Linear equation set solving method and related equipment

Abstract

The embodiment of the invention discloses a linear equation set solving method, in the method, a computing device or a computing device cluster can obtain description information input by a user, the description information comprises linear equation set information, and the linear equation set information comprises a right-end item; then, reasoning the description information through an artificial intelligence AI model to obtain a first initial solution corresponding to a linear equation set; and then, determining a target initial solution according to the first initial solution, carrying out iterative solution on the linear equation set based on the target initial solution, and outputting a solution result of the linear equation set. Through the AI model in the method, the characteristics of the linear equation set can be identified according to the input description information so as to efficiently determine the appropriate first initial solution related to the linear equation set, so that the target initial solution is determined according to the first initial solution, and the linear equation set is efficiently and accurately subjected to iterative solution based on the target initial solution; and the solving efficiency of the system of linear equations is improved.

Description

[0001] This application claims priority to Chinese patent application filed on June 25, 2023, with Chinese application number 202310752934.X and invention name “A method and device for solving a mathematical model”, the entire contents of which are incorporated by reference into this application. Technical Field

[0002] The present application relates to the field of artificial intelligence (AI) technology, and in particular to a method for solving a system of linear equations and related equipment. Background Art

[0003] In fields such as industrial simulation, computer-aided engineering (CAE) simulation in engineering design is often used to analyze the physical properties of engineering and products.

[0004] When using CAE simulation to solve a physical problem, the more important and time-consuming task is usually to solve the linear equations.

[0005] A commonly used method for solving linear equations is the linear iteration method, which is to obtain an approximate solution to a linear equation through a finite number of iterations.

[0006] When using the linear iteration method to solve a system of linear equations, the initial solution has a great influence on the iterative solution process. If the initial solution is far from the true solution, more iterations are required to converge to the true solution, which increases the calculation time. In addition, if the initial solution is not appropriate, it may also cause the iteration to fail to converge.

[0007] Currently, an initial solution suitable for the linear equations to be solved is usually determined based on expert experience, or a default initial solution is used.

[0008] However, due to the large changes in the scale and nature of linear equations, the default initial solution is usually difficult to produce good results in the process of solving linear equations, and expert experience often requires a long time to accumulate, and the participation of relevant experts is required in the solution process, which affects the processing efficiency. Therefore, there is an urgent need for a method that can efficiently generate a suitable initial solution for the linear equations to be solved, so as to better calculate the solution results of the linear equations. Summary of the invention

[0009] The embodiment of the present application provides a method for solving a linear equation system, which can conveniently and efficiently generate a suitable initial solution for the linear equation system to be solved. The present application also provides a corresponding apparatus, a computing device, a computing device cluster, a computer-readable storage medium, and a computer program product.

[0010] The first aspect of the present application provides a method for solving a system of linear equations, which is applied to a computing device or a computing device cluster. In the method, descriptive information input by a user can be obtained, the descriptive information includes information about the system of linear equations, and the information about the system of linear equations includes the right-hand side terms; the descriptive information is inferred through an artificial intelligence (AI) model to obtain a first initial solution corresponding to the system of linear equations; a target initial solution is determined based on the first initial solution, the system of linear equations is iteratively solved based on the target initial solution, and the solution result of the system of linear equations is output.

[0011] In the first aspect, the AI ​​model is able to identify the characteristics of the linear equation system based on the input descriptive information to efficiently determine a suitable first initial solution for the linear equation system, thereby determining the target initial solution based on the first initial solution, and iteratively solving the linear equation system efficiently and accurately based on the target initial solution, thereby improving the efficiency of solving the linear equation system and avoiding the generalization problems brought about by the initial solution determined based on expert experience and the default initial solution.

[0012] In a possible implementation of the first aspect, the description information also includes information about a physical problem to be solved, and the system of linear equations is obtained by numerically simulating the information about the physical problem to be solved. The information about the physical problem to be solved includes at least one of the following: boundary conditions, grid information, and physical equations.

[0013] At present, the traditional algorithms for determining the initial solutions of the linear equations usually use mathematical derivation to predict the initial solutions of the linear equations, for example, the proper orthogonal decomposition (POD) algorithm and the Fischer algorithm.

[0014] These traditional algorithms for determining the initial solution of a system of linear equations usually only consider information such as the coefficient matrix in the system of linear equations. However, the coefficient matrix of the system of linear equations alone cannot well reflect the characteristics of the problem to be solved. Therefore, the effects of the initial solutions predicted by the traditional algorithms for determining the initial solution of a system of linear equations often have large deviations and cannot provide more suitable initial solutions for various scenarios.

[0015] In this possible implementation, it is taken into account that the linear equations are constructed based on physical problem information, that is to say, the physical problem information will affect the subsequently generated linear equations. The physical problem information, as the upper-level scene information of the subsequently generated linear equations, will affect the coefficient matrix and / or right-hand side terms and other parameters in the subsequently generated linear equations.

[0016] It can be seen that the physical problem information, as the upper-level scene information involved in constructing a linear system of equations, is strongly correlated with the constructed linear system of equations. Therefore, in this possible implementation, the description information may include linear system of equations information and physical problem information associated with the linear system of equations. Then, the AI ​​model can be used to fully mine various information such as linear system of equations information and physical problem information associated with the linear system of equations to determine the first initial solution that conforms to the current physical problem characteristics and is suitable for the current linear system of equations to be solved. It can be seen that through this method, suitable initial solutions can be efficiently provided for linear systems of equations corresponding to various physical problems in different scenarios, thereby improving the efficiency of solving the corresponding linear systems of equations.

[0017] In a possible implementation of the first aspect, a target initial solution is determined based on a first initial solution, a linear equation group is iteratively solved based on the target initial solution, and a solution result of the linear equation group is output, including: obtaining first configuration information, the first configuration information carrying at least one initial solution generation method for generating an initial solution; obtaining multiple initial solutions according to at least one initial solution generation method indicated by the first configuration information, the multiple initial solutions including the first initial solution; screening out a target initial solution from the multiple initial solutions; and iteratively solving the linear equation group according to the target initial solution, and outputting the solution result of the linear equation group.

[0018] In this possible implementation, considering that different initial solution generation methods may be applicable to physical problems in different physical scenarios, multiple initial solutions can be provided according to the first configuration information. In this way, the adaptability of different initial solution generation methods in different physical problems can be fully considered, and a more suitable target initial solution in the current category of physical problems can be screened out from multiple initial solutions, thereby improving the quality of the target initial solution finally obtained, and thus improving the solution efficiency of the iterative solution process of the linear equation system.

[0019] In a possible implementation of the first aspect, a target initial solution is screened out from multiple initial solutions, including: obtaining second configuration information, the second configuration information carrying at least one heuristic strategy; and screening out the target initial solution from multiple initial solutions according to the at least one heuristic strategy.

[0020] In this possible implementation, multiple initial solutions are screened by at least one heuristic strategy, and an initial solution that better meets the characteristics of the current physical problem can be screened out from the multiple initial solutions as the target initial solution, thereby improving the quality of the target initial solution finally obtained.

[0021] In a possible implementation of the first aspect, a target initial solution is screened out from multiple initial solutions, including: obtaining third configuration information, the third configuration information carries an evaluation strategy, the evaluation strategy includes evaluation indicators, or includes evaluation indicators and weights corresponding to each evaluation indicator, the evaluation indicators include one or more of solution time, solution accuracy and number of iterations; according to the evaluation strategy, the target initial solution is screened out from multiple initial solutions.

[0022] In this possible implementation, any evaluation index can be used to evaluate the iterative performance of the corresponding initial solution when it is used as the initial solution in the iterative solution process of the linear equation system. In this way, the corresponding target initial solution with better iterative performance can be screened out from multiple initial solutions according to the evaluation index and related weight information in the evaluation strategy.

[0023] In a possible implementation of the first aspect, the method also includes: generating training data, the training data including training samples and labels corresponding to the training samples, the training samples including description information, and the labels corresponding to the training samples are obtained according to the first initial solution; according to the training data, training the AI ​​model to obtain an optimized AI model.

[0024] In this possible implementation method, the AI ​​model can be continuously iterated and updated as the data distribution and scale of users in the actual application scenario change, thereby continuously optimizing the model so that the optimized AI model is more adaptable to the current scenario needs and can generate better initial solutions for different physical problems and corresponding linear equations, thereby improving the solution efficiency.

[0025] In a possible implementation of the first aspect, the method also includes: obtaining performance indicators corresponding to the solution results, the performance indicators including one or more of solution time, solution accuracy, and number of iterations; training the AI ​​model according to the training data to obtain an optimized AI model, including: training the AI ​​model according to the training data and the loss function to obtain the optimized AI model, wherein the loss function is constructed based on the performance indicators.

[0026] In a possible implementation of the first aspect, the AI ​​model is a general model or a model for solving partial differential equations (PDE), the general model includes CNN or PINN, and the model for solving PDE includes deeponet.

[0027] In this possible implementation, the loss function may reflect the performance indicators in the labels of the corresponding samples. Specifically, the performance indicators in the labels of the corresponding training samples indicate that the worse the corresponding solution performance is (for example, the longer the solution time is, the lower the solution accuracy is, and the more iterations are), the greater the corresponding loss value is. In addition, in some examples, the loss function may also evaluate the difference between the initial training solution output by the model to be trained during the iteration process and the initial solution in the label of the corresponding sample.

[0028] The second aspect of the present application provides a data processing device, which has the function of implementing the method of the first aspect or any possible implementation of the first aspect. The function can be implemented by hardware, or by hardware executing corresponding software. The hardware or software includes one or more modules corresponding to the above functions, such as an acquisition module and a processing module.

[0029] The third aspect of the present application provides an electronic device, which includes at least one processor, a memory, and computer execution instructions stored in the memory and executable on the processor. When the computer execution instructions are executed by the processor, the processor executes a method as described in the first aspect or any possible implementation of the first aspect.

[0030] The fourth aspect of the present application provides a computer-readable storage medium storing one or more computer-executable instructions. When the computer-executable instructions are executed by a processor, the processor executes a method as described in the first aspect or any possible implementation of the first aspect.

[0031] The fifth aspect of the present application provides a computer program product storing one or more computer-executable instructions. When the computer-executable instructions are executed by a processor, the processor executes a method as described in the first aspect or any possible implementation of the first aspect.

[0032] In a sixth aspect of the present application, a chip system is provided, which includes a processor for supporting an electronic device to implement the functions involved in the first aspect or any possible implementation of the first aspect. In a possible design, the chip system may also include a memory, which is used to store program instructions and data necessary for the electronic device. The chip system may be composed of a chip, or may include a chip and other discrete devices.

[0033] Among them, the technical effects brought about by the second to sixth aspects or any possible implementation methods thereof can refer to the technical effects brought about by the first aspect or the relevant possible implementation methods of the first aspect, and will not be repeated here. BRIEF DESCRIPTION OF THE DRAWINGS

[0034] Figure 1is an exemplary flow chart of CAE simulation provided by an embodiment of the present application;

[0035] Figure 2 is an exemplary schematic diagram of a data center provided in an embodiment of the present application;

[0036] Figure 3 This is an exemplary schematic diagram of performing CAE simulation-related tasks through a cloud management platform provided in an embodiment of the present application;

[0037] Figure 4 It is a schematic diagram of an embodiment of a method for solving a system of linear equations provided in an embodiment of the present application;

[0038] Figure 5 It is an exemplary schematic diagram of iteratively solving a linear equation system based on an initial solution adaptive optimization module provided in an embodiment of the present application;

[0039] Figure 6 is an exemplary schematic diagram of iteratively solving a system of linear equations provided in an embodiment of the present application;

[0040] Figure 7 This is an exemplary schematic diagram of executing a linear equations solving task through a cloud management platform provided in an embodiment of the present application;

[0041] Figure 8 is an exemplary schematic diagram of a computer model of a solenoid valve provided in an embodiment of the present application;

[0042] Fig. 9 1 is a schematic diagram of an embodiment of a linear equation solving device provided in an embodiment of the present application;

[0043] Fig.10 is a schematic diagram of a structure of a computing device provided in an embodiment of the present application;

[0044] Fig.11 is a schematic diagram of a structure of a computing device cluster provided in an embodiment of the present application;

[0045] Fig.12 It is a structural diagram of a computing device cluster provided in an embodiment of the present application. DETAILED DESCRIPTION

[0046] The following describes the embodiments of the present application in conjunction with the drawings in the embodiments of the present application. The terms used in the implementation method section of the present application are only used to explain the specific embodiments of the present application, and are not intended to limit the present application.

[0047] Those skilled in the art may appreciate that, with the development of technology and the emergence of new scenarios, the technical solutions provided in the embodiments of the present application are also applicable to similar technical problems.

[0048] In the present application, "at least one" means one or more, and "plurality" means two or more. "And / or" describes the association relationship of associated objects, indicating that three relationships may exist. For example, A and / or B can represent: A exists alone, A and B exist at the same time, and B exists alone, where A and B can be singular or plural. The character " / " generally indicates that the objects associated before and after are in an "or" relationship. "At least one of the following" or similar expressions refers to any combination of these items, including any combination of singular or plural items. The terms "first", "second", etc. in the specification and claims of this application and the above-mentioned drawings are used to distinguish similar objects, and do not have to be used to describe a specific order or sequence. It should be understood that the terms used in this way can be interchangeable where appropriate, and this is merely a description of the way in which objects with the same attributes are described in the embodiments of the present application. Furthermore, the terms "comprises," "comprising," and "having," and any variations thereof, are intended to cover a non-exclusive inclusion, so that a process, method, system, product, or apparatus that comprises a list of elements is not necessarily limited to those elements but may include other elements not expressly listed or inherent to such process, method, product, or apparatus.

[0049] CAE simulation refers to the process of analyzing and solving engineering problems through numerical calculation and simulation using computer-aided engineering technology. CAE simulation is an engineering analysis method based on computer technology. It can conduct virtual testing of products during the design phase to evaluate product performance, reliability, and safety, thereby reducing the cost and time of actual testing. CAE simulation can be applied to various engineering fields, such as machinery, electronics, aerospace, automobiles, and construction, and can simulate various physical phenomena, such as structural mechanics, fluid mechanics, and heat conduction.

[0050] like Figure 1 The figure shows an exemplary process flow diagram of CAE simulation.

[0051] Figure 1 In the simulation process shown, first, computer-aided design (CAD) modeling can be performed on the physical problem to obtain a computer model. The computer model can be a digital model obtained by using a specified software in a computer, and can virtually describe the physical structure. The computer model can be newly created by using CAD, or can be obtained and imported from other means (such as other equipment).

[0052] Then, the computer model obtained after modeling can be subjected to geometric pre-processing, for example, threads and slits in the computer model can be removed, and the thin slices can be subjected to dimensionality reduction processing, etc. Then, one or more of the materials, domain equations, boundary conditions, loads, and initial conditions of the computer model can be set, and then the computer model can be meshed. After the meshing is completed, physical equations can be generated according to the physical problem to be solved, and a group of partial differential equations can be constructed, which can then be discretized into a sparse linear equation group.

[0053] After obtaining the linear equations, it is necessary to solve the linear equations. After obtaining the solution results, the corresponding physical problems can be solved according to the solution results to obtain simulation results. For example, Figure 1 In the example shown, after obtaining the solution to the linear equations, three-dimensional drawings, cross-sectional diagrams, and derived values ​​of the computer model can be calculated based on the solution results, for example, integrating a volume, surface, or variable, or calculating the value of an expression along an edge or point, etc.

[0054] After obtaining the simulation results, simulation post-processing can be performed. For example, the defects of the design scheme in the project can be located according to the simulation results, and improvement analysis can be performed. In addition, the design scheme can be updated and iterated. For example, a simulation report can be written according to the simulation results to guide the update of the corresponding design scheme.

[0055] CAE simulation can be used to solve a variety of physical problems, such as Figure 1 As shown in the figure, CAE simulation is widely used in various practical engineering application scenarios in the industrial field.

[0056] In the process of CAE simulation, the more important and time-consuming task is usually to solve the linear equations. At present, a commonly used method for solving linear equations is the linear iteration method. The linear iteration method refers to obtaining the approximate solution of the linear equations through a finite number of iterations.

[0057] When solving a linear system of equations by a linear iteration method, currently, an initial solution suitable for the linear system of equations to be solved is usually determined based on expert experience, or a default initial solution is used.

[0058] However, due to the large changes in the scale and nature of linear equations, the default initial solution is usually difficult to produce good results in the process of solving linear equations, and expert experience often requires a long time to accumulate, and the participation of relevant experts is required in the solution process, which affects the processing efficiency. Therefore, there is an urgent need for a method that can efficiently generate a suitable initial solution for the linear equations to be solved, so as to better calculate the solution results of the linear equations.

[0059] To this end, an embodiment of the present application provides a method for solving a system of linear equations, which can conveniently and efficiently generate a suitable initial solution for the system of linear equations to be solved.

[0060] The method of the embodiment of the present application may be applied to a computing device cluster, which may include one or more computing devices.

[0061] The type of any computing device is not limited herein. Exemplarily, any computing device may be a terminal device, or a server, a container, or a virtual machine.

[0062] In one example, the computing device cluster can be used to implement a cloud management platform. In other words, the embodiments of the present application can be applied to a cloud management platform.

[0063] The cloud management platform is used to manage the infrastructure for providing cloud services, and can provide computing, network and storage capabilities based on services of hardware resources and software resources. Exemplarily, the cloud management platform can include one or more data centers to provide cloud resources through one or more data centers.

[0064] Combine the following Figure 2 An architectural diagram is shown to introduce a data center.

[0065] Figure 2 In the data center, the cloud management platform communicates with one or more servers (such as Figure 2 The server 1 and server 2 in the server exchange information. The server includes a hardware layer and a software layer. The hardware layer includes the hardware configured by the server, wherein the PCI device may be, for example, a network card, a graphics processing unit (GPU), an offload card, etc., which can be inserted into the peripheral component interconnect standard (PCI) or peripheral component interconnect express (PCIe) slot of the server. The software layer includes an operating system installed and running on the server (relative to the operating system of the virtual machine, it can be called the host operating system). The host operating system is provided with a virtual machine manager (also called a hypervisor). The role of the virtual machine manager is to realize the computing virtualization, network virtualization and storage virtualization of the virtual machine, and is responsible for managing the virtual machine. Among them, a virtual machine (virtual machine) refers to a complete computer system with complete hardware system functions simulated by software and running in a completely isolated environment. Figure 2 In the system architecture shown, a data center is equipped with multiple servers, which can be used to run virtual machines. The specifications of each virtual machine can be the same or different. Among them, the virtual machine can also be called a cloud server (elastic compute service, ECS), elastic instance, etc. Different cloud service providers may have different names.

[0066] In one example of the embodiment of the present application, the cloud management platform can be a public cloud platform. In this case, cloud service providers such as individuals or software developers with cloud resource development capabilities can provide cloud services to users. Users obtain cloud services through the Internet but do not own cloud computing resources. In other embodiments of the present application, the cloud management platform can be a private cloud platform or a hybrid cloud platform, and the present application does not limit this.

[0067] Specifically, in Figure 2 In the example shown, the cloud management platform can provide an access interface (such as an interface or application programming interface (API)). Users of the cloud management platform and cloud service providers can operate the client remote access access interface to register a cloud account and password on the cloud management platform, and log in to the cloud management platform after the cloud management platform successfully authenticates the cloud account and password, thereby creating, managing, logging in and operating virtual machines in the cloud data center.

[0068] For example, when there is a need to perform a linear equation solving task, some enterprises, organizations or individuals can purchase cloud services, thereby performing related linear equation solving tasks through the cloud resources of the cloud management platform and obtaining corresponding solution results from the cloud management platform.

[0069] Of course, the cloud management platform may also be other types of cloud management platforms, which is not limited in the embodiments of the present application.

[0070] In the embodiment of the present application, the cloud management platform can provide users with linear iteration initial solution generation services and linear iteration solver services. In addition, it can also provide numerical calculation solver services and CAE simulation services, etc. In this way, users can perform CAE simulation-related tasks through the cloud management platform, for example, they can perform linear equations solving tasks through the cloud management platform.

[0071] like Figure 3 Shown is an exemplary schematic diagram of executing CAE simulation-related tasks through a cloud management platform.

[0072] Among them, the user can send configuration information to the CAE simulation service of the cloud management platform to configure the called service, and can trigger the CAE simulation service to send a numerical calculation request to the numerical calculation solver service. The numerical calculation request is used to request numerical calculations related to the linear equation system. Then, the numerical calculation solver service can select the linear iteration method to solve the linear equation system based on the user's configuration information, and then call the initial solution generation service of the linear equation system, obtain the target initial solution according to the relevant description information of the linear equation system, and transmit the target initial solution to the linear iterative solver service. The linear iterative solver service can iteratively solve the linear equation system according to the target initial solution to obtain a solution result. The solution result can be fed back to the CAE simulation service so that the CAE simulation service can obtain the simulation result and output the simulation result to the user.

[0073] It should be noted that Figure 3 The service in is only an example of the service provided by the cloud management platform, and is not a limitation. For example, in some other examples, the cloud management platform does not provide CAE simulation services, and the user performs CAE simulation through the client to obtain the corresponding computer model and other information. Then, the user can directly send a numerical calculation request to the numerical calculation solver service of the cloud management platform through the client to request numerical calculations related to the linear equation system. In other embodiments provided in this application, the service can be deployed as a whole in an offline data center, and this application does not limit this.

[0074] Based on the above computing device cluster, refer to Figure 3 The cloud management platform architecture shown in Figure 4 As shown, in an embodiment of the present application, a method for solving a system of linear equations can be executed by implementing a computing device cluster of a cloud management platform.

[0075] The method for solving a system of linear equations may include steps 401-403.

[0076] Step 401: Obtain description information input by the user.

[0077] The description information includes linear equation system information, and the linear equation system information includes the right-hand side term.

[0078] In the embodiment of the present application, there are multiple ways for the user to input description information.

[0079] In one example, a user logs in to the cloud management platform through a client, and sends the description information to the cloud management platform through the client.

[0080] In this example, the user can obtain a computer model such as CAE simulation through the client, obtain physical problem information through the computer model, and generate a linear equation group to be solved based on the physical problem information. Then, the client can send description information containing the linear equation group information and related physical problem information to the computing device cluster that implements the cloud management platform.

[0081] In another example, the user may obtain description information through cloud resources of a cloud management platform.

[0082] In this example, the user not only performs the linear equation solving task through the cloud resources of the cloud management platform, but also constructs a computer model for CAE simulation through the first cloud resource of the cloud management platform, and obtains the corresponding physical problem information and constructs a linear equation system based on the physical problem information through the second cloud resource of the cloud management platform. Then, based on the instructions input by the user, the description information containing the linear equation system information and the related physical problem information is transmitted from the first cloud resource to the second cloud resource that executes the linear equation solving method in the embodiment of the present application.

[0083] The linear equation system information is used to describe the linear equation system itself. The linear equation system information may include the right-hand side term in the linear equation system. In addition, in some examples, the linear equation system information may also include the coefficient matrix in the linear equation system.

[0084] For example, in a linear equation system Ax=b, the coefficient matrix is ​​A and the right-hand term is b. In some scenarios, the linear equation system may be deformed, and the linear equation system information may include the right-hand term itself in the linear equation system, the coefficient matrix itself, or the information after the coefficient matrix in the linear equation system is deformed and / or the information after the right-hand term is deformed.

[0085] In addition, in some embodiments, the description information further includes information about the physical problem to be solved, and the linear equations are obtained by numerically simulating the information about the physical problem to be solved, and the information about the physical problem to be solved includes at least one of the following:

[0086] Boundary conditions, mesh information, physical equations.

[0087] Physical problem information is used to describe the physical problems to be solved in industrial application scenarios.

[0088] The specific field of the industrial application scenario is not limited here. For example, the industrial application scenario can be a scenario in an engineering field such as machinery, electronics, aerospace, automobile or construction.

[0089] In some examples, the physical problem information can be described by corresponding CAE simulation scenarios. Figure 1In the process shown, in the CAE simulation scenario, after steps such as geometric preprocessing, setting boundary conditions, meshing, and setting physical equations, one or more of the boundary conditions, mesh information, and corresponding physical equations of the corresponding computer model can be obtained, thereby obtaining the physical problem information associated with the set of linear equations.

[0090] The physical problem information includes at least one of the following information:

[0091] Boundary conditions, mesh information, physical equations.

[0092] Among them, boundary conditions are used to describe the boundary conditions of the computer model in the corresponding CAE simulation. Figure 1 In the process shown, boundary conditions can be generated after geometric preprocessing.

[0093] The grid information is used to describe the grid division method of the corresponding computer model. Specifically, the grid division method refers to the division method of dividing the computer model into multiple grid units. Figure 1 In the process shown, the grid information is completed in the grid generation stage. The grid information includes one or more of the grid point coordinates, grid division accuracy and the like.

[0094] The physical equations are determined according to the physical problems to be solved.

[0095] The linear equations are obtained by numerical simulation of the physical problem information to be solved. It can be seen that the linear equations are constructed based on the physical problem information, that is to say, the physical problem information will affect the subsequently generated linear equations. The physical problem information, as the upper-level scene information of the subsequently generated linear equations, will affect the coefficient matrix and / or right-hand side terms and other parameters in the subsequently generated linear equations.

[0096] The specific form of the above description information is illustrated below through an example.

[0097] In one example, it is necessary to solve the static charge distribution of a part (such as a semiconductor material, etc.) in a physical space by using the electric potential Poisson equation. Exemplarily, the physical space including the relevant computer model is divided into 2704 grid points.

[0098] The specific form of the electric potential Poisson equation is as follows:

[0099]

[0100] Where ε(x,y) is the capacitance of the grid point (x,y), is the electric potential at the grid point (x,y), and ρ(x,y) is the charge density at the grid point (x,y).

[0101] By performing steps such as geometric preprocessing, setting boundary conditions, meshing, and setting physical equations on the computer model of the part in the physical space of the CAD simulation scene, descriptive information such as the physical problem to be solved and the linear equation system information can be obtained.

[0102] At this time, the description information may include part or all of the following:

[0103] 1. The charge density ρ(x,y) of each of the 2704 grid points.

[0104] The charge density ρ(x,y) of each of the 2704 grid points can be described by a 2704×1 matrix. This matrix can be used as the right-hand side term in the corresponding linear equation system.

[0105] 2. The x-coordinate and y-coordinate of each of the 2704 grid points.

[0106] The x-coordinate and y-coordinate of each of the 2704 grid points can be described by a matrix of 5408×1. The matrix can be used as grid information.

[0107] 3. Physical equation information.

[0108] The number of physical equations involved in the description information is not limited here, and it can be one physical equation or a physical equation group including multiple physical equations.

[0109] Exemplarily, the physical equation information may include one or more of the following:

[0110] 1) Physical equations in mathematical form such as partial differential equations, for example, may include the above-mentioned electric potential Poisson equation.

[0111] 2) The values ​​of physical parameters in the physical equations, such as the capacitance ε(x,y) of each of the 2704 grid points.

[0112] The capacitance may be input by the user or pre-configured by the system. In a homogeneous medium, the capacitance is a constant. In this case, the coefficient matrix in the linear equation system is a constant, and the linear equation system information in the description information may only include the right-hand side terms without including the coefficient matrix. In an inhomogeneous medium, the capacitance may be a function of position. In this case, the linear equation system information in the description information may include the coefficient matrix and the right-hand side terms.

[0113] 4. Boundary conditions

[0114] There are many ways to describe boundary conditions. For example, they can be described by grid point information or in the form of equations, which are described below with examples.

[0115] 1) Describe boundary conditions through grid point information.

[0116] Exemplarily, it can be described by a 2704×1 matrix. The 2704 elements in the matrix correspond to the 2704 grid points one by one, and the value of each element is 0 or 1. When the value of an element is 1, it indicates that the corresponding grid point includes an electrode, that is, the grid point is a boundary point. When the value of an element is 0, it indicates that the corresponding grid point is a non-boundary point. It can be seen that the matrix can be used to indicate the boundary points in the corresponding computer model to indicate the corresponding boundary conditions.

[0117] 2) Describe the boundary conditions in the form of equations.

[0118] For example, the boundary conditions can be described by the Dirichlet condition:

[0119]

[0120] in, represents the electric potential of the grid point (x, y), Ω refers to the domain, f1(x, y) represents the value of the electrode voltage, and the value of f1(x, y) is 0 at non-boundary points.

[0121] Alternatively, the boundary conditions can be described by the Neumann conditions:

[0122]

[0123] Among them, f2(x,y) represents the electrode flux, the value of f2(x,y) at non-boundary points is 0, and n represents The normal vector of the plane.

[0124] In addition, during the CAE simulation process, after geometric pre-processing of the computer model, setting boundary conditions and meshing, the discretized linear equations to be solved can be obtained based on physical problem information such as physical equations, boundary conditions and / or mesh information through methods such as finite volume and finite element. In other words, at this time, the coefficient matrix and right-hand side terms in the linear equations to be solved can be determined.

[0125] In this way, linear equation system information and physical problem information such as grid information, boundary conditions and / or physical equations to be solved can be obtained as description information. The linear equation system information in the description information may include the right-hand side terms. In addition, in some scenarios, the coefficient matrix may not be included; for example, if the material in the physical scene is a uniform medium and the corresponding capacitance is a constant, the coefficient matrix in the linear equation system is a constant, and the linear equation system information in the description information may only include the right-hand side terms without including the coefficient matrix. In other scenarios, the linear equation system information may include the coefficient matrix; for example, if the material in the physical scene is an inhomogeneous medium, the corresponding capacitance may be a function of position, in which case the linear equation system information in the description information may include the coefficient matrix and the right-hand side terms.

[0126] In some other scenarios, the physical problem information and the linear equation system information in the description information may be in the same form or may be different.

[0127] For example, in another example, it is necessary to solve the relationship between temperature and pressure in a fluid in a physical space through the pressure Poisson's equation.

[0128] The specific form of the pressure Poisson equation is as follows:

[0129]

[0130] Where ρ is the fluid density at the grid point (x, y), p is the pressure at the grid point (x, y), and f(x, y) is the temperature at the grid point (x, y).

[0131] In this example, the boundary pressure is 0, which means:

[0132]

[0133] in, is the definition domain and p is the pressure.

[0134] In this example, the coordinates of each grid point can be obtained as grid information and physical equations can be obtained based on the same or similar methods as above. The coordinates of the boundary points can also be obtained as boundary conditions. Since the boundary pressure is 0, there is no need to further describe the boundary conditions through methods such as equations. In this way, the physical problem information in this example can be obtained. Then, numerical simulation can be performed based on the physical problem information through methods such as finite elements to obtain the coefficient matrix and right-hand side terms of the discretized linear equations as linear equations information.

[0135] It can be understood that in the embodiment of the present application, the data form of the description information may include one or more forms such as matrix, equation, vector, numerical value, etc.

[0136] It can be seen that in the embodiment of the present application, the physical problem information, as the upper-level scene information involved in constructing the linear equation system, is strongly related to the constructed linear equation system. Therefore, the description information may include the linear equation system information and the physical problem information associated with the linear equation system, so that in the subsequent processing process, the above-mentioned physical problem information and the linear equation system information are used together as the input of the AI ​​model, so that the AI ​​model can mine useful scene feature information and the feature information of the linear equation system itself from the physical problem information.

[0137] Step 402, inferring the description information through an artificial intelligence AI model to obtain a first initial solution corresponding to the linear equations.

[0138] In the embodiment of the present application, the specific type of the AI ​​model is not limited here.

[0139] The AI ​​model can be an existing or subsequently developed model, and is not limited in the embodiments of the present application. For example, the AI ​​model can be a general model such as a physics-informed neural network (PINN) or CNN; or the AI ​​model can also be a model that can solve partial differential equations (PDE), for example, the AI ​​model can be a deeponet, and both training and reasoning are used as the solution process.

[0140] For different AI models, the processing of the description information may be different based on the processing capabilities and requirements of the different AI models themselves. For example, if the AI ​​model is PINN, and the PINN cannot directly process input data in the form of matrices and physical equations, then feature engineering can be performed on the description information including matrices and physical equations, for example, the description information is encoded through a feature extraction model, or the description information is converted into data form (for example, converted into vector data) before inputting into PINN. If the AI ​​model is deeponet, then description information in the form of matrices and / or physical equations can be received as input data.

[0141] In an embodiment of the present application, the AI ​​model may be a trained model so that the AI ​​model can identify the characteristics of a system of linear equations based on input description information, so as to efficiently determine a suitable initial solution to the system of linear equations.

[0142] In addition, in some embodiments, the description information also includes information about the physical problem to be solved, so the AI ​​model can identify the characteristics of the physical problems in different physical scenarios and the characteristics of the linear equations, thereby determining the initial solution of the linear equations to be solved in different physical scenarios.

[0143] The AI ​​model can be trained in a computing device cluster, or it can be trained in other devices and then transmitted and deployed to the computing device cluster.

[0144] The following is an exemplary introduction to the training process of the AI ​​model.

[0145] In the embodiment of the present application, the training process may include one or more of the following steps:

[0146] 1. Obtain a data set, which includes multiple samples and labels corresponding to each sample. Any sample may include physical equations, boundary conditions, grid information, coefficient matrices, and right-hand terms. The label corresponding to the sample includes a corresponding initial solution and may also include performance indicators of the corresponding solution process. The performance indicators may include one or more of solution time, solution accuracy, and number of iterations.

[0147] The data set collection method is not limited here. For example, the data set can be obtained from an open source data set, or the data set can be generated by manually collecting information on iterative solutions of linear equations in various scenarios.

[0148] 2. Preprocess the training data of the dataset.

[0149] The preprocessing method is not limited here. Exemplarily, the preprocessing may include one or more of the following methods:

[0150] 1) Data cleaning: This includes checking and processing missing values, outliers, and data that failed to be solved in the data set, in order to ensure the quality and accuracy of the descriptive information.

[0151] 2) Data integration: Merge multiple data sources into one data set to resolve inconsistencies and duplications between data sources.

[0152] 3) Data conversion: The process of converting samples into a form suitable for AI models, including standardization, normalization, discretization and other operations on data.

[0153] 4) Data reduction: The process of reducing the size of a data set, which can be achieved through methods such as clustering, sampling, and feature extraction, in order to train AI models faster and reduce storage overhead.

[0154] 5) Feature engineering: Extract, transform, and select features from samples to better train AI models.

[0155] 3. Classify the data set and divide it into training set and validation set.

[0156] 4. Train one or more models to be trained according to the training set to obtain a trained model.

[0157] When there are multiple models to be trained, the types and structures of different models to be trained can be the same, similar, or different.

[0158] During the training process, the parameters of the model to be trained in the iteration process can be updated according to the loss function, wherein the specific form of the loss function is not limited here.

[0159] In one example, the loss function can evaluate the difference between the initial training solution output by the model to be trained in the iteration process and the initial solution in the label of the corresponding sample. In addition, the loss function can also reflect the performance index in the label of the corresponding sample.

[0160] Specifically, the difference between the initial training solution output by the model to be trained in the iteration process and the initial solution in the label of the corresponding sample is positively correlated with the loss value, that is, the greater the difference between the initial training solution output by the model to be trained in the iteration process and the initial solution in the label of the corresponding sample, the greater the corresponding loss value is usually. When the performance indicator in the label of the corresponding sample indicates that the corresponding solution performance is worse (for example, the longer the solution time, the lower the solution accuracy, and the more iterations), the corresponding loss value is greater.

[0161] In this way, one or more trained models can be obtained according to the training set and the loss function.

[0162] 5. Use the validation set to verify one or more trained models and select the best model as the AI ​​model.

[0163] 6. Deploy the obtained AI model to a computing device cluster.

[0164] After the obtained AI model is deployed to a computing device cluster, the description information can be processed by the AI ​​model to obtain a first initial solution corresponding to the linear equations.

[0165] Among them, the description information can be input into the AI ​​model after pre-processing such as data conversion and / or feature engineering, so as to determine the first initial solution that conforms to the current physical scene characteristics and is suitable for the current set of linear equations to be solved through the AI ​​model.

[0166] Step 403, determining a target initial solution according to the first initial solution, iteratively solving the linear equations system based on the target initial solution, and outputting the solution result of the linear equations system.

[0167] In an embodiment of the present application, after obtaining the first initial solution, the first initial solution can be used as the target initial solution of the linear equations, so as to iteratively solve the linear equations and obtain the solution of the linear equations; or, after obtaining the first initial solution, a better target initial solution can be further queried based on the first initial solution, so as to iteratively solve the linear equations based on the better target initial solution and obtain the solution of the linear equations.

[0168] In the embodiment of the present application, the functional module that implements the initial solution screening process in the computing device cluster is called an initial solution adaptive optimization module.

[0169] like Figure 5 As shown in FIG. 1 , it is an exemplary schematic diagram of iteratively solving a linear equation system based on an initial solution adaptive optimization module. Figure 5 Taking the initial solution adaptive optimization module as an example, the further initial solution screening process after obtaining the first initial solution is introduced. In the actual implementation process, the initial solution adaptive optimization module can be implemented by one or more cloud services of the cloud management platform, which is not limited in the embodiments of the present application.

[0170] Specifically, Figure 5 As shown, the initial solution screening process may include one or more combinations of the following steps:

[0171] 1. Obtain an initial solution candidate set to filter the target initial solution from the initial solution candidate set.

[0172] In some embodiments, the above step 401 includes:

[0173] Acquire first configuration information, where the first configuration information carries at least one initial solution generation method for generating an initial solution;

[0174] According to at least one initial solution generation method indicated by the first configuration information, multiple initial solutions are obtained, where the multiple initial solutions include a first initial solution;

[0175] Selecting a target initial solution from multiple initial solutions;

[0176] According to the target initial solution, the linear equations are iteratively solved and the solution results of the linear equations are output.

[0177] In the embodiment of the present application, the cloud management platform may provide a first configuration interface, on which a plurality of preset initial solution generation methods are displayed. The user may select a plurality of initial solution generation methods from the first configuration interface and confirm. In this way, the user may input the first configuration information to the cloud management platform, that is, the first configuration information is configured and input by the user.

[0178] Alternatively, the cloud management platform may also be pre-configured by developers based on expert experience to provide users with multiple initial solution generation methods in the cloud service. That is, in this example, the first configuration information may be pre-configured by developers in the relevant cloud service.

[0179] The first configuration information indicates at least one initial solution generating method, each initial solution generating method corresponds to an initial solution to the linear equation system, so that multiple initial solutions can be obtained through the at least one initial solution generating method.

[0180] The specific content of the at least one initial solution generating method is not limited here.

[0181] The at least one initial solution generating method includes a method of generating an initial solution through an AI model, that is, in an embodiment of the present application, includes a method of generating a first initial solution through the above steps 401-402.

[0182] In addition, illustratively, in Figure 5 In the example shown, the multiple initial solution generation methods may also include one or more of the following methods:

[0183] 1) Default initial solution;

[0184] 2) The initial solution obtained by the Fischer algorithm;

[0185] 3) The initial solution obtained by the proper orthogonal decomposition (POD) algorithm.

[0186] The multiple initial solutions may be included in the initial solution candidate set. After obtaining the multiple initial solutions, a target initial solution may be screened out from the multiple initial solutions by means of a search algorithm and / or an evaluation index.

[0187] In the embodiment of the present application, considering that different initial solution generation methods may be applicable to physical problems in different physical scenarios, multiple initial solutions can be provided according to the first configuration information. In this way, the degree of adaptation of different initial solution generation methods in different physical problems can be fully considered, and a more suitable target initial solution in the current category of physical problems can be selected from multiple initial solutions, thereby improving the quality of the target initial solution finally obtained, and thus improving the solution efficiency of the iterative solution process of the linear equation system.

[0188] 2. Based on the heuristic strategy, multiple initial solutions in the initial solution candidate set are screened to obtain the target initial solution.

[0189] In some embodiments, selecting a target initial solution from a plurality of initial solutions includes:

[0190] Acquire second configuration information, where the second configuration information carries at least one heuristic strategy;

[0191] A target initial solution is screened out from a plurality of initial solutions according to at least one heuristic strategy.

[0192] In an embodiment of the present application, the cloud management platform may provide a second configuration interface, on which a plurality of preset heuristic strategies are displayed. The user may select at least one heuristic strategy from the second configuration interface and confirm it. In this way, the user may input the second configuration information to the cloud management platform, that is, the second configuration information is configured by the user.

[0193] There is no restriction on the number and type of preset heuristic strategies on the second configuration interface.

[0194] Exemplarily, the preset heuristic strategy on the second configuration interface may include one or more of the following strategies:

[0195] Greedy search algorithm, simulated annealing algorithm, genetic algorithm, particle swarm algorithm.

[0196] Alternatively, the cloud management platform may also be pre-configured with a target heuristic strategy in the cloud service provided to users by developers based on experience, etc. That is, in this example, the second configuration information may be pre-configured by developers in the relevant cloud service.

[0197] The specific type of the at least one heuristic strategy is not limited here either.

[0198] The second configuration information carrying at least one heuristic strategy may mean that the second configuration information carries at least one heuristic strategy identifier and / or related operator information. In this way, the cloud management platform can screen multiple initial solutions according to the second configuration information using at least one heuristic strategy.

[0199] The specific process of selecting a target initial solution from multiple initial solutions according to at least one heuristic strategy is not limited here. For example, multiple initial solutions can be selected by one heuristic strategy; or, multiple initial solutions can be selected in multiple stages by multiple heuristic strategies, for example, multiple initial solutions can be initially selected by a greedy search algorithm, and then the initial solutions obtained after the initial selection can be further selected by a genetic algorithm.

[0200] By screening multiple initial solutions through at least one heuristic strategy, one or more initial solutions can be screened out from the multiple initial solutions. For ease of description, in the embodiment of the present application, the initial solution screened out from the multiple initial solutions through at least one heuristic strategy is referred to as a second initial solution. The number of the second initial solutions can be one or more.

[0201] If multiple initial solutions are screened by the target heuristic strategy, a second initial solution can be directly screened out from the multiple initial solutions, and the second initial solution can be used as the target initial solution; if multiple initial solutions are screened by the target heuristic strategy, multiple second initial solutions can be screened out from the multiple initial solutions (for example, in Figure 5 In the example shown, the number of the second initial solutions may be multiple), and the multiple second initial solutions may be further screened to select a better target initial solution from the multiple second initial solutions.

[0202] In an embodiment of the present application, multiple initial solutions are screened through a target heuristic strategy, and a part of the initial solutions that are more in line with the characteristics of the current physical problem can be screened out from the multiple initial solutions as the second initial solution. It is possible to screen out a more suitable target initial solution in the current category of physical problems, thereby improving the quality of the target initial solution finally obtained.

[0203] 3. Based on the evaluation strategy, select the target initial solution from multiple initial solutions.

[0204] In some embodiments, selecting a target initial solution from a plurality of initial solutions includes:

[0205] Obtaining third configuration information, where the third configuration information carries an evaluation strategy, where the evaluation strategy includes evaluation indicators, or includes evaluation indicators and weights corresponding to each evaluation indicator, where the evaluation indicators include one or more of solution time, solution accuracy, and number of iterations;

[0206] According to the evaluation strategy, the target initial solution is screened out from multiple initial solutions.

[0207] In an embodiment of the present application, the cloud management platform may provide a third configuration interface, on which a variety of preset evaluation indicators are displayed, and a weight configuration item for each preset evaluation indicator may also be displayed. The user may select one or more evaluation indicators from the third configuration interface, and may also configure the weight corresponding to the corresponding evaluation indicator through the weight configuration item of the selected evaluation indicator. In this way, the user may input the third configuration information to the cloud management platform, that is, the third configuration information is configured and input by the user.

[0208] Alternatively, the cloud management platform may also be pre-configured with evaluation indicators in the cloud services provided to users by developers based on experience, etc. In addition, the weight corresponding to each evaluation indicator may also be configured. That is to say, in this example, the third configuration information may be pre-configured by developers in the relevant cloud services.

[0209] The third configuration information may carry an identifier of the evaluation strategy, and may also carry the content of the evaluation strategy, for example, evaluation indicators and the weight corresponding to each evaluation indicator.

[0210] The evaluation indicators included in the evaluation strategy may include one or more of the following indicators:

[0211] Solution time, solution accuracy, and number of iterations.

[0212] The solution time is the time required for the iterative solution process when the corresponding second initial solution is used as the initial solution in the iterative solution process of the linear equation system.

[0213] The solution accuracy is the accuracy of the solution result obtained by iterative solution when the corresponding second initial solution is used as the initial solution in the iterative solution process of the linear equation system. The accuracy can describe the difference between the solution result and the accurate solution result of the linear equation system.

[0214] The number of iterations is the number of iterations performed in the iterative solution process when the corresponding second initial solution is used as the initial solution in the iterative solution process of the linear equation system.

[0215] The weight corresponding to each evaluation indicator can be configured by the user or pre-configured by developers.

[0216] It can be understood that any evaluation index can be used to evaluate the iterative performance of the corresponding initial solution when it is used as the initial solution in the iterative solution process of the linear equation system. In this way, the corresponding target initial solution with better iterative performance can be screened out from multiple initial solutions based on the evaluation index and related weight information in the evaluation strategy.

[0217] In the embodiment of the present application, when the target initial solution is screened out from multiple initial solutions according to the evaluation strategy, the target initial solution can be directly screened out from the multiple initial solutions according to the evaluation strategy; or Figure 5 In the example shown, after selecting multiple second initial solutions from multiple initial solutions according to at least one heuristic strategy, a target initial solution may be selected from the multiple second initial solutions according to an evaluation strategy.

[0218] That is to say, the three methods of the above-mentioned initial solution screening process can be applied in combination or separately. The initial solution screening process in the embodiment of the present application can be carried out in many ways, which is not limited here.

[0219] In an embodiment of the present application, the characteristic information of a system of linear equations can be mined through an AI model to efficiently determine a suitable initial solution to the current system of linear equations, thereby improving the efficiency of solving the system of linear equations and avoiding the generalization problems caused by the initial solution determined based on expert experience and the default initial solution.

[0220] In addition, currently, conventional algorithms for determining initial solutions of linear equations usually use mathematical derivation to predict initial solutions of linear equations, such as proper orthogonal decomposition (POD) algorithm and Fischer algorithm.

[0221] These traditional algorithms for determining the initial solution of a system of linear equations usually only consider the information of the coefficient matrix in the system of linear equations. However, the coefficient matrix of the system of linear equations alone cannot well reflect the characteristics of the problem to be solved. Therefore, the effects of the initial solutions predicted by the traditional algorithms for determining the initial solution of a system of linear equations often have large deviations and cannot provide more suitable initial solutions for various scenarios.

[0222] In some examples of the present application, the description information may include not only information about the system of linear equations, but also information about the physical problem to be solved. In this way, the AI ​​model can fully explore the solution information of the physical problem of the current physical scene and the information of the system of linear equations itself, so that it can fully determine the initial solution for the current system of linear equations to be solved based on multi-dimensional characteristics. Therefore, it can adapt to the needs of various application scenarios. For example, it can efficiently provide suitable initial solutions for the linear equations to be solved in various engineering application scenarios.

[0223] Specifically, in an embodiment of the present application, the description information can be processed through an AI model.

[0224] The description information includes multi-dimensional features such as linear equations information and physical problem information associated with the linear equations. The AI ​​model is a trained model that has the ability to identify the characteristics of physical problems in different physical scenarios and the characteristics of the linear equations themselves, so that it can determine the first initial solution of the linear equations that meets the characteristics of the current application scenario and is suitable for the current linear equations to be solved based on the multi-dimensional characteristics of the current physical problem to be solved extracted from the input description information.

[0225] It can be seen that through the embodiments of the present application, suitable initial solutions can be efficiently provided for the linear equations corresponding to physical problems in different scenarios, so as to improve the speed of iterative solution of the linear equations, obtain the corresponding solution results more quickly, and improve the solution efficiency of the corresponding linear equations.

[0226] In addition, in some embodiments, after obtaining the solution result, the AI ​​model can be optimized according to the solution result to improve the performance of the AI ​​model so that the AI ​​model can better adapt to the needs of actual application scenarios.

[0227] Specifically, in some embodiments, the method further includes:

[0228] Generate training data, the training data including training samples and labels corresponding to the training samples, the training samples including description information, and the labels corresponding to the training samples are obtained according to the first initial solution;

[0229] According to the training data, the AI ​​model is trained to obtain an optimized AI model.

[0230] like Figure 6 As shown, it is an exemplary schematic diagram of iterative solution of a linear equation system in an embodiment of the present application.

[0231] It can be seen that in the embodiments of the present application, the target initial solutions corresponding to different groups of linear equations can be collected. In addition, in some examples, the target initial solutions corresponding to the groups of linear equations in different physical problem scenarios in actual application scenarios can also be collected, and the relevant performance data of the actual iterative solution results can be obtained, so as to judge whether the corresponding target initial solution is a suitable initial solution and generate corresponding training data.

[0232] Then, the AI ​​model can be trained according to the training data to obtain an optimized AI model, and then the subsequent linear equation solving method can be executed according to the optimized AI model.

[0233] In this way, the AI ​​model can be continuously iterated and updated as the data distribution and scale of users in actual application scenarios change, thereby continuously optimizing the model. This makes the optimized AI model more adaptable to current scenario needs and can generate better initial solutions for different physical problems and corresponding linear equations, thereby improving solution efficiency.

[0234] In some embodiments, the method further comprises:

[0235] Obtaining performance indicators corresponding to the solution results, the performance indicators including one or more of solution time, solution accuracy, and number of iterations;

[0236] According to the training data, the AI ​​model is trained to obtain an optimized AI model, including:

[0237] The AI ​​model is trained according to the training data and the loss function to obtain an optimized AI model. The loss function is constructed based on the performance indicators.

[0238] In the embodiment of the present application, the specific form of the loss function is not limited here.

[0239] In one example, the loss function may reflect the performance indicator in the label of the corresponding sample.

[0240] The performance index can be obtained according to the solution process of the corresponding solution result. For example, the number of iterations of the solution process can be used as a performance index; in addition, the solution time of the solution process can also be used as a performance index. In addition, the difference between the target initial solution and the accurate initial solution of the linear equation system can be calculated to obtain the corresponding solution accuracy as a performance index; for example, the target initial solution x0 can be substituted into the linear equation system Ax=b, and then the difference between b and Ax0 can be calculated. The difference can be considered as the residual corresponding to the target initial solution and can reflect the corresponding solution accuracy.

[0241] Specifically, the performance indicator in the label of the corresponding training sample indicates that the worse the corresponding solution performance is (for example, the longer the solution time is, the lower the solution accuracy is, and the more iterations are), the larger the corresponding loss value is.

[0242] In addition, the loss function can also evaluate the difference between the initial training solution output by the to-be-trained model during the iteration and the initial solution in the label of the corresponding sample.

[0243] The difference between the initial training solution output by the model to be trained in the iteration process and the initial solution in the label of the corresponding sample is positively correlated with the loss value. That is to say, the greater the difference between the initial training solution output by the model to be trained in the iteration process and the initial solution in the label of the corresponding sample, the greater the corresponding loss value is usually.

[0244] In an embodiment of the present application, the loss function is constructed based on performance indicators, which can optimize the AI ​​model towards better performance indicators during the training process, thereby facilitating the improvement of the performance of the AI ​​model.

[0245] It can be seen that based on the introduction of the above embodiments, Figure 3 An exemplary specific implementation of the linear iterative initial solution generation service and the linear iterative solver service is shown as follows Figure 7 shown.

[0246] exist Figure 7In the example shown, the initial solution generation service for the linear equations can call the AI ​​model in the AI ​​model service through the initial solution generation module to process the description information to obtain the first initial solution. Then, the initial solution adaptive optimization module can screen out the target initial solution based on the initial solution candidate set including the first initial solution through the target heuristic strategy, evaluation strategy, etc. Next, the initial solution generation service for the linear equations can send the target initial solution to the linear iterative solver service, so that the linear iterative solver calls the resources of the high-performance computing base through the data computing platform, and iteratively solves the linear equations according to the target initial solution to obtain the calculation results of the linear equations.

[0247] Below, an example is used to illustrate the specific application process of the method for solving a system of linear equations according to an embodiment of the present application in the engineering field.

[0248] In one example, it is necessary to implement an electromagnetic performance optimization simulation of an electromagnetic valve, and the electromagnetic performance optimization simulation of the electromagnetic valve belongs to a two-dimensional low-frequency electromagnetic nonlinear simulation.

[0249] Among them, the solenoid valve is an axisymmetric model, and a two-dimensional axisymmetric computer model can be used for solution and calculation. After the solution, the core electromagnetic performance parameters such as magnetic flux density, current density, loss, current, voltage, inductance, back electromotive force, response time, response acceleration, valve core (plunger) electromagnetic force, etc. can be obtained, so as to carry out a comprehensive electromagnetic performance evaluation, analysis and design optimization of the solenoid valve.

[0250] Figure 8 is an exemplary schematic diagram of a two-dimensional axisymmetric computer model of a solenoid valve.

[0251] Based on the computer model, electromagnetic performance optimization simulation of electromagnetic valve electromagnetic simulation can be performed. In this scenario, the nonlinear physical problem to be solved can adopt Newton iteration method, and in each nonlinear iteration process, a linear equation system can be constructed for solution.

[0252] At this time, the target initial solution of the linear equations in each step of the nonlinear iteration process can be obtained through the AI ​​model. The AI ​​model can be pre-trained based on a historical training data set. In the historical training data set, there are training samples in the electromagnetic performance optimization simulation scenario of the solenoid valve and the initial solution labels corresponding to the training samples, and the training samples in the electromagnetic performance optimization simulation scenario of the solenoid valve include the boundary conditions, grid information and physical equations of the historical computer model in the electromagnetic performance optimization simulation scenario of the solenoid valve.

[0253] Therefore, the AI ​​model trained by the historical training data set has the ability to provide a suitable first initial solution for the linear equations to be solved in the electromagnetic performance optimization simulation scenario of the solenoid valve.

[0254] Specifically, in each nonlinear iteration process, the linear equation system information in this nonlinear iteration process and the physical problem information such as boundary conditions, grid information and physical equations corresponding to the linear equation system can be obtained. After preprocessing the linear equation system information and the corresponding physical problem information, they are input into the AI ​​model to obtain the first initial solution of the linear equation system in this nonlinear iteration process.

[0255] Then, according to the first configuration information, a default initial solution, an initial solution based on the Fischer algorithm, and an initial solution based on the POD algorithm can be obtained. In this way, an initial solution candidate set can be obtained, which includes the first initial solution, the default initial solution, the initial solution based on the Fischer algorithm, and the initial solution based on the POD algorithm.

[0256] Next, based on the second configuration information configured by the user, multiple second initial solutions are screened out from the initial solution candidate set through the target heuristic rule. Then, the score of each second initial solution can be calculated based on the evaluation index configured by the user and the weight corresponding to each evaluation index, and the optimal initial solution is screened out from the multiple second initial solutions according to the score of each second initial solution as the target initial solution. The target initial solution is used as the target initial solution of the linear equation group in this nonlinear iterative process to iteratively solve the linear equation group and obtain the solution result of the linear equation group in this nonlinear iterative process.

[0257] It can be seen that the above-mentioned method for solving the linear equations can be used in each nonlinear iteration process until the iteration termination condition of the nonlinear iteration is met and the final solution result of the nonlinear physical problem to be solved is obtained.

[0258] In the specific implementation process of this example, two computer model grid division accuracies can be used. Regardless of the grid division accuracy, in each nonlinear iteration process, when the linear equations solving method is used to obtain the target initial solution to solve the linear equations, the solution time and the number of linear iterations are less than the traditional method to obtain the target initial solution to solve the linear equations.

[0259] It can be seen that in this example, the method of using the above-mentioned linear equation solving method to obtain the target initial solution to solve the linear equation system can provide a more suitable target initial solution for the linear equation system to be solved, thereby significantly improving the solution speed of the entire nonlinear iterative process.

[0260] The above describes the method for solving a system of linear equations provided in the embodiment of the present application from multiple aspects. The following describes the device for solving a system of linear equations provided in the embodiment of the present application in conjunction with the accompanying drawings.

[0261] like Fig. 9 As shown, the embodiment of the present application provides a linear equation solving device 90, and the linear equation solving device 90 includes:

[0262] An acquisition module 901 is used to acquire description information input by a user, where the description information includes linear equation system information, and the linear equation system information includes a right-hand side term;

[0263] The processing module 902 is used to:

[0264] The description information is inferred through an artificial intelligence (AI) model to obtain the first initial solution corresponding to the linear equation system;

[0265] A target initial solution is determined according to the first initial solution, the linear equation system is iteratively solved based on the target initial solution, and the solution result of the linear equation system is output.

[0266] Optionally, the description information further includes information about a physical problem to be solved, and the system of linear equations is obtained by numerically simulating the information about the physical problem to be solved, and the information about the physical problem to be solved includes at least one of the following:

[0267] Boundary conditions, mesh information, physical equations.

[0268] Optionally, the acquisition module 901 is used to:

[0269] Acquire first configuration information, where the first configuration information carries at least one initial solution generation method for generating an initial solution;

[0270] The processing module 902 is used for:

[0271] According to at least one initial solution generation method indicated by the first configuration information, multiple initial solutions are obtained, where the multiple initial solutions include a first initial solution;

[0272] Selecting a target initial solution from multiple initial solutions;

[0273] According to the target initial solution, the linear equations are iteratively solved and the solution results of the linear equations are output.

[0274] Optionally, the acquisition module 901 is used to: acquire second configuration information, where the second configuration information carries at least one heuristic strategy;

[0275] The processing module 902 is used to select a target initial solution from multiple initial solutions according to at least one heuristic strategy.

[0276] Optionally, the acquisition module 901 is used to: acquire third configuration information, where the third configuration information carries an evaluation strategy, where the evaluation strategy includes evaluation indicators, or includes evaluation indicators and a weight corresponding to each evaluation indicator, where the evaluation indicator includes one or more of solution time, solution accuracy, and number of iterations;

[0277] The processing module 902 is used to select a target initial solution from multiple initial solutions according to an evaluation strategy.

[0278] Optionally, the device 90 further includes a training module 903;

[0279] The training module 903 is used to:

[0280] Generate training data, the training data including training samples and labels corresponding to the training samples, the training samples including description information, and the labels corresponding to the training samples are obtained according to the first initial solution;

[0281] According to the training data, the AI ​​model is trained to obtain an optimized AI model.

[0282] Optionally, the acquisition module 901 is further used for:

[0283] Obtaining performance indicators corresponding to the solution results, the performance indicators including one or more of solution time, solution accuracy, and number of iterations;

[0284] The training module 903 is used to:

[0285] The AI ​​model is trained according to the training data and the loss function to obtain an optimized AI model. The loss function is constructed based on the performance indicators.

[0286] Optionally, the AI ​​model is a general model or a model for solving partial differential equations (PDEs), the general models include CNN or PINN, and the models for solving PDEs include deeponet.

[0287] In some examples, the acquisition module 901 can implement interaction with the user, and the processing module 902 can execute some or all steps in the linear iterative initial solution generation service and the linear iterative solver service in any of the above method embodiments. The training module can execute the training and optimization steps of the AI ​​model in the linear iterative initial solution generation service in any of the above method embodiments.

[0288] In an embodiment of the present application, a module is used as an example of a software functional unit, and a linear equation solving device may include code running on a computing instance. Among them, the computing instance may be at least one of a physical host (computing device), a virtual machine, a container and other computing devices. Furthermore, the above-mentioned computing device may be one or more. For example, the linear equation solving device may include code running on multiple hosts / virtual machines / containers. It should be noted that the multiple hosts / virtual machines / containers used to run the application may be distributed in the same region or in different regions. The multiple hosts / virtual machines / containers used to run the code may be distributed in the same available zone (availablezone, AZ) or in different AZs, each AZ including a data center or multiple data centers with close geographical locations. Among them, usually a region may include multiple AZs.

[0289] Similarly, multiple hosts / virtual machines / containers used to run the code can be distributed in the same virtual private cloud (VPC) or in multiple VPCs. Usually, a VPC is set up in a region. For cross-region communication between two VPCs in the same region and between VPCs in different regions, a communication gateway must be set up in each VPC to achieve interconnection between VPCs through the communication gateway.

[0290] As an example of a hardware functional unit, the linear equations solving device may include at least one computing device, such as a server, etc. Alternatively, the linear equations solving device may also be a device implemented by an application specific integrated circuit (ASIC) or a programmable logic device (PLD). The PLD may be a complex PLD (CPLD), a field programmable gate array (FPGA), a generic array logic (GAL) or any combination thereof.

[0291] The multiple computing devices included in the linear equations solving apparatus can be distributed in the same region or in different regions. The multiple computing devices included in the linear equations solving apparatus can be distributed in the same AZ or in different AZs. Similarly, the multiple computing devices included in the linear equations solving apparatus can be distributed in the same VPC or in multiple VPCs. The multiple computing devices can be any combination of computing devices such as servers, ASICs, PLDs, CPLDs, FPGAs, and GALs.

[0292] It should be noted that, in other embodiments, the acquisition module can be used to execute any step in the method for solving a system of linear equations, the processing module can be used to execute any step in the method for solving a system of linear equations, and the training module can be used to execute any step in the method for solving a system of linear equations. The steps that the acquisition module, the processing module, and the training module are responsible for implementing can be specified as needed. The full functions of the linear equation solving device are realized by respectively implementing different steps in the method for solving a system of linear equations through the acquisition module, the processing module, and the training module.

[0293] The present application embodiment also provides a computing device 100. Fig.10 As shown, the computing device 100 includes: a bus 102, a processor 104, a memory 106, and a communication interface 108. The processor 104, the memory 106, and the communication interface 108 communicate with each other through the bus 102. The computing device 100 can be a server or a terminal device. It should be understood that the present application does not limit the number of processors and memories in the computing device 100.

[0294] The bus 102 may be a peripheral component interconnect (PCI) bus or an extended industry standard architecture (EISA) bus. The bus may be divided into an address bus, a data bus, a control bus, etc. For ease of representation, Fig.10 The bus 104 is represented by only one line, but does not mean that there is only one bus or one type of bus. The bus 104 may include a path for transmitting information between various components of the computing device 100 (eg, the memory 106, the processor 104, and the communication interface 108).

[0295] The processor 104 may include any one or more of a central processing unit (CPU), a graphics processing unit (GPU), a microprocessor (MP), or a digital signal processor (DSP).

[0296] The memory 106 may include a volatile memory, such as a random access memory (RAM). The processor 104 may also include a non-volatile memory, such as a read-only memory (ROM), a flash memory, a hard disk drive (HDD), or a solid state drive (SSD).

[0297] The memory 106 stores executable program codes, and the processor 104 executes the executable program codes to respectively implement the functions of the aforementioned acquisition module, processing module and / or training module, thereby implementing the method for solving a system of linear equations applied to a computing device cluster in the above-mentioned embodiment. That is, the memory 106 stores instructions for executing the method for solving a system of linear equations applied to a computing device cluster in the above-mentioned embodiment.

[0298] The communication interface 108 uses a transceiver module such as, but not limited to, a network interface card or a transceiver to implement communication between the computing device 100 and other devices or a communication network.

[0299] The embodiment of the present application also provides a computing device cluster. The computing device cluster includes at least one computing device. The computing device can be a server, such as a central server, an edge server, or a local server in a local data center. In some embodiments, the computing device can also be a terminal device such as a desktop computer, a laptop computer, or a smart phone.

[0300] like Fig.11 As shown, the computing device cluster includes at least one computing device 100. The memory 106 in one or more computing devices 100 in the computing device cluster may store the same instructions for executing the method for solving a linear equation system.

[0301] In some possible implementations, the memory 106 of one or more computing devices 100 in the computing device cluster may also store partial instructions for executing the method for solving a system of linear equations. In other words, the combination of one or more computing devices 100 may jointly execute instructions for executing the method for solving a system of linear equations.

[0302] It should be noted that the memory 106 in different computing devices 100 in the computing device cluster can store different instructions, which are respectively used to execute part of the functions of the method for solving a system of linear equations. That is, the instructions stored in the memory 106 in different computing devices 100 can implement the functions of one or more modules in the acquisition module, the processing module and the training module.

[0303] In some possible implementations, one or more computing devices in the computing device cluster may be connected via a network, which may be a wide area network or a local area network. Fig.12 A possible implementation is shown. Fig.12 As shown, two computing devices 100A and 100B are connected via a network. Specifically, the connection to the network is made through the communication interface in each computing device. In this type of possible implementation, the memory 106 in the computing device 100A may store instructions for executing the functions of the acquisition module. At the same time, the memory 106 in the computing device 100B may store instructions for executing the functions of the processing module. Alternatively, the memory 106 in the computing device 100A may store instructions for executing part of the functions of the training module. At the same time, the memory 106 in the computing device 100B may store instructions for executing another part of the functions of the processing module.

[0304] It should be understood that Fig.12 The functions of the computing device 100A shown in FIG. 1 may also be completed by multiple computing devices 100. Similarly, the functions of the computing device 100B may also be completed by multiple computing devices 100.

[0305] The present application embodiment also provides another computing device cluster. The connection relationship between the computing devices in the computing device cluster can be similar to that of Fig.11 and Fig.12 Connection mode of computing device cluster. The difference is that the memory 106 in one or more computing devices 100 in the computing device cluster may store the same instructions for executing the method for solving the linear equation system.

[0306] In some possible implementations, the memory 106 of one or more computing devices 100 in the computing device cluster may also store partial instructions for executing the method for solving a system of linear equations. In other words, the combination of one or more computing devices 100 may jointly execute instructions for executing the method for solving a system of linear equations.

[0307] It should be noted that the memory 106 in different computing devices 100 in the computing device cluster may store different instructions for executing partial functions of the method for solving a system of linear equations. That is, the instructions stored in the memory 106 in different computing devices 100 may implement the functions of one or more modules among the acquisition module, the processing module, and the training module.

[0308] The present application also provides a computer program product including instructions. The computer program product may be software or a program product including instructions that can be run on a computing device or stored in any available medium. When the computer program product is run on at least one computing device, the at least one computing device executes a method for solving a system of linear equations.

[0309] The embodiment of the present application also provides a computer-readable storage medium. The computer-readable storage medium can be any available medium that can be stored by the computing device or a data storage device such as a data center containing one or more available media. The available medium can be a magnetic medium (e.g., a floppy disk, a hard disk, a tape), an optical medium (e.g., a DVD), or a semiconductor medium (e.g., a solid-state hard disk). The computer-readable storage medium includes instructions that instruct the computing device to execute a method for solving a system of linear equations.

[0310] The embodiment of the present application also provides a chip system, which includes a processor, and the processor is used to implement the steps performed by the above-mentioned computing device cluster. In a possible design, the chip system may also include a memory, and the memory is used to store necessary program instructions and data. The chip system can be composed of a chip, or it can include a chip and other discrete devices.

[0311] Those skilled in the art can clearly understand that, for the convenience and brevity of description, the specific working processes of the systems, devices and units described above can refer to the corresponding processes in the aforementioned method embodiments and will not be repeated here.

[0312] In the several embodiments provided in the present application, it should be understood that the disclosed systems, devices and methods can be implemented in other ways. For example, the device embodiments described above are only schematic. For example, the division of units is only a logical function division. There may be other division methods in actual implementation. For example, multiple units or components can be combined or integrated into another system, or some features can be ignored or not executed. Another point is that the mutual coupling or direct coupling or communication connection shown or discussed can be an indirect coupling or communication connection through some interfaces, devices or units, which can be electrical, mechanical or other forms.

[0313] The units described as separate components may or may not be physically separated, and the components shown as units may or may not be physical units, that is, they may be located in one place or distributed on multiple network units. Some or all of the units may be selected according to actual needs to achieve the purpose of the solution of this embodiment.

[0314] In addition, each functional unit in each embodiment of the present application may be integrated into one processing unit, or each unit may exist physically separately, or two or more units may be integrated into one unit. The above-mentioned integrated unit may be implemented in the form of hardware or in the form of software functional units.

[0315] If the integrated unit is implemented in the form of a software functional unit and sold or used as an independent product, it can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of the present application, or the part that contributes to the prior art, or all or part of the technical solution can be embodied in the form of a software product, which is stored in a storage medium and includes several instructions for a computer device (which can be a personal computer, server, or network device, etc.) to perform all or part of the steps of the various embodiments of the present application. The aforementioned storage medium includes: U disk, mobile hard disk, read-only memory (ROM, read-only memory), random access memory (RAM, random access memory), disk or optical disk, etc. Various media that can store program codes.

Claims

1. A method for solving a system of linear equations, characterized in that: Applied to a computing device or a computing device cluster, the method comprises: Acquire description information input by a user, wherein the description information includes linear equation system information, and the linear equation system information includes a right-hand side term; Reasoning the description information through an artificial intelligence (AI) model to obtain a first initial solution corresponding to the linear equations; A target initial solution is determined according to the first initial solution, the linear equation system is iteratively solved based on the target initial solution, and a solution result of the linear equation system is output.

2. The method according to claim 1, characterized in that The description information also includes information about a physical problem to be solved, and the linear equation system is obtained by numerically simulating the physical problem information to be solved, and the physical problem information to be solved includes at least one of the following: Boundary conditions, mesh information, physical equations.

3. The method according to claim 1 or 2, characterized in that: The step of determining a target initial solution according to the first initial solution, iteratively solving the linear equation system based on the target initial solution, and outputting a solution result of the linear equation system includes: Acquire first configuration information, where the first configuration information carries at least one initial solution generation method for generating an initial solution; Obtaining a plurality of initial solutions according to the at least one initial solution generation mode indicated by the first configuration information, wherein the plurality of initial solutions include the first initial solution; Filtering the target initial solution from the multiple initial solutions; According to the target initial solution, the linear equation system is iteratively solved and the solution result of the linear equation system is output.

4. The method according to claim 3, characterized in that The step of selecting the target initial solution from the multiple initial solutions comprises: Acquire second configuration information, where the second configuration information carries at least one heuristic strategy; The target initial solution is screened out from the multiple initial solutions according to the at least one heuristic strategy.

5. The method according to claim 3 or 4, characterized in that: The step of selecting the target initial solution from the multiple initial solutions comprises: Acquire third configuration information, where the third configuration information carries an evaluation strategy, where the evaluation strategy includes evaluation indicators, or includes evaluation indicators and weights corresponding to each evaluation indicator, where the evaluation indicators include one or more of solution time, solution accuracy, and number of iterations; According to the evaluation strategy, the target initial solution is screened out from the multiple initial solutions.

6. The method according to any one of claims 1 to 5, characterized in that: The method further comprises: Generate training data, the training data including training samples and labels corresponding to the training samples, the training samples including the description information, and the labels corresponding to the training samples are obtained according to the first initial solution; According to the training data, the AI ​​model is trained to obtain an optimized AI model.

7. The method according to claim 6, characterized in that The method further comprises: Obtaining a performance indicator corresponding to the solution result, wherein the performance indicator includes one or more of solution time, solution accuracy, and number of iterations; The step of training the AI ​​model according to the training data to obtain an optimized AI model includes: The AI ​​model is trained according to the training data and the loss function to obtain an optimized AI model, and the loss function is constructed based on the performance indicator.

8. The method according to any one of claims 1 to 7, characterized in that: The AI ​​model is a general model or a model for solving partial differential equations (PDEs). The general model includes CNN or PINN, and the model for solving PDEs includes deeponet.

9. A linear equation solving device, characterized in that: Includes an acquisition module and a processing module; The acquisition module is used to acquire description information input by a user, wherein the description information includes linear equation system information, and the linear equation system information includes a right-hand side term; The processing module is used for: Reasoning the description information through an artificial intelligence (AI) model to obtain a first initial solution corresponding to the linear equations; A target initial solution is determined according to the first initial solution, the linear equation system is iteratively solved based on the target initial solution, and a solution result of the linear equation system is output.

10. The device according to claim 9, characterized in that The description information also includes information about a physical problem to be solved, and the linear equation system is obtained by numerically simulating the physical problem information to be solved, and the physical problem information to be solved includes at least one of the following: Boundary conditions, mesh information, physical equations.

11. The device according to claim 9 or 10, characterized in that The acquisition module is used for: Acquire first configuration information, where the first configuration information carries at least one initial solution generation method for generating an initial solution; The processing module is used for: Obtaining a plurality of initial solutions according to the at least one initial solution generation mode indicated by the first configuration information, wherein the plurality of initial solutions include the first initial solution; Filtering the target initial solution from the multiple initial solutions; According to the target initial solution, the linear equation system is iteratively solved and the solution result of the linear equation system is output.

12. The device according to claim 11, characterized in that The acquisition module is used to: acquire second configuration information, where the second configuration information carries at least one heuristic strategy; The processing module is used to select the target initial solution from the multiple initial solutions according to the at least one heuristic strategy.

13. The device according to claim 11 or 12, characterized in that The acquisition module is used to: acquire third configuration information, the third configuration information carries an evaluation strategy, the evaluation strategy includes evaluation indicators, or includes evaluation indicators and weights corresponding to each evaluation indicator, the evaluation indicators include one or more of solution time, solution accuracy and number of iterations; The processing module is used to: select the target initial solution from the multiple initial solutions according to the evaluation strategy.

14. The device according to any one of claims 9 to 13, characterized in that: The device also includes a training module; The training module is used to: Generate training data, the training data including training samples and labels corresponding to the training samples, the training samples including the description information, and the labels corresponding to the training samples are obtained according to the first initial solution; According to the training data, the AI ​​model is trained to obtain an optimized AI model.

15. The device according to claim 14, characterized in that The acquisition module is used to: acquire performance indicators corresponding to the solution results, wherein the performance indicators include one or more of solution time, solution accuracy and number of iterations; The processing module is used to: train the AI ​​model according to the training data and the loss function to obtain an optimized AI model, and the loss function is constructed based on the performance indicator.

16. The device according to any one of claims 9 to 15, characterized in that The AI ​​model is a general model or a model for solving partial differential equations (PDEs). The general model includes CNN or PINN, and the model for solving PDEs includes deeponet.

17. A computing device, characterized in that include: at least one memory for storing a program; at least one processor, configured to execute the program stored in the memory; Wherein, when the program stored in the memory is executed, the processor is used to execute the method according to any one of claims 1-8.

18. A computing device cluster, characterized in that: comprising at least one computing device, each computing device comprising a processor and a memory; The processor of the at least one computing device is used to execute instructions stored in the memory of the at least one computing device, so that the computing device cluster executes the method according to any one of claims 1-8.

19. A computer-readable storage medium storing a computer program, wherein when the computer program is executed on a processor, the processor is caused to execute the method according to any one of claims 1 to 8.

20. A computer program product, characterized in that When the computer program product runs on a processor, the processor is caused to execute the method according to any one of claims 1 to 8.

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