 6 on the display section 14, accepts an operation of connecting the target function G to an arbitrary component model of the first layer of the system model, and an operation of inputting a specific function of the target function G, and accepts the target function G for optimization from the user. Further, the setting accepting section 11b accepts a constraint condition for each component model from the user by accepting an operation of selecting a component model from the displayed hierarchical structure of the system model, and an operation of inputting a specific constraint condition for the selected component model. Note that the method of input accepting the target function and the constraint condition is one example, and is not limited thereto. The setting accepting section 11b can accept settings by any method.

[0054] The optimization processing section 11c determines an operation condition of the substrate processing system 3 so as to optimize the target represented by the target function, based on the system model of the substrate processing system 3 stored in the model information storage section 12b and the target function and the constraint condition accepted from the user by the setting accepting section 11b. In the present embodiment, the system model linked to the target function becomes a tree structure having the target function as a root node. The optimization processing section 11c traces the layers from the upper level to the lower level recursively from the target function as the root node, through the component model of the first layer, the component model of the second layer, and the like, and determines a range (allowable region) in which the input data of each component model is desirable, for optimization of the target function. By tracing the hierarchical structure of the system model from the upper level to the lower level, the optimization processing section 11c can finally determine the allowable region of the input data to the system model. The determined allowable region of the input data to the system model is the input data to the substrate processing system 3 for which the target function is optimized, and by operating within the allowable region, the substrate processing system 3 can be optimally operated.

[0055] The display processing section 11d performs processing of displaying various characters and images on the display section 14. In the present embodiment, the display processing section 11d displays various data obtained from the substrate processing system 3 operated by the control of the control processing section 11a on the display section 14. Further, the display processing section 11d performs display of a screen for accepting settings by the setting accepting section 11b. Further, the display processing section 11d displays information related to the result of optimization by the optimization processing section 11c.

[0056] < Optimization Processing >

[0057] Figure 3is a flowchart showing one example of a step of the optimization processing by the information processing apparatus 1 of the present embodiment. The setting accepting section lib of the processing section 11 of the information processing apparatus 1 of the present embodiment accepts input of a setting of an objective function related to optimization of the substrate processing system 3 based on the user's operation of the operation section 15 (step S1). In addition, the setting accepting section lib accepts a setting of a constraint condition related to a component model included in the system model of the substrate processing system 3 (step S2). At this time, the processing section 11 can display an input screen including a graph or the like showing the structure of the system model of the substrate processing system 3 on the display section 14, for example, and accept input of the objective function and the constraint condition by the user.

[0058] The optimization processing section lie of the processing section 11 links the objective function whose setting is accepted in step S1 to the system model to form a tree structure, and determines a range (an allowable region) of input that optimizes (maximizes or minimizes) the output of the uppermost layer (the root node) of the tree structure, that is, the objective function (step S3).

[0059] Figure 4 is a schematic diagram for explaining one example of a method of determining an allowable region. In the present example, a case is assumed in which two component models of the first layer of the system model are linked to the uppermost objective function. Figure 4 The graph shown in the drawing is a graph in which the output value of the first component model of the first layer is set as fl, the output value of the second component model is set as f2, the output value of the objective function corresponding to the two values fl, f2 is set as G, and the correspondence relation of fl, f2, and G is graphed in three dimensions. In the present example, as the target of optimization, the output value G of the objective function is set to exceed a prescribed threshold value, and the constraint conditions of fl > 0 and f2 > 0 are set. In this case, in the graph shown in the drawing, the boundary line 101 shown by the broken line corresponds to the threshold value, and the region above the boundary line 101 becomes a region satisfying the target. The boundary line 101 projected onto the fl-f2 plane is the boundary line 102 shown by the broken line in the graph shown in the drawing. The region surrounded by the boundary line 102 and the fl axis and the f2 axis is a region in which the objective function can be optimized, and hereinafter, this region is referred to as an allowable region in distinction from the allowable region. If the combination of fl and f2 included in this allowable region is obtained, the output value G of the objective function exceeds the threshold value.

[0060] Further, the information processing apparatus 1 of the present embodiment determines a rectangular region (a super-rectangular region) included in the admissible region obtained by the above-described method. In the illustrated graph, one example of the rectangular region is indicated by a dotted line. Further, a plurality of rectangular regions can be included in one admissible region, but the information processing apparatus 1 selects, for example, the rectangular region having the largest area from among the plurality of rectangular regions. However, the information processing apparatus 1 can also select, for example, the rectangular region closest to a square, and the like, and further, for example, can randomly select one rectangular region. The information processing apparatus 1 can determine a rectangular region in accordance with an appropriate procedure prescribed in advance. The information processing apparatus 1 sets the rectangular region determined from the non-rectangular admissible region as Figure 3 The admissible region of the processing result of step S3 of the flowchart illustrated in the drawing is subjected to the processing of the subsequent step.

[0061] In the rectangular admissible region thus determined, the input to the objective function, that is, f1 and f2, can be independently varied. The range of f1 falling within the rectangular region can be set as the objective with respect to the optimization of the component model outputting the f1. Similarly, the range of f2 falling within the rectangular region can be set as the objective with respect to the optimization of the component model outputting the f2. Since f1 and f2 can be independently varied, the optimization of the component model outputting f1 and the optimization of the component model outputting f2 can be separately performed. The information processing apparatus 1 can determine the admissible range of the input with respect to the component model outputting f1 by the same method, and can determine the admissible range of the input with respect to the component model outputting f2 by the same method. The information processing apparatus 1 can finally determine the admissible region related to the input to the system model by sequentially and recursively repeating the processing of determining the rectangular admissible region from the upper layer to the lower layer.

[0062] Further, in a case where the rectangular region is determined as the admissible region from the upper layer to the lower layer in sequence, a situation where the admissible region or the rectangular region cannot be obtained in the lower layer can occur in the rectangular region determined by the upper layer. In such a case, the information processing apparatus 1 can trace back one or more layers and reselect the rectangular region. For example, the information processing apparatus 1 first repeatedly traces back only one layer to the upper layer and reselects another rectangular region in a case where the admissible region or the rectangular region cannot be obtained, and traces back to a higher layer and reselects the rectangular region in a case where the admissible region or the rectangular region still cannot be obtained even after reselection is performed a prescribed number of times. The information processing apparatus 1 can reselect the rectangular region in accordance with an arbitrary criterion, and can also feed back information that can be helpful for reselection from the lower layer to the upper layer.

[0063] Further, the information processing apparatus 1 can select two or more rectangular regions from the admissible region, and set the plurality of rectangular regions as the admissible region. In this case, it is preferable that the information processing apparatus 1 select the plurality of rectangular regions in a manner that they do not have a common portion, but a portion of the plurality of rectangular regions can be a common portion. In a case where the information processing apparatus 1 determines a plurality of admissible regions in the upper layer, the information processing apparatus 1 can determine an admissible region for each of the admissible regions in the lower layer, select a rectangular region from each of the admissible regions, and select one rectangular region from the selected plurality of rectangular regions in accordance with a prescribed condition, for example, select a rectangular region having a large area and discard the remaining rectangular regions. Further, the information processing apparatus 1 can not discard the rectangular regions in the lower layer, but maintain the plurality of admissible regions in parallel and repeatedly perform selection of the rectangular regions until the lowermost layer. The information processing apparatus 1 can determine a plurality of rectangular regions as the admissible region, for example, to prevent a rectangular region having a sufficient area from being unable to be obtained due to the admissible region being a complex shape, and to significantly limit selection of the rectangular region in the lower layer.

[0064] Further, in the present example, a case where the input to the objective function is two inputs is exemplified, but an admissible region can be determined similarly in a case where the input is one or three or more. For example, in a case where the input is one, the above-described rectangular region becomes a region in a straight line (line segment) shape, for example. For example, in a case where the input is three, the above-described rectangular region becomes a region in a cuboid shape, for example. That is, the expression of the "rectangular region" used in the above-described description is limited to a two-dimensional expression, and in a case where it is extended to a multi-dimensional, it can be called a "hyper rectangular region", for example. The hyper rectangular region is a region in a line segment in one dimension, a rectangle (a rectangular region) in two dimensions, a cuboid in three dimensions, and is defined similarly with respect to four or more dimensions.

[0065] In Figure 3 The optimization processing section 11c determines an admissible region for the input data of the next layer one or a plurality of component models by the same method as in step S3 (step S4). The optimization processing section 11c determines whether the processing of determining the admissible region for the input data reaches the lowermost layer with respect to the plurality of levels of the component models constituting the system model (step S5). In a case where the lowermost layer is not reached (S5: No), the optimization processing section 11c returns the processing to step S4, and performs the processing of determining the admissible region for the input data with respect to the component model of the next layer. The optimization processing section 11c recursively repeatedly performs the processing of determining the admissible region from the upper layer to the lower layer, and in a case where it is determined that the lowermost layer is reached (S5: Yes), stores information of the admissible region determined with respect to the input data of the lowermost layer as a result of the optimization in the storage section 12 (step S6).

[0066] Next, the optimization processing section 11c performs processing of modifying the allowable region for the component model of the upper layer based on the allowable region decided for the input data of the lowest layer (step S7). At this time, the optimization processing section 11c, in a case where data within the allowable region decided for the lowest layer is input to the component model, calculates the range of data output from the component model, and modifies the allowable region related to the input of the component model of the upper layer in a manner so as to become the calculated range. The optimization processing section 11c similarly recursively repeats the processing of modifying the allowable region from the component model of the lowest layer to the objective function of the highest layer, and finally is able to modify the allowable region of the input data with respect to the objective function. Thus, the optimization processing section 11c, in a case where the allowable region of the lower layer is limited due to constraints such as restrictions of hardware, is able to feedback this to the upper layer, and modify the allowable region of the upper layer to a range that can be achieved.

[0067] The optimization processing section 11c determines whether or not the processing of modifying the allowable region for the component model of the upper layer has reached the highest layer (step S8). In a case where the highest layer has not been reached (S8: No), the optimization processing section 11c returns the processing to step S7, and performs the processing of modifying the allowable region for the component model of the upper layer. The optimization processing section 11c repeatedly performs the processing of modifying the allowable region in order from the lower layer to the upper layer, and in a case where it is determined that the highest layer has been reached (S8: Yes), calculates the output value (or the range of the output value) of the objective function corresponding to the modified allowable region with respect to the objective function as the highest layer (step S9).

[0068] Next, the optimization processing section 11c calculates a margin indicating how much leeway there is with respect to the set objective of optimization with respect to the value of the objective function calculated in step S9 or the range thereof (step S10). For example, in a case where the output of the objective function needs to exceed a set threshold value, the difference or the ratio or the like between the output value of the objective function calculated in step S9 and the set threshold value can be set as the margin. The display processing section 11d of the processing section 11 displays the result of the optimization including the information of the allowable region stored in step S6, the value of the objective function calculated in step S9, and the margin calculated in step S10, and the like on the display section 14 (step Sll), and ends the processing.

[0069] Further, the information processing apparatus 1 can adjust the threshold value for the output of the objective function in the direction of being stricter (increase the threshold value if maximizing, or decrease the threshold value if minimizing) and repeat the processing of steps S3 to S10, for example, in a case where the margin calculated in step S10 exceeds a prescribed margin prescribed in advance, that is, in a case where there is sufficient margin. The threshold value is adjusted until the margin becomes 0 or in the vicinity thereof, and the processing of optimization is repeated, whereby the information processing apparatus 1 can obtain a more suitable (optimal) output value of the objective function and an input value of the system model that realizes it.

[0070] Figure 5 is a schematic view of one display example of the optimization result. The information processing apparatus 1 of the present embodiment displays, in step S11, an optimization result display screen shown in Figure 3 based on the optimization processing of steps S1 to S10 of the flowchart shown in Figure 5 in the display section 14. In the optimization result display screen of the present example, for example, a model structure display region 111 and an optimization result display region 112 are arranged side by side to the left and right, the model structure display region 111 displays the hierarchical structure of the system model that is the object of optimization, and the optimization result display region 112 displays various information obtained by the optimization processing. In the model structure display region 111, a graph obtained by connecting a plurality of nodes with lines is displayed, the nodes being a plurality of component models included in the system model of the substrate processing system 3 that is the object of optimization, and the associated objective function and input data.

[0071] Further, in the optimization result display region 112, for example, a title string of "optimization result" is displayed at the uppermost portion, and various information is displayed in a list below the title string. In the illustrated example, as the input data to the system model, for example, it is shown that the best is that the cooler set temperature is X°C to Y°C, the heater set temperature is Z°C to W°C, and the set on is set as the heater on / off set. It is also shown that the predicted value of the value of the objective function in a case where the substrate processing of the substrate processing system 3 is performed within these set ranges is a, and the margin with respect to the target set in advance is β.

[0072] Further, the information processing apparatus 1, in a case where the optimization result display screen is displayed in the display section 14, for example, accepts an operation of selecting the objective function displayed in the model structure display region 111. The information processing apparatus 1, in accordance with the selection operation of the objective function, displays a setting screen or the like of the objective function in the display section 14 and accepts an operation of re-setting the objective function by the user. The information processing apparatus 1 that has accepted the re-setting of the objective function can perform the processing of optimization based on the re-set objective function by the same steps and update the information of the optimization result displayed in the optimization result display screen.

[0073] Further,Figure 5 The structure of the optimized result display shown is an example and is not limited to this. The information processing device 1 can also display and provide the optimized information to the user in any manner.

[0074] <Variation Example>

[0075] Figure 6 This is a schematic diagram of a structural example representing a modified system model. The above... Figure 1 The system model shown is a structure where the objective function is the root node, and multiple component models are connected as nodes in a tree structure relative to that root node. In this tree-structured system model, the output of a node is input to a node in the next higher level. However, when modeling the substrate processing system 3, it may be difficult to achieve such a complete tree structure model.

[0076] Therefore, in the modified system model, the basic structure is based on a tree-structured connection of the root node (objective function) and multiple nodes (component model). Parts of this structure allow, for example, a structure where the output data of one node can be input to multiple nodes in a higher level, and a structure where the output data of one node can be input to other nodes in the same level. Figure 6 In the system model of the variant example shown, for example, the output data of the constituent element model C is input to the constituent element model T of the upper layer, and is also input to the constituent element model E of the upper layer and the constituent element model B of the same layer.

[0077] In a modified example, the information processing apparatus 1 determines, for instance, an allowable region (rectangular region) related to the output data of the constituent element model C based on a rectangular region determined based on constituent element model T, a rectangular region determined based on constituent element model E, and a rectangular region determined based on constituent element model B. The information processing apparatus 1 can, for instance, set the overlapping area of ​​the three rectangular regions as the rectangular region related to the output data of the constituent element model C.

[0078] <Summary>

[0079] In the information processing system of the present embodiment of the above structure, the information processing apparatus 1 stores, in the model information storage section 12b, a system model that is formed by hierarchically linking a plurality of element models that are obtained by modeling a plurality of physical elements included in a physical system such as the substrate processing system 3, respectively. The information processing apparatus 1 determines an allowable region of input data in a manner that an output value of the objective function satisfies a prescribed condition. The information processing apparatus 1 determines an allowable region of input data of an element model that outputs the input data, in a manner that an output value of the element model falls within the determined allowable region. The information processing apparatus 1 repeatedly determines an allowable region of input data recursively from the upper layer to the lower layer (from the output side of the layers to the input side) for a plurality of element models that constitute the system model, and finally determines an allowable region of input data of the system model. Thus, the information processing system of the present embodiment can determine an allowable region of input data of the system model that optimizes the objective function, and can expect to optimize the operation of the substrate processing system 3 by causing the substrate processing system 3 to operate with input data within the determined allowable region.

[0080] In addition, in the information processing system of the present embodiment, the information processing apparatus 1 determines a rectangular region that is enclosed in the determined allowable region. The information processing apparatus 1 repeatedly determines a rectangular region recursively from the upper layer to the lower layer for a plurality of element models that constitute the system model. Thus, the information processing system can independently process the allowable regions determined for a plurality of input data to the element models, respectively, and can expect to make it easy to determine the allowable regions recursively from the upper layer to the lower layer.

[0081] In addition, in the information processing system of the present embodiment, the information processing apparatus 1 repeatedly corrects an allowable region recursively from the lower layer to the upper layer (from the input side to the output side) after determining an allowable region of input data of the system model, and finally calculates an output value of the objective function. Thus, the information processing system can predict an output value of the objective function in a case where the substrate processing system 3 is caused to operate with input data within the allowable region, and calculate, for example, a margin with respect to a set target or the like.

[0082] In addition, in the information processing system of the present embodiment, the information processing apparatus 1 displays, as a result of optimization, information related to the determined allowable region of input data of the system model and the calculated output value of the objective function on the display section 14. At this time, the information processing apparatus 1 can also display, for example, a graph that represents the structure of the system model by connecting a plurality of nodes with lines, the nodes being constituted by the element models. Based on the display of this information, a user can re-study the pros and cons of the set objective function, for example, and perform re-setting of the objective function.

[0083] In addition, in the information processing system of the present embodiment, the system model modeled on the substrate processing system 3 is a tree structure model in which a target function is a root node and a plurality of component models are connected hierarchically. Such a tree structure model is suitable for the optimization process of recursively repeating the determination of the allowable region from the upper layer to the lower layer by the information processing apparatus 1.

[0084] Further, in the present embodiment, the substrate processing system 3 is described as one example of a physical system processed as the information processing system, but the physical system is not limited to the substrate processing system 3 and can be various systems in which modeling of physical components is possible. Figure 1 The structure of the system model illustrated is one example and is not limited thereto.

[0085] [Embodiment 2]

[0086] Figure 7 is a schematic diagram for explaining an outline of the information processing system of Embodiment 2. The information processing system of Embodiment 2 optimizes the system model and the target function and the like possessed by the information processing system of Embodiment 1 using a method of learning or data assimilation and the like.

[0087] Further, in Embodiment 2, the system model and the target function (the block surrounded by the broken line in Figure 7 are referred to as a digital twin. The digital twin is configured of a hardware model that imitates the action of a unit of an apparatus as an object, an interaction model that reflects the physical correlation of a plurality of units, a control model that controls the unit, and the like.

[0088] In a case where the physical system processed by the system model is the substrate processing system 3, the substrate processing system 3 needs to act in accordance with a plurality of action conditions (recipes), and thus internal parameters of the digital twin and parameters used for the optimization process and the like are held in the information processing apparatus 1 as parameters that differ for each action condition. The information processing apparatus 1 can use the digital twin by switching these parameters in accordance with the action condition of the substrate processing system 3. The internal parameters of the digital twin can include, for example, the state of each apparatus included in the system model, the internal parameters of a prediction model that makes a prediction in accordance with the apparatus state and an input signal, and the like.

[0089] The information processing apparatus 1 of Embodiment 2 further possesses a second optimization processing section 11e and a learning processing section 11f and the like in addition to the structure of the information processing apparatus 1 of Embodiment 1. The second optimization processing section 11e and the learning processing section 11f are software functional sections realized by the processing section 11 executing the program 12a of the storage section 12.

[0090] The second optimization processing section 11e causes the substrate processing system 3 to operate via the control processing section 11a on the basis of the optimal operation condition of the digital twin (substrate processing system 3) obtained through the optimization processing by the optimization processing section 11c. The second optimization processing section 11e compares the sensor value obtained as a result of the operation of the substrate processing system 3 with the predicted value of the sensor value obtained using the digital twin.

[0091] In a case where it is determined that the actual operation result of the substrate processing system 3 and the predicted result of the digital twin are largely different, the second optimization processing section 11e implements learning (optimization) of the digital twin or data assimilation, updates the internal parameter of the digital twin, and thereby optimizes the digital twin. Further, the internal parameter of the digital twin can also include a parameter for which update at this point in time is prohibited.

[0092] The learning processing section 11f acquires input data (operation condition, etc.) and output data (sensor value, etc.) to the substrate processing system 3 in a case where the operation of the substrate processing system 3 is implemented by the second optimization processing section 11e, and stores the acquired input and output data in correspondence with each other as learning data. In a case where it is determined that the second optimization processing section 11e performs optimization of the digital twin, the learning processing section 11f performs learning (optimization) using the stored learning data, and thereby updates the internal parameter of the digital twin. Further, the update of the internal parameter of the digital twin can employ, for example, a deep unfolding, a differentiable algorithm, a gradient method, a grid search, a random search, evolutionary computation (genetic algorithm or swarm intelligence, etc.), Bayesian optimization, quantum annealing, or a combination optimization or a continuous value optimization using a gate-type quantum computer, or the like.

[0093] Further, in the present embodiment, the learning processing section 11f realizes improvement in prediction accuracy by performing learning of the digital twin, but is not limited thereto, and for example, can realize improvement in prediction accuracy of the digital twin by performing data assimilation processing. Data assimilation is, for example, a method of performing prediction and update of the internal state of the digital twin using both observation data including an error of a sensor value, etc. and predicted data of the digital twin, like a Kalman filter or a particle filter, etc.

[0094] In addition, the information processing apparatus 1 can also perform updating of parameters of an optimization algorithm at the time of optimally determining the allowable region of input data by the same method as the updating of internal parameters of the digital twin. The parameters of the optimization algorithm are values that can be set by the user, such as a learning rate or the number of repetitions, in the case where, for example, the steepest descent method is adopted as the optimization algorithm for determining the allowable region of input data, and are so-called hyperparameters. The information processing apparatus 1 can, for example, carefully perform optimization (correction of the allowable region) by setting the learning rate to be small and the maximum number of repetitions to be large at the initial stage of optimization for determining the allowable region of input data, and gradually update (optimize) the learning rate and the maximum number of repetitions, thereby gradually shortening the time required for optimization. Furthermore, the optimization algorithm is not limited to the steepest descent method, and various algorithms such as the quasi-Newton method or the Newton method can be employed, and, for example, a neural network or the like can also be included in the optimization algorithm, and in these cases, it is also possible to expect that the time required for processing of optimization can be shortened by updating the parameters that can be adjusted by the information processing apparatus 1.

[0095] Figure 8 is a flowchart showing one example of the steps of the optimization processing performed by the information processing apparatus 1 of Embodiment 2. The second optimization processing section 11e of the processing section 11 of the information processing apparatus 1 of Embodiment 2 acquires condition information for optimization, such as the action conditions, the device state, or the constraint conditions, related to the substrate processing system 3 that is the object (step S31).

[0096] Next, the optimization processing section 11c of the processing section 11 performs optimization processing using the digital twin (step S32). Furthermore, the processing performed by the optimization processing section 11c in this step is Figure 3 the optimization processing shown in FIG. 12 is processing for predicting the optimal value with respect to the range of input and the value of output of the substrate processing system 3 using the digital twin.

[0097] The second optimization processing section 11e of the processing section 11 performs the action of the substrate processing system 3 based on the optimal input range obtained by the optimization processing of step S32 (step S33). At this time, the second optimization processing section 11e determines the action conditions and the like of the substrate processing system 3 based on the optimal input range, and provides a command to perform the action based on the determined action conditions and the like to the control processing section 11a, thereby causing the substrate processing system 3 to act.

[0098] The second optimization processing section 11e acquires a sensor value measured by a sensor possessed by the substrate processing system 3 as a result of the operation of the substrate processing system 3 (step S34). The second optimization processing section 11e compares the sensor value acquired in step S34 with the predicted value of the sensor value obtained as the output of the digital twin in the optimization processing of step S32 (step S35). Further, for example, in a case where the value predicted using the digital twin is a value that cannot be directly measured by the sensor of the substrate processing system 3 or the like, the second optimization processing section 11e can also perform appropriate calculation on the obtained sensor value, convert the sensor value into information of the same kind as the predicted value, and perform comparison. Similarly, the second optimization processing section 11e can also perform appropriate calculation on the predicted value obtained using the digital twin, convert the predicted value into information of the same kind as the sensor value, and perform comparison.

[0099] The second optimization processing section 11e determines whether or not the prediction using the digital twin has sufficient accuracy on the basis of the result of the comparison in step S35, for example, whether or not the error of the sensor value and the predicted value is less than a threshold value or the like (step S36).

[0100] In a case where the prediction using the digital twin does not obtain sufficient accuracy (S36: No), the learning processing section 11f of the processing section 11 performs learning processing on the basis of data obtained in association with the operation of the substrate processing system 3 of step S33 (step S37), and the processing returns to step S31. In a case where the prediction using the digital twin obtains sufficient accuracy (S36: Yes), the second optimization processing section 11e ends the processing.

[0101] Further, the information processing apparatus 1 can predict whether or not the substrate processing system 3 has a failure on the basis of the result of comparison of the sensor value measured by the sensor of the substrate processing system 3 with the predicted value of the sensor value obtained as the output of the digital twin by the optimization processing.

[0102] In addition, the information processing apparatus 1 can also decide experimental conditions necessary to supplement insufficient data and display the decided experimental conditions to make a suggestion to the user in a case where data necessary for learning processing is insufficient.

[0103] The determination of whether or not data necessary for learning processing is sufficient or insufficient can be performed, for example, by a method of existing Bayesian optimization. For example, in a case where the width of a distribution including a parameter of a model adjusted by learning processing is narrowed in the process of Bayesian optimization of the distribution, it can be considered that information is increased by new data and uncertainty of the model is reduced, and it can be determined that data necessary for learning processing is sufficient. The information processing apparatus 1 can determine that data is sufficient in a case where a statistic quantity (variance, standard deviation, interval of quartiles, or the like) related to the distribution satisfies a prescribed criterion, and determine that data is insufficient in a case where the criterion is not satisfied.

[0104] The determination of the experimental condition required to supplement insufficient data can also be performed by the method of Bayesian optimization. The information processing apparatus 1 can determine the experimental condition that reduces the uncertainty of the model by the method of Bayesian optimization. In addition, in a case where Bayesian optimization is not used, for example, the information processing apparatus 1 can perform prediction using the existing model according to a certain experimental condition, add data taking the prediction result as a measured value, perform learning processing using the data to calculate the uncertainty of the model, and determine the experimental condition in a manner that the amount of reduction of the uncertainty is the largest.

[0105] In addition, the determination of whether the data required for the learning processing is sufficient or insufficient and the determination of the experimental condition required to supplement insufficient data can be performed by the user instead of the information processing apparatus 1. The information processing apparatus 1 can display information indicating the value of the uncertainty of the model, for example, and ask the user whether the data required for the learning processing is sufficient or insufficient, and accept the judgment of the user. Furthermore, in a case where the user judges that the data is insufficient, the information processing apparatus 1 can accept the input of the experimental condition for supplementing the insufficient data from the user, and perform the substrate processing using the substrate processing system 3 with the accepted experimental condition to collect the required data.

[0106] In the information processing system of Embodiment 2 of the above structure, the information processing apparatus 1 causes the physical substrate processing system 3 to operate based on the allowable region of the input to the digital twin determined by the optimization of Embodiment 1. The information processing apparatus 1 acquires a sensor value or the like as a result of the operation of the substrate processing system 3, and performs learning of the digital twin or optimization such as data assimilation based on the acquired sensor value. Thus, it is expected that the information processing system of Embodiment 2 optimizes the digital twin to achieve improvement in prediction accuracy or the like. Part or all of the digital twin obtained by the optimization with sufficient accuracy can also be transferred to a system different from the information processing system of the present embodiment. For example, it is expected that the digital twin is utilized in failure prediction of a physical system, model-based hardware development, or recipe design of the substrate processing system 3 or the like.

[0107] In addition, the other structures of the information processing system of Embodiment 2 are the same as those of the information processing system of Embodiment 1, and thus the same reference numerals are assigned to the same parts, and detailed description is omitted.

[0108] The embodiments disclosed this time are illustrative in all aspects and are not intended to limit the present invention. The scope of the present disclosure is not represented by the above description but is represented by the claims, and is intended to include the meanings equivalent to the claims and all modifications within the scope.

[0109] The matters described in the embodiments can be combined with each other. In addition, the independent claims and the dependent claims described in the claims can be combined with each other in all combinations regardless of the citation form. Also, the claims are described using the form in which the claim citing two or more other claims is described (multiple claim form), but are not limited thereto. The claims can also be described using the form in which the multiple claim citing at least one multiple claim is described (multiple citing multiple claim).

[0110] Explanation of Reference Signs

[0111] 1…information processing apparatus (computer); 3…substrate processing system; 11…processing section; 11a…control processing section; 11b…setting accepting section; 11c…optimization processing section; 11d…display processing section; 11e…second optimization processing section; 11f…learning processing section; 12…storage section; 12a…program (computer program); 12b…model information storage section; 13…communication section; 14…display section; 15…operation section.

Claims

1. An information processing method of performing the following processes by an information processing apparatus: storing a system model in a storage section in advance, the system model being obtained by linking a plurality of element models each modeling a plurality of physical elements included in a physical system and modeling the physical system; accepting a setting of an objective function that performs an operation based on an output value of the system model; deciding an allowable region of an input value in which an output value of the objective function satisfies a prescribed condition; deciding, for the element model that outputs the input value, an allowable region of an input value of the element model in which an output value of the element model falls within the allowable region; and deciding the allowable region of the input value of the system model by deciding the allowable region of the input value for a plurality of element models that constitute the system model.

2. The information processing method according to claim 1, wherein the system model is a model in which a plurality of element models are linked in a hierarchical manner, the allowable region of the input value is decided recursively in order from an output side to an input side of a layer for a plurality of element models that constitute the system model, thereby deciding the allowable region of the input value of the system model.

3. The information processing method according to claim 2, wherein an allowable region of an input value in which an output value satisfies the allowable region is decided, a hyper-rectangular region that is enclosed in the decided allowable region is decided, the decided hyper-rectangular region is set as the allowable region of the input value.

4. The information processing method according to claim 2, wherein an allowable region of an output value of the element model that is inputted with the input value is corrected based on the decided allowable region of the input value of the system model, an allowable region of an output value of the element model that is inputted with the output value is corrected based on the corrected allowable region of the output value, the correction of the allowable region of the output value is recursively performed in order from the input side to the output side of a layer for a plurality of element models that constitute the system model, the output value of the objective function is calculated based on the corrected allowable region.

5. The information processing method according to claim 4, wherein information related to the decided allowable region of the input value of the system model and the calculated output value of the objective function is displayed on a display section, a re-setting of the objective function is accepted.

6. The information processing method according to claim 5, wherein a graph of the system model is generated with the element models as nodes and a plurality of nodes being connected by lines, the generated graph is displayed on the display section together with the information.

7. The information processing method according to claim 1, wherein the system model is a tree-structured model in which the objective function is a root node and a plurality of element models are linked in a hierarchical manner.

8. The information processing method according to claim 1, wherein the physical system is caused to operate based on the decided allowable region, an operation result of the physical system is acquired, optimizing parameters of the system model or parameters of an algorithm for determining an allowable region of input values of the system model based on the acquired action result.

9. The information processing method according to claim 8, wherein optimizing parameters of the system model or parameters of an algorithm for determining an allowable region of input values of the system model based on a comparison between an action result of the physical system and a prediction result of the system model.

10. The information processing method according to claim 8, wherein the optimization of the parameters of the system model or the parameters of the algorithm for determining the allowable region of the input values of the system model is performed by data assimilation.

11. The information processing method according to claim 8, wherein in a case where data related to the action result of the physical system is insufficient when optimizing the parameters, estimating an action condition of the physical system for acquiring the insufficient data, outputting the estimated action condition.

12. The information processing method according to claim 1, wherein a plurality of the system models or parameters of the system models are pre-stored in the storage section, the system model or the parameters of the system model are selected in accordance with an action condition of the physical system.

13. A computer program that causes a computer to execute the following processing: pre-storing a system model in a storage section, the system model being obtained by linking a plurality of component models obtained by modeling a plurality of physical components included in a physical system respectively and modeling the physical system; accepting a setting of an objective function that performs an operation based on an output value of the system model; determining an allowable region of input values in which an output value of the objective function satisfies a prescribed condition; for the component models that output the input values, determining an allowable region of input values of the component models in which an output value of the component models falls within the allowable region; and for the plurality of component models that constitute the system model, determining the allowable regions, thereby determining an allowable region of input values of the system model.

14. An information processing apparatus comprising: a processing section; and a storage section that stores a system model, the system model being obtained by linking a plurality of component models obtained by modeling a plurality of physical components included in a physical system respectively and modeling the physical system, the processing section performing the following processing: accepting a setting of an objective function that performs an operation based on an output value of the system model; determining an allowable region of input values in which an output value of the objective function satisfies a prescribed condition; for the component models that output the input values, determining an allowable region of input values of the component models in which an output value of the component models falls within the allowable region; and for the plurality of component models that constitute the system model, determining the allowable regions, thereby determining an allowable region of input values of the system model.

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