Mathematical model solving method and device and computing equipment cluster

Abstract

The mathematical model solving method comprises the steps that a matrix of a linear equation set and a solving parameter recommendation request are obtained, the solving parameter recommendation request is used for indicating solving parameters expected to be recommended by a user, and the solving parameters expected to be recommended by the user correspond to a parameter level; the solution parameter corresponding to the next parameter level in the different parameter levels is the refinement of the solution parameter corresponding to the previous parameter level; according to the parameter level corresponding to the solution parameter expected to be recommended by the user, the matrix of the linear equation set is input into a parameter recommendation engine of the corresponding level to obtain the value of the solution parameter expected to be recommended by the user, and the parameter recommendation engine of the corresponding level is used for recommending the value of the solution parameter of the parameter level where the solution parameter expected to be recommended by the user is located; and based on the value of the solution parameter expected to be recommended by the user, solving the system of linear equations to obtain a solution result of the system of linear equations. According to the method, the parameter selection requirements of different users with large knowledge spans are met, and the solving efficiency is improved.

Description

[0001] This application claims priority to the Chinese patent application filed with the State Intellectual Property Office of China on August 1, 2023, with application number 202310960473.5 and application name “A method, device and system for solving a mathematical model”, the entire contents of which are incorporated by reference in this application. Technical Field

[0002] The present application relates to the field of information technology (IT) technology, and in particular to a mathematical model solving method, a database cluster, and a computing device cluster. Background Art

[0003] In the field of industrial simulation, computer-aided engineering (CAE) can be used to analyze the structural mechanical properties of complex engineering and products using computer-aided solutions, as well as to optimize structural performance. When using CAE to perform numerical simulations on real physical problems, the real physical problems can be modeled using computer-aided design (CAD) software. Then, the model obtained by modeling is imported into the CAE software, so that the geometric model can be divided into small finite elements or calculation units through the CAE software, so as to perform discrete calculations in numerical analysis. Next, boundary conditions are set on the CAE software, such as fixed points, loading points, application of external loads, constraints, and other physical conditions. After that, the CAE software can simulate the finite elements or calculation units obtained through boundary conditions and division to obtain a set of linear equations of a mathematical model. Finally, the set of linear equations obtained using the CAE software is numerically solved, and the simulation results are obtained through the solution results.

[0004] Generally, in the linear equations obtained by CAE software simulation, the matrix obtained by integrating coefficients and constant terms is often very large, and may contain millions or billions of unknowns and equations. Processing such large-scale matrices requires the use of high-performance computing and optimization algorithms, so it is very important to select the optimal parameters (i.e., the parameters in the solution method that solves the problem fastest while satisfying the accuracy) to achieve performance improvement. However, due to the unclear relationship between the real physical problem and the solution method, and the excessive number of parameters in the solution method, it is difficult to select the optimal parameters. Therefore, how to efficiently obtain the optimal parameters in order to use the optimal parameters for solution is a technical problem that needs to be solved urgently. Summary of the invention

[0005] The present application provides a mathematical model solving method, apparatus, computing device cluster, computer storage medium and computer product, which can efficiently obtain the value of the optimal parameter and solve the problem using the value of the optimal parameter.

[0006] In a first aspect, the present application provides a method for solving a mathematical model, including: obtaining a matrix of a linear equation group and a solution parameter recommendation request, the solution parameter recommendation request is used to indicate the solution parameters that a user expects to be recommended, the solution parameters that the user expects to be recommended correspond to a parameter level, and the solution parameters that the user expects to be recommended include: a pre-processing method, an iteration method, a parameter of the iteration method, a preprocessor, and one or more of the parameters of the preprocessor, wherein the solution parameters corresponding to the next parameter level in different parameter levels are a refinement of the solution parameters corresponding to the previous parameter level; according to the parameter level corresponding to the solution parameters that the user expects to recommend, the matrix of the linear equation group is input into a parameter recommendation engine of a corresponding level to obtain the values ​​of the solution parameters that the user expects to recommend, wherein the parameter recommendation engine of the corresponding level is used to recommend the values ​​of the solution parameters of the parameter level where the solution parameters that the user expects to recommend are located; based on the values ​​of the solution parameters that the user expects to recommend, the linear equation group is solved to obtain a solution result of the linear equation group.

[0007] In this way, based on the matrix of the linear equations of the mathematical model to be solved and the solution parameter recommendation request, different levels of parameter recommendation engines can be used to automatically select the values ​​of the solution parameters desired by the user, and use the selected solution parameter values ​​to solve the linear equations, thereby meeting the parameter selection needs of different users with a wide range of knowledge and improving the solution efficiency of the solver.

[0008] In a possible implementation, the iterative method includes an iterative method cluster, and the preprocessing sub-cluster includes a preprocessing sub-cluster. Wherein, before the matrix of the linear equation group is input into the parameter recommendation engine of the corresponding level to obtain the value of the solution parameter that the user expects to recommend, the method also includes: when the solution parameter recommendation request indicates that the user expects to recommend one or more of the preprocessing method, the iterative method cluster and the preprocessing sub-cluster, the first-level recommendation engine is used as the parameter recommendation engine of the corresponding level, wherein the first-level recommendation engine is used to recommend one or more of the preprocessing method, the iterative method cluster and the preprocessing sub-cluster. At this time, the matrix is ​​input into the parameter recommendation engine of the corresponding level to obtain the value of the solution parameter that the user expects to recommend, including: inputting the matrix into the first-level recommendation engine to obtain one or more of the preprocessing method, the iterative method cluster and the preprocessing sub-cluster. In this way, the first-level recommendation engine can be used to recommend suitable solution parameter values ​​for the user.

[0009] In a possible implementation, the parameters of the iterative method include the parameters of the sub-iterative method of the iterative method cluster, and the parameters of the preprocessor include the parameters of the sub-preprocessor of the preprocessor cluster. The method further includes: receiving a parameter recommendation enhancement mode instruction, the parameter recommendation enhancement mode instruction is used to indicate the start of the parameter recommendation enhancement mode. At this time, the matrix of the linear equation group is input into the parameter recommendation engine of the corresponding level to obtain the values ​​of the solution parameters that the user expects to recommend, and further includes: when the parameter recommendation enhancement mode is turned on, the matrix, the iterative method and the preprocessor set by the user or recommended by the first-level recommendation engine are input into the third-level recommendation engine to obtain the values ​​of the solution parameters that the user expects to recommend, wherein the third-level recommendation engine is used to recommend the parameters of the iterative method and / or the parameters of the preprocessor. In this way, the first-level recommendation engine and the third-level recommendation engine can be combined to recommend better values ​​of the solution parameters for the user.

[0010] In a possible implementation, before inputting the matrix into the parameter recommendation engine of the corresponding level, the method further includes: when the user expects to recommend the sub-iterative method in the iterative method cluster and / or the sub-preprocessor in the preprocessing sub-cluster, using the secondary recommendation engine as the parameter recommendation engine of the corresponding level, wherein the iterative method cluster and / or the preprocessing sub-cluster are specified by the user, and the secondary recommendation engine is used to recommend the sub-iterative method in the iterative method cluster and / or the sub-preprocessor in the preprocessing sub-cluster. At this time, inputting the matrix of the linear equation group into the parameter recommendation engine of the corresponding level to obtain the value of the solution parameter that the user expects to recommend includes: inputting the matrix into the secondary recommendation engine to obtain the sub-iterative method in the iterative method cluster and / or the sub-preprocessor in the preprocessing sub-cluster. In addition, the method further includes: receiving a first parameter configuration instruction, the first parameter configuration instruction is used to configure the iterative method cluster and / or the preprocessing sub-cluster. In this way, the secondary recommendation engine can be used to recommend suitable solution parameter values ​​for the user.

[0011] In a possible implementation, the parameters of the iterative method include the parameters of the sub-iterative method of the iterative method cluster, and the parameters of the preprocessor include the parameters of the sub-preprocessor of the preprocessor subcluster. The method further includes: receiving a parameter recommendation enhancement mode instruction, the parameter recommendation enhancement mode instruction is used to indicate the start of the parameter recommendation enhancement mode. At this time, the matrix of the linear equation group is input to the parameter recommendation engine of the corresponding level to obtain the values ​​of the solution parameters that the user expects to recommend, and further includes: when the parameter recommendation enhancement mode is turned on, the matrix, the sub-iterative method in the iterative method cluster recommended by the secondary recommendation engine and / or the sub-preprocessor in the preprocessor cluster are input to the tertiary recommendation engine to obtain the solution parameters, wherein the tertiary recommendation engine is used to recommend the parameters of the iterative method and the parameters of the preprocessor. In this way, the secondary recommendation engine and the tertiary recommendation engine can be combined to recommend better values ​​of the solution parameters for the user.

[0012] In a possible implementation, before inputting the matrix into the parameter recommendation engine of the corresponding level, the method includes: when the user desires to recommend the parameters of the sub-iterative method of the iterative method cluster and / or the parameters of the sub-preprocessor in the preprocessing subcluster, using the three-level recommendation engine as the parameter recommendation engine of the corresponding level, wherein the sub-iterative method of the iterative method cluster and the sub-preprocessor in the preprocessing subcluster are specified by the user, and the three-level recommendation engine is used to recommend the parameters of the sub-iterative method of the iterative method cluster and / or the parameters of the sub-preprocessor in the preprocessing subcluster. At this time, the method also includes: receiving a second parameter configuration instruction, the second parameter configuration instruction is used to configure the sub-iterative method of the iterative method cluster and / or the sub-preprocessor in the preprocessing subcluster. In this way, the three-level recommendation engine can be used to recommend appropriate solution parameter values ​​for the user.

[0013] In a possible implementation, the method further includes: receiving a third parameter configuration instruction, the third parameter configuration instruction is used to configure the first parameter of the sub-iteration method of the iterative method cluster and / or the second parameter of the sub-preprocessor in the preprocessing sub-cluster. At this time, before inputting the matrix into the parameter recommendation engine of the corresponding level, the method includes: using the four-level recommendation engine as the parameter recommendation engine of the corresponding level, the four-level recommendation engine is used to recommend the sub-parameters of the first parameter and / or the sub-parameters of the second parameter. In this way, the four-level recommendation engine can be used to recommend suitable solution parameter values ​​for users.

[0014] In one possible implementation, solving a system of linear equations based on the values ​​of solution parameters that a user expects to recommend includes: inputting the system of linear equations and the values ​​of solution parameters that a user expects to recommend into a numerical calculation solver; and solving the system of linear equations using the numerical calculation solver.

[0015] In a possible implementation, the pre-processing method includes ordering or scaling, and the iterative method includes a Krylov subspace method.

[0016] In one possible implementation, the parameter recommendation engine at the corresponding level is a neural network engine, wherein the value of the solution parameter that the user expects to be recommended is inferred by the parameter recommendation engine based on the properties of the matrix of the linear equation system.

[0017] In a second aspect, the present application provides a mathematical model solving device, including: an acquisition module and a processing module. The acquisition module is used to obtain a matrix of a linear equation group and a solution parameter recommendation request, and the solution parameter recommendation request is used to indicate the solution parameter that the user expects to recommend. The solution parameter that the user expects to recommend corresponds to a parameter level, and the solution parameter that the user expects to recommend includes: one or more of the pre-processing method, the iteration method, the parameter of the iteration method, the preprocessor, and the parameter of the preprocessor, wherein the solution parameter corresponding to the next parameter level in different parameter levels is a refinement of the solution parameter corresponding to the previous parameter level. The processing module is used to input the matrix of the linear equation group into the parameter recommendation engine of the corresponding level according to the parameter level corresponding to the solution parameter that the user expects to recommend, so as to obtain the value of the solution parameter that the user expects to recommend, wherein the parameter recommendation engine of the corresponding level is used to recommend the value of the solution parameter of the parameter level where the solution parameter that the user expects to recommend is located. The processing module is also used to solve the linear equation group based on the value of the solution parameter that the user expects to recommend, and obtain the solution result of the linear equation group.

[0018] In a possible implementation, the iterative method includes an iterative method cluster, and the preprocessing sub-cluster includes a preprocessing sub-cluster. Before the processing module inputs the matrix of the linear equation system into the parameter recommendation engine of the corresponding level to obtain the value of the solution parameter that the user expects to be recommended, the processing module is further used to: when the solution parameter recommendation request indicates that the user expects to recommend one or more of the preprocessing method, the iterative method cluster, and the preprocessing sub-cluster, use the first-level recommendation engine as the parameter recommendation engine of the corresponding level, wherein the first-level recommendation engine is used to recommend one or more of the preprocessing method, the iterative method cluster, and the preprocessing sub-cluster.

[0019] When the processing module inputs the matrix into the parameter recommendation engine of the corresponding level to obtain the value of the solution parameter that the user expects to be recommended, it is specifically used to: input the matrix into the first-level recommendation engine to obtain one or more of the pre-processing method, iterative method cluster and pre-processing sub-cluster.

[0020] In a possible implementation, the parameters of the iteration method include parameters of a sub-iteration method of the iteration method cluster, and the parameters of the preprocessor include parameters of a sub-preprocessor of the preprocessor cluster.

[0021] The acquisition module is further used to: receive a parameter recommendation enhancement mode instruction, where the parameter recommendation enhancement mode instruction is used to instruct to start the parameter recommendation enhancement mode.

[0022] When the processing module inputs the matrix of the linear equation group into the parameter recommendation engine of the corresponding level to obtain the values ​​of the solution parameters that the user expects to be recommended, it is specifically used to: when the parameter recommendation enhancement mode is turned on, the matrix, the iterative method and the preprocessor set by the user or recommended by the first-level recommendation engine are input into the third-level recommendation engine to obtain the values ​​of the solution parameters that the user expects to be recommended, wherein the third-level recommendation engine is used to recommend the parameters of the iterative method and / or the parameters of the preprocessor.

[0023] In one possible implementation, before inputting the matrix into the parameter recommendation engine of the corresponding level, the processing module is further used to: when the user desires to recommend a sub-iterative method in an iterative method cluster and / or a sub-preprocessor in a preprocessing subcluster, use the secondary recommendation engine as the parameter recommendation engine of the corresponding level, wherein the iterative method cluster and / or the preprocessing subcluster are specified by the user, and the secondary recommendation engine is used to recommend the sub-iterative method in the iterative method cluster and / or the sub-preprocessor in the preprocessing subcluster.

[0024] When the processing module inputs the matrix of the linear equation group into the parameter recommendation engine of the corresponding level to obtain the values ​​of the solution parameters that the user expects to be recommended, it is specifically used to: input the matrix into the secondary recommendation engine to obtain the sub-iterative method in the iterative method cluster and / or the sub-preprocessing sub-cluster in the preprocessing sub-cluster.

[0025] The acquisition module is further used to: receive a first parameter configuration instruction, where the first parameter configuration instruction is used to configure the iteration method cluster and / or the preprocessing sub-cluster.

[0026] In a possible implementation, the parameters of the iteration method include parameters of a sub-iteration method of the iteration method cluster, and the parameters of the preprocessor include parameters of a sub-preprocessor of the preprocessor cluster.

[0027] The acquisition module is further used to: receive a parameter recommendation enhancement mode instruction, where the parameter recommendation enhancement mode instruction is used to instruct to start the parameter recommendation enhancement mode.

[0028] When the processing module inputs the matrix of the linear equation group into the parameter recommendation engine of the corresponding level to obtain the values ​​of the solution parameters that the user expects to be recommended, it is specifically used to: when the parameter recommendation enhancement mode is turned on, input the matrix, the sub-iterative method in the iterative method cluster and / or the sub-preprocessor in the preprocessing sub-cluster recommended by the secondary recommendation engine into the tertiary recommendation engine to obtain the solution parameters, wherein the tertiary recommendation engine is used to recommend the parameters of the iterative method and the parameters of the preprocessor.

[0029] In one possible implementation, before inputting the matrix into the parameter recommendation engine of the corresponding level, the processing module is further used to: when the user desires to recommend parameters of sub-iterative methods of the iterative method cluster and / or parameters of sub-preprocessors in the preprocessing subcluster, use the three-level recommendation engine as the parameter recommendation engine of the corresponding level, wherein the sub-iterative methods of the iterative method cluster and the sub-preprocessors in the preprocessing subcluster are specified by the user, and the three-level recommendation engine is used to recommend parameters of sub-iterative methods of the iterative method cluster and / or parameters of sub-preprocessors in the preprocessing subcluster.

[0030] The acquisition module is further used to: receive a second parameter configuration instruction, where the second parameter configuration instruction is used to configure a sub-iterative method of the iterative method cluster and / or a sub-preprocessor in a preprocessing sub-cluster.

[0031] In a possible implementation, the acquisition module is further used to: receive a third parameter configuration instruction, where the third parameter configuration instruction is used to configure a first parameter of a sub-iteration method in the iterative method cluster and / or a second parameter of a sub-preprocessor in the preprocessing sub-cluster.

[0032] Before inputting the matrix into the parameter recommendation engine of the corresponding level, the processing module is further used to: use the four-level recommendation engine as the parameter recommendation engine of the corresponding level, and the four-level recommendation engine is used to recommend sub-parameters of the first parameter and / or sub-parameters of the second parameter.

[0033] In one possible implementation, when solving a system of linear equations based on the values ​​of the solution parameters that a user expects to recommend, the processing module is specifically used to: input the system of linear equations and the values ​​of the solution parameters that a user expects to recommend into a numerical calculation solver; and solve the system of linear equations using the numerical calculation solver.

[0034] In a possible implementation, the pre-processing method includes ordering or scaling, and the iterative method includes a Krylov subspace method.

[0035] In one possible implementation, the parameter recommendation engine at the corresponding level is a neural network engine, wherein the value of the solution parameter that the user expects to be recommended is inferred by the parameter recommendation engine based on the properties of the matrix of the linear equation system.

[0036] In a third aspect, the present application provides a computing device cluster, comprising at least one computing device, each computing device comprising a processor and a memory; the processor of at least one computing device is used to execute instructions stored in the memory of at least one computing device, so that the computing device cluster performs the method described in the first aspect or any possible implementation of the first aspect.

[0037] In a fourth aspect, the present application provides a computer-readable storage medium, including computer program instructions, when the computer program instructions are executed by a computing device cluster, the computing device cluster executes the method described in the first aspect or any possible implementation of the first aspect. Exemplarily, the computing device cluster may include one or more computing devices.

[0038] In a fifth aspect, the present application provides a computer program product including instructions, which, when executed by a computing device cluster, enables the computing device cluster to perform the method described in the first aspect or any possible implementation of the first aspect. Exemplarily, the computing device cluster may include one or more computing devices.

[0039] It can be understood that the beneficial effects of the second to fifth aspects mentioned above can be found in the relevant description of the first aspect mentioned above, and will not be repeated here. BRIEF DESCRIPTION OF THE DRAWINGS

[0040] Figure 1 It is a schematic diagram of the architecture of a mathematical model solving system provided in an embodiment of the present application;

[0041] Figure 2 It is a schematic diagram of an interaction form between a tenant and a cloud computing platform provided in an embodiment of the present application;

[0042] Figure 3 It is a flow chart of a mathematical model solving method provided in an embodiment of the present application;

[0043] Figure 4 This is a schematic diagram of a parameter recommendation process provided by an embodiment of the present application;

[0044] Figure 5 It is a structural schematic diagram of a mathematical model solving device provided in an embodiment of the present application;

[0045] Figure 6 is a schematic diagram of the structure of a computing device provided in an embodiment of the present application;

[0046] Figure 7 is a schematic diagram of the structure of a computing device cluster provided in an embodiment of the present application;

[0047] Figure 8 It is a structural diagram of another computing device cluster provided in an embodiment of the present application. DETAILED DESCRIPTION

[0048] The term "and / or" in this article is a description of the association relationship of associated objects, indicating that there can be three relationships. For example, A and / or B can represent: A exists alone, A and B exist at the same time, and B exists alone. The symbol " / " in this article indicates that the associated objects are in an or relationship, for example, A / B means A or B.

[0049] The terms "first" and "second" in the specification and claims herein are used to distinguish different objects rather than to describe a specific order of the objects. For example, a first response message and a second response message are used to distinguish different response messages rather than to describe a specific order of the response messages.

[0050] In the embodiments of the present application, words such as "exemplary" or "for example" are used to indicate examples, illustrations or descriptions. Any embodiment or design described as "exemplary" or "for example" in the embodiments of the present application should not be interpreted as being more preferred or more advantageous than other embodiments or designs. Specifically, the use of words such as "exemplary" or "for example" is intended to present related concepts in a specific way.

[0051] In the description of the embodiments of the present application, unless otherwise specified, "multiple" means two or more than two. For example, multiple processing units refer to two or more processing units, etc.; multiple elements refer to two or more elements, etc.

[0052] Generally, the linear equations obtained by simulating the mathematical model through CAE software simulation can be solved by using a manually selected solver to obtain the solution result. At this time, the user needs to export the linear equations obtained by simulation. Then, using numerical calculation software, manually selected iteration methods, preprocessors and parameters corresponding to various algorithms, the linear equations are processed to obtain the solution result. Finally, the solution result is imported into the CAE software, and the CAE software processes the solution result to obtain the simulation result. However, this method is only suitable for users who have a deep understanding of both physical problems and numerical methods. In addition, because the parameter space is too large, it is difficult for humans to quickly and efficiently select the optimal parameters.

[0053] In view of this, an embodiment of the present application provides a mathematical model solving system, which can automatically select the values ​​of the solving parameters desired by the user according to the matrix of the linear equation group of the mathematical model to be solved and the solution parameter recommendation request, and use the selected solution parameter values ​​to solve the linear equation group, thereby meeting the parameter selection needs of different users with a wide range of knowledge and improving the solving efficiency of the solver. Optionally, when the linear equation group is simulated by CAE simulation software, the mathematical model solving system provided by the present application improves the CAE simulation efficiency.

[0054] For example, Figure 1 FIG. 1 is a schematic diagram showing the architecture of a mathematical model solving system provided in an embodiment of the present application. Figure 1 As shown, the mathematical model solving system 100 may include: a CAE simulation service 110 , a numerical calculation solving service 120 , a multi-level parameter tuning service 130 and an iterative solution service 140 .

[0055] Among them, the CAE simulation service 110 is a solution based on computer simulation and analysis, which can be used to predict and evaluate the behavior and performance of products, components or systems under different conditions. The user can request to use the CAE simulation service 110. When the user requests to use the CAE simulation service 110, the user imports the geometric model obtained by CAD modeling into the CAE simulation service 110 through the user interface provided by the CAE simulation service 110, and selects the mesh type and sets the boundary conditions according to the nature of the problem and the simulation type. At the same time, the user can also choose whether to use the parameter recommendation service in the user interface, and which level of solution parameters need to be recommended. In this embodiment, the parameter level can be but is not limited to four levels. When selecting, the user can choose to recommend the first-level solution parameters, the second-level solution parameters, the third-level solution parameters or the fourth-level solution parameters, or can choose to recommend the default solution parameters of a certain level. Among them, as the level of the solution parameters required to be recommended gradually increases, the granularity of the recommended solution parameters gradually becomes finer, that is, the granularity of the recommended fourth-level solution parameters is the finest, and the granularity of the recommended first-level solution parameters is the coarsest. The solution parameters may include: one or more of: a pre-processing method, an iteration method, parameters of the iteration method, a pre-processor, and parameters of the pre-processor.

[0056] When the user completes the settings through the user interface provided by the CAE simulation service 110, the CAE simulation service 110 may send a numerical calculation request to the numerical calculation solver service 120 to call the numerical calculation solver service 120 for solving. The numerical calculation request may include one or more of the following information: the field to which the problem to be solved belongs, the matrix of the linear equation system obtained by the problem, whether to use the parameter recommendation service, and which level of solution parameters need to be recommended.

[0057] The numerical calculation solution service 120 is a service that provides numerical calculation and simulation solution capabilities. After the numerical calculation solver service 120 obtains the numerical calculation request transmitted by the CAE simulation service 110, when the user chooses to use the parameter recommendation service, the numerical calculation solution service 120 can send a solution parameter recommendation request to the multi-level parameter tuning service 130 to call the multi-level parameter tuning service 130 to recommend the optimal solution parameter value. The solution parameter recommendation request can be used to indicate the solution parameter that the user expects to be recommended.

[0058] It is understandable that in other embodiments provided in the present application, the user can also complete the setting of numerical calculations or groups of linear equations through the interface provided by the numerical calculation solution service 120 or other numerical calculation services, so that the numerical calculation solution service 120 obtains the numerical calculation request and performs the solution. At the same time, when the user chooses to use the parameter recommendation service, the numerical calculation solution service 120 can send a solution parameter recommendation request to the multi-level parameter tuning service 130 to call the multi-level parameter tuning service 130 to recommend the optimal solution parameter value.

[0059] The multi-level parameter tuning service 130 is a service that provides the ability to recommend optimal parameters. After obtaining the solution parameter recommendation request, the multi-level parameter tuning service 130 can input the matrix of the linear equation group of the mathematical model into the parameter recommendation engine of the corresponding level according to the parameter level corresponding to the solution parameter that the user expects to recommend, so as to obtain the value of the solution parameter that the user expects to recommend. Among them, the parameter recommendation engine of the corresponding level is mainly used to recommend the value of the solution parameter of the parameter level where the solution parameter that the user expects to recommend is located. Among them, the value of the solution parameter may include: the name of the pre-processing method, the name of the iteration method, the name of the preprocessor, the parameters of the iteration method, the parameters of the preprocessor, and one or more of the sub-parameters contained in the parameters of the preprocessor. After obtaining the optimal solution parameter value, the multi-level parameter tuning service 130 can send a solution calculation request to the iterative solution service 140 to call the iterative solution service 140 for solution. Exemplarily, the solution calculation request may include the value of the solution parameter and the matrix of the linear equation group of the mathematical model to be solved.

[0060] The iterative solution service 140 is a service that uses iterative methods to perform solution calculations. After obtaining a solution calculation request, the iterative solution service 140 can solve the linear equations of the mathematical model based on the values ​​of the solution parameters that the user expects to recommend, so as to obtain the solution result of the linear equations.

[0061] In addition, after obtaining the solution result, the iterative solution service 140 may transmit the solution result to the numerical calculation solution service 120. Then, the numerical calculation solver service 120 may transmit the solution result to the CAE simulation service 110. Finally, the CAE simulation service 110 may perform simulation calculation using the solution result to obtain a simulation result, and present the simulation result to the user.

[0062] The above is an introduction to the mathematical model solving system 100 provided in the embodiment of the present application. Among them, the services included in the above-mentioned mathematical model solving system 100 can all be configured on the cloud computing platform. For example, they can be deployed on at least one virtual machine or container instance. Of course, the services included in the mathematical model solving system 100 can also be configured on nodes other than the cloud computing platform. For example, they can be deployed in at least one data center, or deployed on at least one server. The specific situation can be determined according to the actual situation and is not limited here. Among them, the cloud computing platform can provide pages related to public cloud services for tenants to remotely access public cloud services. In this embodiment, tenants (also referred to as "users") can purchase CAE simulation-related services on the cloud computing platform in advance, such as: one or more services in the mathematical model solving system 100. For ease of understanding, the interaction between tenants and the cloud computing platform is described below. As Figure 2 As shown, the interaction between the tenant and the cloud computing platform mainly includes: the tenant logs in to the cloud computing platform 200 through the client web page, selects and purchases cloud services related to CAE simulation (i.e., services related to CAE simulation) in the cloud computing platform 200, and after the purchase, the tenant can perform CAE simulation based on the functions provided by the services related to CAE simulation. Among them, the cloud computing platform 200 is mainly used to manage the infrastructure for running services related to CAE simulation. Exemplarily, the infrastructure for running services related to CAE simulation may include multiple data centers set up in different regions, each data center including multiple servers. The data center may provide basic resources for services related to CAE simulation, such as computing resources, storage resources, etc. Therefore, when the tenant purchases and uses services related to CAE simulation, it mainly pays for the resources used. In other embodiments provided in the present application, the tenant may also select or purchase other numerical calculation solution services including parameter recommendation services in the cloud computing platform 200, and enter information related to the linear equation system on the configuration interface provided by the service, and call the parameter recommendation service and the numerical calculation solution service for solution. In an embodiment provided in the present application, the user inputs information related to the linear equation system by uploading a .mtx format file of the linear equation system to be solved.

[0063] When the CAE simulation service 110 in the mathematical model solving system 100 is configured in the cloud computing platform 200, after using the services related to CAE simulation, the tenant can complete the import of the geometric model through the configuration interface provided by the cloud computing platform 200 or the interface for interacting with the tenant, and select the mesh type and set the boundary conditions according to the nature of the problem and the simulation type. At the same time, the tenant can also complete the settings of whether to use the parameter recommendation service and which level of solution parameters need to be recommended through the configuration interface provided by the cloud computing platform 200 or the interface for interacting with the tenant. After the tenant completes the settings, the cloud computing platform 200 can perform simulation calculations according to the tenant settings.

[0064] When the CAE simulation service 110 in the mathematical model solving system 100 is not configured in the cloud computing platform 200, the tenant can call the service provided on the cloud computing platform 200 through the CAE simulation service 110. After the CAE simulation service 110 calls the service provided on the cloud computing platform 200, the cloud computing platform 200 can perform parameter recommendation, numerical calculation, etc. to obtain the solution result, and return the solution result to the CAE simulation service 110.

[0065] The above is an introduction to the mathematical model solving system 100 provided in the embodiment of the present application, and the interaction between the tenant and the cloud computing platform. Based on the above content, a mathematical model solving method provided in the embodiment of the present application is introduced below.

[0066] For example, Figure 3 The flowchart of a mathematical model solving method provided by the embodiment of the present application is shown. It can be understood that the method can be executed by any device, equipment, platform, or equipment cluster with computing and processing capabilities. For example, the above Figure 2 The cloud computing platform 200 described in the above is executed. For the convenience of description, the following description is based on the cloud computing platform 200 as the execution subject. Of course, the cloud computing platform can also be replaced by other execution subjects, and the replaced solutions are still within the protection scope of this application. Figure 3 As shown, the mathematical model solving method may include the following steps:

[0067] S301. The cloud computing platform obtains a matrix of a linear equation group and a solution parameter recommendation request, where the solution parameter recommendation request is used to indicate the solution parameters that the user expects to be recommended, and the solution parameters that the user expects to be recommended correspond to a parameter level, and the solution parameters that the user expects to be recommended include: one or more of a pre-processing method, an iteration method, a parameter of an iteration method, a preprocessor, and a parameter of a preprocessor, wherein the solution parameters corresponding to the next parameter level in different parameter levels are a refinement of the solution parameters corresponding to the previous parameter level.

[0068] In this embodiment, the matrix of the linear equations can be, but is not limited to, obtained by parsing the geometric model obtained by the cloud computing platform modeling the tenant. The solution parameter recommendation request can be used to indicate the solution parameters that the user expects to be recommended, such as: one or more of: pre-processing method, iteration method, parameters of iteration method, preprocessor, parameters of preprocessor, etc. The solution parameter recommendation request can be, but is not limited to, sent by a client associated with the cloud computing platform to the cloud computing platform. Among them, the client associated with the cloud computing platform can be a desktop application, a mobile application, a web application, or a web-based application. Exemplarily, the user can select the solution parameters that he expects to be recommended on the client associated with the cloud computing platform.

[0069] In addition, the solution parameters that the user expects to be recommended correspond to a parameter level, and the solution parameters corresponding to the next parameter level in different parameter levels are refinements of the solution parameters corresponding to the previous parameter level. In other words, the granularity of the solution parameters of the previous parameter level is greater than the granularity of the solution parameters of the next parameter level.

[0070] S302. The cloud computing platform inputs the matrix of the linear equation group into the parameter recommendation engine of the corresponding level according to the parameter level corresponding to the solution parameters that the user expects to be recommended, so as to obtain the values ​​of the solution parameters that the user expects to be recommended, wherein the parameter recommendation engine of the corresponding level is used to recommend the values ​​of the solution parameters of the parameter level where the solution parameters that the user expects to be recommended are located.

[0071] In this embodiment, the cloud computing platform can select a parameter recommendation engine of the corresponding level from the pre-configured parameter recommendation engines according to the parameter level corresponding to the solution parameters that the user expects to recommend. Then, the cloud computing platform can input the matrix of the linear equations into the parameter recommendation engine of the corresponding level, so that the parameter recommendation engine can perform reasoning based on the properties of the matrix of the linear equations to obtain the values ​​of the solution parameters that the user expects to recommend. For example, the name of the pre-processing method, the name of the iteration method, the name of the preprocessor, the parameters of the iteration method, the parameters of the preprocessor, or the sub-parameters contained in the parameters of the preprocessor are obtained. Exemplarily, the parameter recommendation engine of the corresponding level can be, but is not limited to, a neural network engine, which can be used to recommend the values ​​of the solution parameters of the parameter level where the solution parameters that the user expects to recommend are located.

[0072] As a possible implementation, the user can select the recommended solution parameters on the client associated with the cloud computing platform without selecting the pre-processing method, the iterative method cluster or the pre-processing sub-cluster, which indicates that the user expects the recommended solution parameters to be one or more of the pre-processing method, the iterative method cluster and the pre-processing sub-cluster. Exemplarily, the pre-processing method may include ordering or scaling, the iterative method cluster may include a generalized minimal residual (GMRES) cluster, a biconjugate gradient (BiCG) cluster, and the pre-processing sub-cluster may include an incomplete lower-upper (ILU) cluster or a multigrid (MG) cluster. At this time, the solution parameter recommendation request received by the cloud computing platform may indicate that the user expects to recommend one or more of the pre-processing method, the iterative method cluster and the pre-processing sub-cluster. In this case, the cloud computing platform can use the first-level recommendation engine as the parameter recommendation engine of the corresponding level. The first-level recommendation engine can be used to recommend one or more of the pre-processing method, the iterative method cluster and the pre-processing sub-cluster. After selecting the primary recommendation engine, the cloud computing platform can input the matrix of the linear equation group into the primary recommendation engine to obtain one or more of the pre-processing method, the iteration method cluster and the pre-processing sub-cluster, thereby obtaining the value of the solution parameter that the user expects to be recommended.

[0073] In addition, the user can also choose to turn on the parameter recommendation enhancement mode on the client associated with the cloud computing platform. When the user turns on the parameter recommendation enhancement mode, it indicates that the user expects to recommend the parameters of the sub-iteration method of the iterative method cluster and / or the parameters of the sub-preprocessor of the preprocessing sub-cluster. At this time, the client associated with the cloud computing platform can send a parameter recommendation enhancement mode instruction to the cloud computing platform, which can be used to indicate the turn on of the parameter recommendation enhancement mode. In this case (i.e., the case of turning on the parameter recommendation enhancement mode), the cloud computing platform can input the matrix of the linear equation group, the iterative method and the preprocessor set by the user or recommended by the first-level recommendation engine into the third-level recommendation engine to obtain the value of the solution parameter that the user expects to recommend. Among them, the third-level recommendation engine is used to recommend the parameters of the iterative method and / or the parameters of the preprocessor. In this way, without the user having to set more parameters, the value of the solution parameter of finer granularity can be automatically recommended to the user, which reduces the difficulty of solving the mathematical model and improves the user experience.

[0074] As another possible implementation, the user can select an iterative method cluster and / or a preprocessing subcluster on a client associated with a cloud computing platform. When the user selects an iterative method cluster and / or a preprocessing subcluster (i.e., the user specifies an iterative method cluster and / or a preprocessing subcluster), it indicates that the user desires to recommend a sub-iterative method of the iterative method cluster and / or a sub-preprocessing subcluster of the preprocessing subcluster. For example, when the user selects a GMRES cluster, it indicates that the user desires to recommend GMRES, EGMRES, or FGMRES, etc. under the GMRES cluster. At this point, the client associated with the cloud computing platform can send a parameter configuration instruction to the cloud computing platform, and the parameter configuration instruction can be used to configure the iterative method cluster and / or the preprocessing subcluster. After receiving the parameter configuration instruction, the cloud computing platform can configure the iterative method cluster and / or the preprocessing subcluster selected by the user, and use the secondary recommendation engine as the parameter recommendation engine of the corresponding level. The secondary recommendation engine can be used to recommend a sub-iterative method in an iterative method cluster and / or a sub-preprocessing subcluster in a preprocessing subcluster. Then, the cloud computing platform may input the matrix of the linear equation group into the secondary recommendation engine to obtain the sub-iterative method in the iterative method cluster and / or the sub-preprocessing sub-cluster in the preprocessing sub-cluster.

[0075] In addition, the user can also choose to turn on the parameter recommendation enhancement mode on the client associated with the cloud computing platform. When the user turns on the parameter recommendation enhancement mode, it indicates that the user expects to recommend the parameters of the sub-iteration method of the iterative method cluster and / or the parameters of the sub-preprocessor of the preprocessing sub-cluster. At this time, the client associated with the cloud computing platform can send a parameter recommendation enhancement mode instruction to the cloud computing platform, which can be used to indicate the turn on of the parameter recommendation enhancement mode. In this case (i.e., the case of turning on the parameter recommendation enhancement mode), the cloud computing platform can input the matrix of the linear equation group, the sub-iteration method in the iterative method cluster set by the user or recommended by the secondary recommendation engine, and / or the sub-preprocessor in the preprocessing sub-cluster, into the tertiary recommendation engine to obtain the value of the solution parameter that the user expects to recommend. Among them, the tertiary recommendation engine is used to recommend the parameters of the iterative method and / or the parameters of the preprocessor. In this way, without the user having to set more parameters, the value of the solution parameter of finer granularity can be automatically recommended to the user, which reduces the difficulty of solving the mathematical model and improves the user experience.

[0076] As another possible implementation, the user can select a sub-iterative method under an iterative method cluster and / or a sub-preprocessor under a preprocessor sub-cluster on a client associated with a cloud computing platform. When the user selects a sub-iterative method under an iterative method cluster and / or a sub-preprocessor under a preprocessor sub-cluster (i.e., the user specifies a sub-iterative method under an iterative method cluster and / or a sub-preprocessor under a preprocessor sub-cluster), it indicates that the user expects to recommend the parameters of the sub-iterative method of the iterative method cluster and / or the parameter values ​​of the sub-preprocessor of the preprocessor sub-cluster. For example, when the user selects ILUT, it indicates that the user expects to recommend specific values ​​of parameters such as ilut_drop_tol and ilut_pivoting. At this point, the client associated with the cloud computing platform can send a parameter configuration instruction to the cloud computing platform, and the parameter configuration instruction can be used to configure the sub-iterative method of the iterative method cluster and / or the sub-preprocessor in the preprocessor sub-cluster. After receiving the parameter configuration instruction, the cloud computing platform can configure the sub-iterative method and / or the sub-preprocessor selected by the user, and use the three-level recommendation engine as the parameter recommendation engine of the corresponding level. The three-level recommendation engine can be used to recommend the parameters of the sub-iterative methods of the iterative method cluster and / or the values ​​of the parameters of the sub-preprocessors in the preprocessing sub-cluster. Then, the cloud computing platform can input the matrix of the linear equation system into the three-level recommendation engine to obtain the values ​​of the parameters of the sub-iterative methods and / or the parameters of the sub-preprocessors.

[0077] As another possible implementation, the user can select the parameters of a sub-iteration method and / or the parameters of a sub-preprocessor on the client associated with the cloud computing platform. When the user selects the parameters of a sub-iteration method and / or the parameters of a sub-preprocessor (that is, the user specifies the parameters of a sub-iteration method and / or the parameters of a sub-preprocessor), it indicates that the user expects to recommend the sub-parameters contained in the parameters of a sub-iteration method and / or the sub-parameters contained in the parameters of a sub-preprocessor. For example, when the user sets the preprocessor used in each block in Block Jacobi to be ILU, it indicates that the user expects to recommend the specific values ​​of the parameters of ILU. At this time, the client associated with the cloud computing platform can send a parameter configuration instruction to the cloud computing platform, and the parameter configuration instruction can be used to configure the parameters of a sub-iteration method and / or the parameters of a sub-preprocessor. After receiving the parameter configuration instruction, the cloud computing platform can configure the parameters of a sub-iteration method and / or the parameters of a sub-preprocessor selected by the user, and use the four-level recommendation engine as the parameter recommendation engine of the corresponding level. The four-level recommendation engine can be used to recommend the values ​​of the sub-parameters included in the parameters of a certain sub-iteration method and / or the sub-parameters included in the parameters of a certain sub-preprocessing sub-processor. Then, the cloud computing platform can input the matrix of the linear equation group into the four-level recommendation engine to obtain the values ​​of the sub-parameters included in the parameters of a certain sub-iteration method and / or the sub-parameters included in the parameters of a certain sub-preprocessing sub-processor.

[0078] S303: The cloud computing platform solves the linear equations based on the values ​​of the solution parameters recommended by the user to obtain a solution result of the linear equations.

[0079] In this embodiment, after obtaining the values ​​of the solution parameters that the user expects to recommend, the cloud computing platform can input the linear equations and the values ​​of the solution parameters that the user expects to recommend into a numerical calculation solver, and use the numerical calculation solver to solve the linear equations to obtain the solution result of the linear equations.

[0080] In this way, according to the matrix of the linear equations of the mathematical model to be solved and the solution parameter recommendation request, different levels of parameter recommendation engines can be used to automatically select the values ​​of the solution parameters desired by the user, and use the selected solution parameter values ​​to solve the linear equations, thereby meeting the parameter selection needs of different users with a wide range of knowledge and improving the efficiency of CAE simulation.

[0081] The above is an introduction to the mathematical model solving method provided in this embodiment. For ease of understanding, the following example is used for illustration.

[0082] For example, Figure 4 As shown in the figure, when the user chooses not to recommend solution parameters, the user can select the pre-processing method, iterative method (such as Krylov subspace method (KSP)) and preconditioner (PC) by himself. Finally, the matrix of the linear equation system can be solved using the pre-processing method, iterative method and preconditioner selected by the user.

[0083] When the user chooses to recommend solution parameters, if the user does not have fixed pre-processing methods, iterative methods and pre-processors, the first-level recommendation engine can be used as a parameter recommendation engine, and at least the matrix of the linear system of equations is input into the first-level parameter recommendation engine to obtain the pre-processing method, iterative method and / or pre-processor. Exemplarily, the output of the first-level parameter recommendation engine may be, but is not limited to, the name of the pre-processing method, iterative method and / or pre-processor. Finally, the matrix of the linear system of equations can be solved using the obtained pre-processing method, iterative method and / or pre-processor. Exemplarily, when solving, the default parameter values ​​of the pre-processing method, iterative method and / or pre-processor used may be used but is not limited to be solved. In addition, if the user chooses to turn on the parameter enhancement mode at this time, the matrix of the linear system of equations and the results output by the first-level recommendation engine can be transmitted to the third-level recommendation engine to obtain the values ​​of the solution parameters of finer granularity through the third-level recommendation engine.

[0084] When the user chooses to recommend solution parameters, if the user has fixed the iteration method cluster and / or preprocessor cluster, such as the GMRES cluster, but has not fixed a specific iteration method and / or preprocessor, the secondary recommendation engine can be used as a parameter recommendation engine, and at least the matrix of the linear system of equations is input into the secondary parameter recommendation engine to obtain the iteration method and / or preprocessor under the specific cluster. Exemplarily, the secondary parameter recommendation engine outputs the name of the iteration method and / or preprocessor, but is not limited to it. Finally, the matrix of the linear system of equations can be solved using the iteration method and / or preprocessor obtained under the specific cluster. Exemplarily, when solving, the default parameter values ​​of the iteration method and / or preprocessor used can be used, but are not limited to be solved. In addition, if the user chooses to turn on the parameter enhancement mode at this time, the matrix of the linear system of equations and the results output by the secondary recommendation engine can be transmitted to the tertiary recommendation engine to obtain the values ​​of the solution parameters of finer granularity through the tertiary recommendation engine.

[0085] When the user selects the recommended solution parameters, if the user fixes a specific iteration method and / or preprocessor, but does not fix the specific parameters of the iteration method and / or preprocessor, such as fixing GMRES, but not fixing the parameter value of GMRES, etc., the three-level recommendation engine can be used as a parameter recommendation engine, and at least the matrix of the linear system of equations is input into the three-level parameter recommendation engine to obtain the parameter values ​​of the specific iteration method and / or preprocessor. Finally, the obtained parameter values ​​of the iteration method and / or preprocessor can be used to solve the matrix of the linear system of equations.

[0086] When the user selects the recommended solution parameters, if the user fixes a specific iteration method and / or preprocessor, and fixes the specific parameters of the iteration method and / or preprocessor, the four-level recommendation engine can be used as the parameter recommendation engine, and at least the matrix of the linear system of equations is input into the four-level parameter recommendation engine to obtain the sub-parameter values ​​contained in the parameters of the specific iteration method and / or preprocessor. Finally, the sub-parameter values ​​contained in the obtained parameter values ​​of the iteration method and / or preprocessor can be used to solve the matrix of the linear system of equations.

[0087] In some embodiments, the user can choose to recommend any one or more of the pre-processing method, the iterative method, and the pre-processing sub-processor. When the user selects any one or both, the cloud computing platform can use the system default to solve the remaining one or both. For example, when the user only chooses to recommend the pre-processing method, but does not set the iterative method and the pre-processing sub-processor by himself, the cloud computing platform can recommend the pre-processing method for the user and select the system default iterative method and pre-processing sub-processor. Of course, the user can also be required to set or choose to recommend these three. When the user does not set or choose to recommend any one of them, an error can be reported to allow the user to complete the setting or choose to recommend these three.

[0088] In addition, the granularity of the solution parameters recommended by the cloud computing platform to the user in a parameter recommendation process can be the same or different, depending on the actual situation, and is not limited here. For example, the cloud computing platform can use a secondary recommendation engine to recommend KSPs under a specific cluster to the user, and use a tertiary recommendation engine to recommend parameter values ​​for a specific PC.

[0089] It is understandable that the order of execution of the steps in the above embodiments does not mean the order of execution. The execution order of each process should be determined by its function and internal logic, and should not constitute any limitation on the implementation process of the embodiments of the present application. In addition, the various embodiments described above can be combined according to actual conditions, and the combined solutions are still within the scope of protection of the present application.

[0090] The above is an introduction to the mathematical model solving method provided in the embodiment of the present application. Next, based on the method in the above embodiment, a mathematical model solving device provided in the embodiment of the present application is introduced.

[0091] For example, Figure 5 FIG. 1 is a schematic diagram showing the structure of a mathematical model solving device provided in an embodiment of the present application. For example, the mathematical model solving device can be deployed on a cloud computing platform but is not limited to it. Figure 5 As shown, the mathematical model solving device 500 includes: an acquisition module 501 and a processing module 502. The acquisition module 501 is used to obtain the matrix of the linear equation group and the solution parameter recommendation request, and the solution parameter recommendation request is used to indicate the solution parameters that the user expects to recommend. The solution parameters that the user expects to recommend correspond to a parameter level, and the solution parameters that the user expects to recommend include: one or more of the pre-processing method, the iteration method, the parameters of the iteration method, the preprocessor, and the parameters of the preprocessor, wherein the solution parameters corresponding to the next parameter level in different parameter levels are the refinement of the solution parameters corresponding to the previous parameter level. The processing module 502 is used to input the matrix of the linear equation group into the parameter recommendation engine of the corresponding level according to the parameter level corresponding to the solution parameters that the user expects to recommend, so as to obtain the values ​​of the solution parameters that the user expects to recommend, wherein the parameter recommendation engine of the corresponding level is used to recommend the values ​​of the solution parameters of the parameter level where the solution parameters that the user expects to recommend are located. The processing module 502 is further used to solve the linear equation system based on the values ​​of the solution parameters that the user expects to recommend, and obtain the solution results of the linear equation system.

[0092] In some embodiments, the iterative method includes an iterative method cluster, and the preprocessing sub-cluster includes a preprocessing sub-cluster. Before inputting the matrix of the linear equation system to the parameter recommendation engine of the corresponding level to obtain the value of the solution parameter that the user expects to recommend, the processing module 502 is also used to: when the solution parameter recommendation request indicates that the user expects to recommend one or more of the preprocessing method, the iterative method cluster, and the preprocessing sub-cluster, use the first-level recommendation engine as the parameter recommendation engine of the corresponding level, wherein the first-level recommendation engine is used to recommend one or more of the preprocessing method, the iterative method cluster, and the preprocessing sub-cluster.

[0093] When the processing module 502 inputs the matrix into the parameter recommendation engine of the corresponding level to obtain the value of the solution parameter that the user expects to be recommended, it is specifically used to: input the matrix into the first-level recommendation engine to obtain one or more of the pre-processing method, iterative method cluster and pre-processing sub-cluster.

[0094] In some embodiments, the parameters of the iterative method include parameters of a sub-iterative method of the iterative method cluster, and the parameters of the preprocessor include parameters of a sub-preprocessor of the preprocessor cluster.

[0095] The acquisition module 501 is further used to: receive a parameter recommendation enhancement mode instruction, where the parameter recommendation enhancement mode instruction is used to instruct to start the parameter recommendation enhancement mode.

[0096] When the processing module 502 inputs the matrix of the linear equation group into the parameter recommendation engine of the corresponding level to obtain the values ​​of the solution parameters that the user expects to be recommended, it is specifically used to: when the parameter recommendation enhancement mode is turned on, the matrix, the iterative method and the preprocessor set by the user or recommended by the first-level recommendation engine are input into the third-level recommendation engine to obtain the values ​​of the solution parameters that the user expects to be recommended, wherein the third-level recommendation engine is used to recommend the parameters of the iterative method and / or the parameters of the preprocessor.

[0097] In some embodiments, before inputting the matrix into the parameter recommendation engine of the corresponding level, the processing module 502 is also used to: when the user desires to recommend a sub-iterative method in an iterative method cluster and / or a sub-preprocessor in a preprocessing subcluster, use the secondary recommendation engine as the parameter recommendation engine of the corresponding level, wherein the iterative method cluster and / or the preprocessing subcluster are specified by the user, and the secondary recommendation engine is used to recommend the sub-iterative method in the iterative method cluster and / or the sub-preprocessor in the preprocessing subcluster.

[0098] When the processing module 502 inputs the matrix of the linear equation system into the parameter recommendation engine of the corresponding level to obtain the values ​​of the solution parameters that the user expects to be recommended, it is specifically used to: input the matrix into the secondary recommendation engine to obtain the sub-iterative method in the iterative method cluster and / or the sub-preprocessing sub-cluster in the preprocessing sub-cluster.

[0099] The acquisition module 501 is further used to: receive a first parameter configuration instruction, where the first parameter configuration instruction is used to configure the iteration method cluster and / or the preprocessing sub-cluster.

[0100] In some embodiments, the parameters of the iterative method include parameters of a sub-iterative method of the iterative method cluster, and the parameters of the preprocessor include parameters of a sub-preprocessor of the preprocessor cluster.

[0101] The acquisition module 501 is further used to: receive a parameter recommendation enhancement mode instruction, where the parameter recommendation enhancement mode instruction is used to instruct to start the parameter recommendation enhancement mode.

[0102] When the processing module 502 inputs the matrix of the linear equation group into the parameter recommendation engine of the corresponding level to obtain the values ​​of the solution parameters that the user expects to be recommended, it is specifically used to: when the parameter recommendation enhancement mode is turned on, input the matrix, the sub-iterative method in the iterative method cluster and / or the sub-preprocessor in the preprocessing sub-cluster recommended by the secondary recommendation engine into the tertiary recommendation engine to obtain the solution parameters, wherein the tertiary recommendation engine is used to recommend the parameters of the iterative method and the parameters of the preprocessor.

[0103] In some embodiments, before inputting the matrix into the parameter recommendation engine of the corresponding level, the processing module 502 is also used to: when the user desires to recommend parameters of sub-iterative methods of the iterative method cluster and / or parameters of sub-preprocessors in the preprocessing subcluster, use the three-level recommendation engine as the parameter recommendation engine of the corresponding level, wherein the sub-iterative methods of the iterative method cluster and the sub-preprocessors in the preprocessing subcluster are specified by the user, and the three-level recommendation engine is used to recommend parameters of sub-iterative methods of the iterative method cluster and / or parameters of sub-preprocessors in the preprocessing subcluster.

[0104] The acquisition module 501 is further used to: receive a second parameter configuration instruction, where the second parameter configuration instruction is used to configure a sub-iterative method of the iterative method cluster and / or a sub-preprocessing sub-cluster in the preprocessing sub-cluster.

[0105] In some embodiments, the acquisition module 501 is further used to: receive a third parameter configuration instruction, where the third parameter configuration instruction is used to configure a first parameter of a sub-iteration method of an iterative method cluster and / or a second parameter of a sub-preprocessor in a preprocessing sub-cluster.

[0106] Before inputting the matrix into the parameter recommendation engine of the corresponding level, the processing module 502 is further used to: use the four-level recommendation engine as the parameter recommendation engine of the corresponding level, and the four-level recommendation engine is used to recommend sub-parameters of the first parameter and / or sub-parameters of the second parameter.

[0107] In some embodiments, when solving a system of linear equations based on the values ​​of solution parameters that a user expects to recommend, the processing module 502 is specifically used to: input the system of linear equations and the values ​​of solution parameters that a user expects to recommend into a numerical calculation solver; and solve the system of linear equations using the numerical calculation solver.

[0108] In some embodiments, the pre-processing method includes ordering or scaling, and the iterative method includes a Krylov subspace method.

[0109] In some embodiments, the parameter recommendation engine at the corresponding level is a neural network engine, wherein the value of the solution parameter that the user desires to recommend is inferred by the parameter recommendation engine based on the properties of the matrix of the linear equation system.

[0110] In some embodiments, Figure 5 The acquisition module 501 and the processing module 502 shown in the figure can be implemented by software or by hardware. For example, the implementation of the acquisition module 501 is described below by taking the acquisition module 501 as an example. Similarly, the implementation of the processing module 502 can refer to the implementation of the acquisition module 501.

[0111] As an example of a software functional unit, the acquisition module 501 may include code running on a computing instance. Among them, the computing instance may include at least one of a physical host (computing device), a virtual machine, and a container. Further, the above-mentioned computing instance may be one or more. For example, the acquisition module 501 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 code may be distributed in the same region (region) or in different regions. Furthermore, the multiple hosts / virtual machines / containers used to run the code may be distributed in the same availability zone (AZ) or in different AZs, each AZ including a data center or multiple data centers with similar geographical locations. Among them, usually a region may include multiple AZs.

[0112] 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 needs to be set up in each VPC to achieve interconnection between VPCs through the communication gateway.

[0113] As an example of a hardware functional unit, the acquisition module 501 may include at least one computing device, such as a server, etc. Alternatively, the acquisition module 501 may also be a device implemented using an application-specific integrated circuit (ASIC) or a programmable logic device (PLD). The PLD may be a complex programmable logical device (CPLD), a field-programmable gate array (FPGA), a generic array logic (GAL) or any combination thereof.

[0114] The multiple computing devices included in the acquisition module 501 can be distributed in the same region or in different regions. The multiple computing devices included in the acquisition module 501 can be distributed in the same AZ or in different AZs. Similarly, the multiple computing devices included in the acquisition module 501 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.

[0115] It should be noted that, in other embodiments, the acquisition module 501 can be used to execute any step in the mathematical model solving method described in the above embodiment, and the processing module 502 can also be used to execute any step in the mathematical model solving method described in the above embodiment. In addition, the acquisition module 501 can also be combined with the processing module 502 to be responsible for executing any step in the mathematical model solving method described in the above embodiment. In addition, the steps that the acquisition module 501 and the processing module 502 are responsible for implementing can also be specified as needed, and the acquisition module 501 and the processing module 502 can respectively implement different steps in the mathematical model solving method described in the above embodiment to achieve Figure 5 The overall functionality of the mathematical model solving device 500 is shown.

[0116] The present application also provides a computing device 600. Figure 6 As shown, computing device 600 includes: bus 602, processor 604, memory 606 and communication interface 608. Processor 604, memory 606 and communication interface 608 communicate through bus 602. Computing device 600 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 computing device 600.

[0117] The bus 602 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, Figure 6 The bus 604 is represented by only one line, but does not mean that there is only one bus or one type of bus. The bus 604 may include a path for transmitting information between various components of the computing device 600 (eg, the memory 606, the processor 604, and the communication interface 608).

[0118] The processor 604 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).

[0119] The memory 606 may include a volatile memory, such as a random access memory (RAM). The processor 604 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).

[0120] The memory 606 stores executable program codes, and the processor 604 executes the executable program codes to respectively implement the aforementioned Figure 5 The functions of the acquisition module 501 and the processing module 502 shown in the embodiment are implemented to realize the mathematical model solving method described in the above embodiment. That is, the memory 606 stores instructions for executing the mathematical model solving method described in the above embodiment.

[0121] Alternatively, the memory 606 stores executable codes, and the processor 604 executes the executable codes to respectively implement the aforementioned Figure 5 The functions of the mathematical model solving device 500 shown in the figure are implemented to realize the mathematical model solving method described in the above embodiment. That is, the memory 606 stores instructions for executing the mathematical model solving method described in the above embodiment.

[0122] The communication interface 603 uses a transceiver module such as, but not limited to, a network interface card or a transceiver to implement communication between the computing device 600 and other devices or a communication network.

[0123] 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.

[0124] like Figure 7 As shown, the computing device cluster includes at least one computing device 600. The memory 606 in one or more computing devices 600 in the computing device cluster may store the same instructions for executing the mathematical model solving method described in the above embodiment.

[0125] In some possible implementations, the memory 606 of one or more computing devices 600 in the computing device cluster may also store some instructions for executing the mathematical model solving method described in the above embodiment. In other words, the combination of one or more computing devices 600 can jointly execute the instructions for executing the mathematical model solving method described in the above embodiment.

[0126] It should be noted that the memory 606 in different computing devices 600 in the computing device cluster may store different instructions, which are respectively used to execute the aforementioned Figure 7 Part of the functions of the mathematical model solving device 700 shown. That is, the instructions stored in the memory 606 in different computing devices 600 can implement the functions of one or more modules in the acquisition module 501 and the processing module 502.

[0127] 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. Figure 8 A possible implementation is shown. Figure 8 As shown, two computing devices 600A and 600B are connected via a network. Specifically, the network is connected via a communication interface in each computing device. In this type of possible implementation, the memory 606 in the computing device 600A stores instructions for executing the functions of the acquisition module 501. At the same time, the memory 606 in the computing device 600B stores instructions for executing the functions of the processing module 502.

[0128] It should be understood that Figure 8The functions of the computing device 600A shown in FIG. 6A may also be completed by multiple computing devices 600. Similarly, the functions of the computing device 600B may also be completed by multiple computing devices 600.

[0129] 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 Figure 7 and Figure 8 The connection mode of the computing device cluster is different in that the memory 606 in one or more computing devices 600 in the computing device cluster may store the same instructions for executing the method in the above embodiment.

[0130] In some possible implementations, the memory 606 of one or more computing devices 600 in the computing device cluster may also store partial instructions for executing the aforementioned mathematical model solving method. In other words, the combination of one or more computing devices 600 may jointly execute instructions for executing the aforementioned mathematical model solving method.

[0131] Based on the method in the above embodiment, the embodiment of the present application provides a computer-readable storage medium, including computer program instructions. When the computer program instructions are executed by a computing device, the computing device executes the method in the above embodiment; or, when the computer program instructions are executed by a computing device cluster, the computing device cluster executes the method in the above embodiment. Exemplarily, the computer-readable storage medium can be any available medium that can be stored by a computing device or a data storage device such as a data center that includes 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), etc.

[0132] Based on the method in the above embodiment, an embodiment of the present application provides a computer program product containing instructions, which, when executed by a computing device, enables the computing device to execute the method in the above embodiment, or, when executed by a computing device cluster, enables the computing device cluster to execute the method in the above embodiment.

[0133] It is understood that the processor in the embodiments of the present application may be a central processing unit (CPU), or other general-purpose processors, digital signal processors (DSP), application specific integrated circuits (ASIC), field programmable gate arrays (FPGA) or other programmable logic devices, transistor logic devices, hardware components or any combination thereof. The general-purpose processor may be a microprocessor or any conventional processor.

[0134] The method steps in the embodiments of the present application can be implemented by hardware or by a processor executing software instructions. The software instructions can be composed of corresponding software modules, and the software modules can be stored in random access memory (RAM), flash memory, read-only memory (ROM), programmable read-only memory (PROM), erasable programmable read-only memory (EPROM), electrically erasable programmable read-only memory (EEPROM), registers, hard disks, mobile hard disks, CD-ROMs, or any other form of storage medium known in the art. An exemplary storage medium is coupled to the processor so that the processor can read information from the storage medium and write information to the storage medium. Of course, the storage medium can also be a component of the processor. The processor and the storage medium can be located in an ASIC.

[0135] In the above embodiments, it can be implemented in whole or in part by software, hardware, firmware or any combination thereof. When implemented using software, it can be implemented in whole or in part in the form of a computer program product. The computer program product includes one or more computer instructions. When the computer program instructions are loaded and executed on a computer, the process or function described in the embodiment of the present application is generated in whole or in part. The computer may be a general-purpose computer, a special-purpose computer, a computer network, or other programmable device. The computer instructions may be stored in a computer-readable storage medium or transmitted through the computer-readable storage medium. The computer instructions may be transmitted from a website site, computer, server or data center to another website site, computer, server or data center by wired (e.g., coaxial cable, optical fiber, digital subscriber line (DSL)) or wireless (e.g., infrared, wireless, microwave, etc.) means. The computer-readable storage medium may be any available medium that a computer can access or a data storage device such as a server or data center that includes one or more available media integrated. The available medium may 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 disk (SSD)), etc.

[0136] It should be understood that the various numerical numbers involved in the embodiments of the present application are only used for the convenience of description and are not used to limit the scope of the embodiments of the present application.

[0137] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present application, rather than to limit it. Although the present application has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the aforementioned embodiments, or make equivalent replacements for some of the technical features therein. However, these modifications or replacements do not cause the essence of the corresponding technical solutions to deviate from the protection scope of the technical solutions of the embodiments of the present application.

Claims

1. A mathematical model solving method, characterized in that: The method comprises: Obtaining a matrix and a solution parameter recommendation request for a linear equation system, wherein the solution parameter recommendation request is used to indicate a solution parameter that a user expects to be recommended, wherein the solution parameter that a user expects to be recommended corresponds to a parameter level, and the solution parameter that a user expects to be recommended includes: one or more of a pre-processing method, an iteration method, a parameter of an iteration method, a pre-processor, and a parameter of a pre-processor, wherein the solution parameter corresponding to a next parameter level in different parameter levels is a refinement of the solution parameter corresponding to a previous parameter level; According to the parameter level corresponding to the solution parameter that the user expects to be recommended, the matrix of the linear equation group is input into the parameter recommendation engine of the corresponding level to obtain the value of the solution parameter that the user expects to be recommended, wherein the parameter recommendation engine of the corresponding level is used to recommend the value of the solution parameter of the parameter level where the solution parameter that the user expects to be recommended is located; The linear equation group is solved based on the values ​​of the solution parameters that the user expects to recommend, and a solution result of the linear equation group is obtained.

2. The method according to claim 1, characterized in that The iterative method includes an iterative method cluster, the preprocessing sub includes a preprocessing sub cluster, and before inputting the matrix of the linear equation group into a parameter recommendation engine of a corresponding level to obtain the value of the solution parameter that the user expects to recommend, the method includes: In the case where the solution parameter recommendation request indicates that the user desires to recommend one or more of the pre-processing method, the iterative method cluster, and the pre-processing sub-cluster, using a first-level recommendation engine as the parameter recommendation engine of the corresponding level, wherein the first-level recommendation engine is used to recommend one or more of the pre-processing method, the iterative method cluster, and the pre-processing sub-cluster; The step of inputting the matrix into a parameter recommendation engine at a corresponding level to obtain the values ​​of the solution parameters that the user desires to recommend includes: The matrix is ​​input into the primary recommendation engine to obtain one or more of the pre-processing method, the iterative method cluster and the pre-processing sub-cluster.

3. The method according to claim 2, characterized in that The parameters of the iterative method include the parameters of the sub-iterative method of the iterative method cluster, the parameters of the preprocessor include the parameters of the sub-preprocessor of the preprocessor cluster, and the method further includes: receiving a parameter recommendation enhanced mode instruction, wherein the parameter recommendation enhanced mode instruction is used to instruct to enable the parameter recommendation enhanced mode; The step of inputting the matrix of the linear equation group into a parameter recommendation engine at a corresponding level to obtain the values ​​of the solution parameters that the user desires to recommend further includes: When the parameter recommendation enhancement mode is turned on, the matrix, the iterative method and the preprocessor set by the user or recommended by the first-level recommendation engine are input into the third-level recommendation engine to obtain the values ​​of the solution parameters that the user expects to be recommended, wherein the third-level recommendation engine is used to recommend the parameters of the iterative method and / or the parameters of the preprocessor.

4. The method according to any one of claims 1 to 3, characterized in that: Before inputting the matrix into the parameter recommendation engine of the corresponding level, the method includes: In the case where the user desires to recommend a sub-iterative method in an iterative method cluster and / or a sub-preprocessor in a preprocessing sub-cluster, using a secondary recommendation engine as a parameter recommendation engine at the corresponding level, wherein the iterative method cluster and / or the preprocessing sub-cluster are specified by the user, and the secondary recommendation engine is used to recommend the sub-iterative method in the iterative method cluster and / or the sub-preprocessor in the preprocessing sub-cluster; The step of inputting the matrix of the linear equation group into a parameter recommendation engine at a corresponding level to obtain the values ​​of the solution parameters that the user desires to recommend includes: Inputting the matrix into the secondary recommendation engine to obtain the sub-iterative method in the iterative method cluster and / or the sub-preprocessing sub-cluster in the preprocessing sub-cluster; The method further comprises: A first parameter configuration instruction is received, where the first parameter configuration instruction is used to configure an iteration cluster and / or a preprocessing sub-cluster.

5. The method according to claim 4, characterized in that The parameters of the iterative method include the parameters of the sub-iterative method of the iterative method cluster, the parameters of the preprocessor include the parameters of the sub-preprocessor of the preprocessor cluster, and the method further includes: receiving a parameter recommendation enhanced mode instruction, wherein the parameter recommendation enhanced mode instruction is used to instruct to enable the parameter recommendation enhanced mode; The step of inputting the matrix of the linear equation group into a parameter recommendation engine at a corresponding level to obtain the values ​​of the solution parameters that the user desires to recommend further includes: When the parameter recommendation enhancement mode is turned on, the matrix, the sub-iterative method in the iterative method cluster and / or the sub-preprocessor in the preprocessing subcluster recommended by the secondary recommendation engine are input into the tertiary recommendation engine to obtain the solution parameters, wherein the tertiary recommendation engine is used to recommend the parameters of the iterative method and the parameters of the preprocessor.

6. The method according to any one of claims 1 to 5, characterized in that: Before inputting the matrix into the parameter recommendation engine of the corresponding level, the method includes: In the case where the user desires to recommend parameters of the sub-iterative methods of the iterative method cluster and / or parameters of the sub-preprocessors in the preprocessing sub-cluster, a three-level recommendation engine is used as the parameter recommendation engine of the corresponding level, wherein the sub-iterative methods of the iterative method cluster and the sub-preprocessors in the preprocessing sub-cluster are specified by the user, and the three-level recommendation engine is used to recommend parameters of the sub-iterative methods of the iterative method cluster and / or parameters of the sub-preprocessors in the preprocessing sub-cluster; The method further comprises: A second parameter configuration instruction is received, where the second parameter configuration instruction is used to configure a sub-iterative method in the iterative method cluster and / or a sub-preprocessor in the preprocessor sub-cluster.

7. The method according to any one of claims 1 to 6, characterized in that: The method further comprises: receiving a third parameter configuration instruction, wherein the third parameter configuration instruction is used to configure a first parameter of a sub-iteration method of the iterative method cluster and / or a second parameter of a sub-preprocessor in the preprocessing sub-cluster; Before inputting the matrix into the parameter recommendation engine of the corresponding level, the method includes: A four-level recommendation engine is used as the parameter recommendation engine of the corresponding level, and the four-level recommendation engine is used to recommend sub-parameters of the first parameter and / or sub-parameters of the second parameter.

8. The method according to any one of claims 1 to 7, characterized in that: The step of solving the linear equations based on the values ​​of the solution parameters that the user expects to recommend includes: Inputting the linear equation system and the values ​​of the solution parameters that the user desires to recommend into a numerical calculation solver; The linear equations are solved using the numerical solver.

9. The method according to any one of claims 1 to 8, characterized in that: The pre-processing method includes ordering or scaling, and the iterative method includes the Krylov subspace method.

10. The method according to any one of claims 1 to 9, characterized in that: The parameter recommendation engine of the corresponding level is a neural network engine, wherein the value of the solution parameter that the user expects to be recommended is inferred by the parameter recommendation engine based on the properties of the matrix of the linear equations.

11. A mathematical model solving device, characterized in that: include: An acquisition module is used to acquire a matrix of a linear equation system and a solution parameter recommendation request, wherein the solution parameter recommendation request is used to indicate a solution parameter that a user expects to be recommended, and the solution parameter that the user expects to be recommended corresponds to a parameter level, and the solution parameter that the user expects to be recommended includes: one or more of a pre-processing method, an iteration method, a parameter of an iteration method, a preprocessor, and a parameter of a preprocessor, wherein the solution parameter corresponding to the next parameter level in different parameter levels is a refinement of the solution parameter corresponding to the previous parameter level; A processing module, configured to input the matrix of the linear equation group into a parameter recommendation engine of a corresponding level according to the parameter level corresponding to the solution parameter that the user expects to be recommended, so as to obtain the value of the solution parameter that the user expects to be recommended, wherein the parameter recommendation engine of the corresponding level is configured to recommend the value of the solution parameter of the parameter level where the solution parameter that the user expects to be recommended is located; The processing module is further used to solve the linear equation system based on the values ​​of the solution parameters that the user expects to recommend, so as to obtain the solution results of the linear equation system.

12. The device according to claim 11, characterized in that The iterative method includes an iterative method cluster, and the preprocessor includes a preprocessor cluster; Before inputting the matrix of the linear equation group into the parameter recommendation engine of the corresponding level to obtain the value of the solution parameter that the user expects to be recommended, the processing module is further used to: In the case where the solution parameter recommendation request indicates that the user desires to recommend one or more of the pre-processing method, the iterative method cluster, and the pre-processing sub-cluster, using a first-level recommendation engine as the parameter recommendation engine of the corresponding level, wherein the first-level recommendation engine is used to recommend one or more of the pre-processing method, the iterative method cluster, and the pre-processing sub-cluster; When the processing module inputs the matrix into the parameter recommendation engine of the corresponding level to obtain the value of the solution parameter that the user expects to be recommended, it is specifically used to: The matrix is ​​input into the primary recommendation engine to obtain one or more of the pre-processing method, the iterative method cluster and the pre-processing sub-cluster.

13. The device according to claim 12, characterized in that The parameters of the iterative method include the parameters of the sub-iterative method of the iterative method cluster, and the parameters of the preprocessor include the parameters of the sub-preprocessor of the preprocessor sub-cluster; The acquisition module is further used to: receive a parameter recommendation enhancement mode instruction, where the parameter recommendation enhancement mode instruction is used to instruct to turn on the parameter recommendation enhancement mode; When the processing module inputs the matrix of the linear equation group into the parameter recommendation engine of the corresponding level to obtain the value of the solution parameter that the user expects to be recommended, it is specifically used to: When the parameter recommendation enhancement mode is turned on, the matrix, the iterative method and the preprocessor set by the user or recommended by the first-level recommendation engine are input into the third-level recommendation engine to obtain the values ​​of the solution parameters that the user expects to be recommended, wherein the third-level recommendation engine is used to recommend the parameters of the iterative method and / or the parameters of the preprocessor.

14. The device according to any one of claims 11 to 13, characterized in that: Before inputting the matrix into the parameter recommendation engine at the corresponding level, the processing module is further configured to: In the case where the user desires to recommend a sub-iterative method in an iterative method cluster and / or a sub-preprocessor in a preprocessing sub-cluster, using a secondary recommendation engine as a parameter recommendation engine at the corresponding level, wherein the iterative method cluster and / or the preprocessing sub-cluster are specified by the user, and the secondary recommendation engine is used to recommend the sub-iterative method in the iterative method cluster and / or the sub-preprocessor in the preprocessing sub-cluster; When the processing module inputs the matrix of the linear equation group into the parameter recommendation engine of the corresponding level to obtain the value of the solution parameter that the user expects to be recommended, it is specifically used to: Inputting the matrix into the secondary recommendation engine to obtain the sub-iterative method in the iterative method cluster and / or the sub-preprocessing sub-cluster in the preprocessing sub-cluster; The acquisition module is further used for: A first parameter configuration instruction is received, where the first parameter configuration instruction is used to configure an iteration cluster and / or a preprocessing sub-cluster.

15. The device according to claim 14, characterized in that The parameters of the iterative method include the parameters of the sub-iterative method of the iterative method cluster, and the parameters of the preprocessor include the parameters of the sub-preprocessor of the preprocessor sub-cluster; The acquisition module is further used for: receiving a parameter recommendation enhanced mode instruction, wherein the parameter recommendation enhanced mode instruction is used to instruct to enable the parameter recommendation enhanced mode; When the processing module inputs the matrix of the linear equation group into the parameter recommendation engine of the corresponding level to obtain the value of the solution parameter that the user expects to be recommended, it is specifically used to: When the parameter recommendation enhancement mode is turned on, the matrix, the sub-iterative method in the iterative method cluster and / or the sub-preprocessor in the preprocessing subcluster recommended by the secondary recommendation engine are input into the tertiary recommendation engine to obtain the solution parameters, wherein the tertiary recommendation engine is used to recommend the parameters of the iterative method and the parameters of the preprocessor.

16. The device according to any one of claims 11 to 15, characterized in that: Before inputting the matrix into the parameter recommendation engine at the corresponding level, the processing module is further configured to: In the case where the user desires to recommend parameters of the sub-iterative methods of the iterative method cluster and / or parameters of the sub-preprocessors in the preprocessing sub-cluster, a three-level recommendation engine is used as the parameter recommendation engine of the corresponding level, wherein the sub-iterative methods of the iterative method cluster and the sub-preprocessors in the preprocessing sub-cluster are specified by the user, and the three-level recommendation engine is used to recommend parameters of the sub-iterative methods of the iterative method cluster and / or parameters of the sub-preprocessors in the preprocessing sub-cluster; The acquisition module is further used for: A second parameter configuration instruction is received, where the second parameter configuration instruction is used to configure a sub-iterative method in the iterative method cluster and / or a sub-preprocessor in the preprocessor sub-cluster.

17. The device according to any one of claims 11 to 16, characterized in that: The acquisition module is further used to: receive a third parameter configuration instruction, wherein the third parameter configuration instruction is used to configure a first parameter of a sub-iteration method of the iterative method cluster and / or a second parameter of a sub-preprocessor in the preprocessing sub-cluster; Before inputting the matrix into the parameter recommendation engine of the corresponding level, the processing module is also used to: use the four-level recommendation engine as the parameter recommendation engine of the corresponding level, and the four-level recommendation engine is used to recommend sub-parameters of the first parameter and / or sub-parameters of the second parameter.

18. The device according to any one of claims 11 to 17, characterized in that: When solving the linear equation system based on the values ​​of the solution parameters that the user expects to recommend, the processing module is specifically used to: Inputting the linear equation system and the values ​​of the solution parameters that the user desires to recommend into a numerical calculation solver; The linear equations are solved using the numerical solver.

19. The device according to any one of claims 11 to 18, characterized in that: The pre-processing method includes ordering or scaling, and the iterative method includes the Krylov subspace method.

20. The device according to any one of claims 11 to 19, characterized in that: The parameter recommendation engine of the corresponding level is a neural network engine, wherein the value of the solution parameter that the user expects to be recommended is inferred by the parameter recommendation engine based on the properties of the matrix of the linear equations.

21. 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 1-10.

22. A computer-readable storage medium, characterized in that: The method comprises computer program instructions, and when the instructions are executed by a computing device cluster, the computing device cluster enables the computing device cluster to perform the method according to any one of claims 1 to 10, wherein the computing device cluster comprises at least one computing device.

23. A computer program product comprising instructions, characterized in that When the instructions are executed by a computing device cluster, the computing device cluster executes the method according to any one of claims 1 to 10, wherein the computing device cluster includes at least one computing device.

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