Mathematical model solving method and apparatus, and computing device cluster

Abstract

A mathematical model solving method, comprising: acquiring a matrix of a system of linear equations and a solving parameter recommendation request, wherein the solving parameter recommendation request is used for indicating a solving parameter expected to be recommended for a user, the solving parameter expected to be recommended for the user corresponds to one parameter level, and a solving parameter corresponding to the next parameter level among different parameter levels is the refinement of a solving parameter corresponding to the previous parameter level; on the basis of the parameter level corresponding to the solving parameter expected to be recommended for the user, inputting the matrix of the system of linear equations into a corresponding level of parameter recommendation engine, to obtain the value of the solving parameter expected to be recommended for the user, wherein the corresponding level of parameter recommendation engine is used for recommending the value of a solving parameter of the parameter level where the solving parameter expected to be recommended for the user is located; and solving the system of linear equations on the basis of the value of the solving parameter expected to be recommended for the user, to obtain a solving result of the system of linear equations. According to the method, the parameter selection requirements of different users with a large knowledge span are met, and the solving efficiency is improved.

Description

A mathematical model solving method, device and computing device cluster Technical Field

[0001] The present application relates to the field of information technology (IT), and in particular to a mathematical model solving method, a database cluster, and a computing device cluster. Background Art

[0002] In the field of industrial simulation, computer-aided engineering (CAE) can be used to analyze the structural mechanical properties of complex projects and products using computer-aided solutions, as well as to optimize structural performance. When using CAE to numerically simulate real-world physical problems, the real-world physical problem can first be modeled using computer-aided design (CAD) software. The resulting model is then imported into the CAE software, where it is used to divide the geometric model into small finite elements or computational units for discrete calculations in numerical analysis. Next, boundary conditions are set in the CAE software, such as fixed points, loading points, applied external loads, constraints, and other physical conditions. The CAE software can then perform simulations using the boundary conditions and the resulting finite elements or computational units to obtain a set of linear equations for the mathematical model. Finally, the resulting linear equations are numerically solved using the CAE software, and the simulation results are obtained from the solution.

[0003] Generally, in the linear equations obtained by CAE software simulation, the matrix obtained by integrating the 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 meeting 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 so as to solve them using the optimal parameters is a technical problem that needs to be solved urgently.

[0004] 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 use the value of the optimal parameter to solve the problem.

[0006] In the 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 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: a pre-processing method, an iteration method, parameters 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 the parameter recommendation engine of the 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 the 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 one possible implementation, 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 group into the parameter recommendation engine of the corresponding level to obtain the values ​​of the solution parameters that the user expects to recommend, the method further 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, inputting the matrix into the parameter recommendation engine of the corresponding level to obtain the values ​​of the solution parameters that the user expects to recommend includes: 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 values ​​of the solution parameters for the user.

[0009] In one 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 be recommended. The method 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. 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 to the user.

[0010] In one possible implementation, before inputting the matrix into the parameter recommendation engine of the corresponding level, the method further includes: when the user desires to recommend a sub-iterative method in the iterative method cluster and / or a 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 system into the parameter recommendation engine of the 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-preprocessor in the preprocessing sub-cluster. In addition, the method further includes: receiving a first parameter configuration instruction, the first parameter configuration instruction being 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 appropriate solution parameter values ​​to 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 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 be recommended. It also 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 preprocessor cluster 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. In this way, the secondary recommendation engine and the tertiary recommendation engine can be combined to recommend better values ​​of the solution parameters to the user.

[0012] In one possible implementation, before inputting the matrix into the parameter recommendation engine of the corresponding level, the method includes: when the user desires to recommend parameters of the sub-iterative method of the iterative method cluster and / or 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 parameters of the sub-iterative method of the iterative method cluster and / or 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 ​​to the user.

[0013] In one possible implementation, the method further includes receiving a third parameter configuration instruction, the third parameter configuration instruction being used to configure a first parameter of a sub-iterative method in the iterative method cluster and / or a second parameter of a sub-preprocessing sub-cluster in the preprocessing sub-cluster. In this case, before inputting the matrix into the parameter recommendation engine at the corresponding level, the method includes using a four-level recommendation engine as the parameter recommendation engine at the corresponding level, the four-level recommendation engine being used to recommend sub-parameters of the first parameter and / or sub-parameters of the second parameter. In this way, the four-level recommendation engine can be used to recommend appropriate solution parameter values ​​for the user.

[0014] In one possible implementation, solving a system of linear equations based on the values ​​of the solution parameters that a user expects to recommend includes: inputting the system of linear equations and the values ​​of the solution parameters that the 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, comprising: an acquisition module and a processing module. The acquisition module is used to obtain a matrix of a linear equation system and a solution parameter recommendation request, the solution parameter recommendation request is used to indicate the solution parameters that the 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: one or more of: a pre-processing method, an iterative method, parameters of the iterative method, a preprocessor, and parameters of the preprocessor, wherein 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. The processing module is used to input the matrix of the linear equation system into a 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. The processing module is also used to solve the linear equation system based on the values ​​of the solution parameters that the user expects to be recommended, and obtain a solution result for the linear equation system.

[0018] In one possible implementation, 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 into the parameter recommendation engine of the corresponding level to obtain the values ​​of the solution parameters that the user desires to be recommended, the processing module is further configured to: if the solution parameter recommendation request indicates that the user desires 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 configured 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 iterative method include parameters of sub-iterative methods in the iterative method cluster, and the parameters of the preprocessor include parameters of sub-preprocessors in 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 turn on 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 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 iterative method cluster and / or the preprocessing sub-cluster.

[0026] In a possible implementation, the parameters of the iterative method include parameters of sub-iterative methods in the iterative method cluster, and the parameters of the preprocessor include parameters of sub-preprocessors in 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 turn on 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, the matrix, the sub-iterative method in the iterative method cluster recommended by the secondary recommendation engine and / or the sub-preprocessor in the preprocessing subcluster 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.

[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 the sub-iterative methods of the iterative method cluster and / or parameters of the 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 the sub-iterative methods of the iterative method cluster and / or parameters of the 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 the sub-iterative method of the iterative method cluster and / or the sub-preprocessing sub-cluster in the preprocessing sub-cluster.

[0031] In a possible implementation, the acquisition module is further configured to: receive a third parameter configuration instruction, where the third parameter configuration instruction is used to configure a first parameter of a sub-iterative 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 the 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 the user expects to recommend into a numerical calculation solver; and use the numerical calculation solver to solve the system of linear equations.

[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 comprising computer program instructions. When the computer program instructions are executed by a computing device cluster, the computing device cluster performs the method described in the first aspect or any possible implementation of the first aspect. For example, the computing device cluster may include one or more computing devices.

[0038] In a fifth aspect, the present application provides a computer program product comprising instructions that, when executed by a computing device cluster, cause the computing device cluster to perform the method described in the first aspect or any possible implementation of the first aspect. For example, 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] FIG1 is a schematic diagram of the architecture of a mathematical model solving system provided in an embodiment of the present application;

[0041] FIG2 is a schematic diagram of an interaction between a tenant and a cloud computing platform provided in an embodiment of the present application;

[0042] FIG3 is a flow chart of a mathematical model solving method provided in an embodiment of the present application;

[0043] FIG4 is a schematic diagram of a parameter recommendation process provided by an embodiment of the present application;

[0044] FIG5 is a schematic structural diagram of a mathematical model solving device provided in an embodiment of the present application;

[0045] FIG6 is a schematic diagram of the structure of a computing device provided in an embodiment of the present application;

[0046] FIG7 is a schematic diagram of the structure of a computing device cluster provided in an embodiment of the present application;

[0047] FIG8 is a schematic diagram of the structure of another computing device cluster provided in an embodiment of the present application. DETAILED DESCRIPTION

[0048] The term "and / or" as used herein describes an association between related objects, indicating that three possible relationships exist. For example, "A and / or B" can represent: A exists alone, A and B exist simultaneously, or B exists alone. The symbol " / " as used herein indicates that the related objects are in an "or" relationship, for example, A / B means either A or B.

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

[0050] In the embodiments of this 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 this application should not be interpreted as being preferred or advantageous over other embodiments or designs. Rather, the use of words such as "exemplary" or "for example" is intended to present the relevant concepts in a concrete manner.

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

[0052] Generally, a manually selected solver can be used to solve the linear equations obtained by simulating the mathematical model through CAE software to obtain the solution. At this time, the user needs to export the linear equations obtained by simulation. Then, using numerical calculation software, manually selected iterative methods, preprocessors and parameters corresponding to various algorithms, the linear equations are processed to obtain the solution. Finally, the solution is imported into the CAE software, and the CAE software processes the solution 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. This system can automatically select the values ​​of the user's desired solution parameters based on the matrix of the linear equation system 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 system, thereby meeting the parameter selection needs of different users with a wide range of knowledge and improving the solution efficiency of the solver. Optionally, when the linear equation system is simulated by CAE simulation software, the mathematical model solving system provided by this application improves the efficiency of CAE simulation.

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

[0055] The CAE simulation service 110 is a computer simulation and analysis solution that can be used to predict and evaluate the behavior and performance of products, components, or systems under different conditions. Users can request access to the CAE simulation service 110. When a user requests access to the CAE simulation service 110, they import the geometric model generated through CAD modeling into the CAE simulation service 110 through the user interface provided by the CAE simulation service 110. Based on the nature of the problem and the simulation type, they select the mesh type and set boundary conditions. Furthermore, within the user interface, the user can choose whether to use the parameter recommendation service and which level of solution parameters to recommend. In this embodiment, the parameter hierarchy can be, but is not limited to, four levels. Users can choose to recommend first-level, second-level, third-level, or fourth-level solution parameters, or they can select default solution parameters. As the level of recommended solution parameters increases, the granularity of the recommended solution parameters decreases, with fourth-level solution parameters being the finest and first-level solution parameters being the coarsest. The solution parameters may include one or more of: a pre-processing method, an iterative method, parameters of the iterative method, a pre-processor, and parameters of the pre-processor.

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

[0057] Numerical Computing Solver Service 120 provides numerical computing and simulation solving capabilities. After receiving a numerical computing request from CAE Simulation Service 110, if the user chooses to use the parameter recommendation service, Numerical Computing Solver Service 120 can send a solution parameter recommendation request to Multi-Level Parameter Tuning Service 130, invoking Multi-Level Parameter Tuning Service 130 to recommend optimal solution parameter values. The solution parameter recommendation request can indicate the solution parameters that the user desires to be recommended.

[0058] It is understandable that in other embodiments provided in the present application, users can also complete the settings of numerical calculations or 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 optimal parameter recommendation capabilities. After receiving a solution parameter recommendation request, the multi-level parameter tuning service 130 can input the matrix of the linear equation system of the mathematical model into the parameter recommendation engine at the corresponding parameter level, based on the parameter level corresponding to the solution parameter the user desires to recommend, to obtain the values ​​of the solution parameters the user desires to recommend. The parameter recommendation engine at the corresponding level is primarily used to recommend the values ​​of the solution parameters for the parameter level containing the solution parameters the user desires to recommend. The solution parameter values ​​can include one or more of the following: the name of the preprocessing method, the name of the iterative method, the name of the preprocessor, the parameters of the iterative method, the parameters of the preprocessor, or the subparameters contained in the parameters of the preprocessor. After obtaining the optimal solution parameter values, the multi-level parameter tuning service 130 can send a solution calculation request to the iterative solution service 140, invoking the iterative solution service 140 for solution. For example, the solution calculation request can include the values ​​of the solution parameters and the matrix of the linear equation system of the mathematical model to be solved.

[0060] Iterative solution service 140 is a service that uses iterative methods to perform solution calculations. After receiving a solution calculation request, iterative solution service 140 can solve the linear equations of the mathematical model based on the values ​​of the solution parameters recommended by the user to obtain a solution result for the linear equations.

[0061] In addition, after obtaining a solution result, the iterative solution service 140 may transmit the solution result to the numerical solution service 120. The numerical solution service 120 may then transmit the solution result to the CAE simulation service 110. Finally, the CAE simulation service 110 may use the solution result to perform simulation calculations to obtain simulation results, and present the simulation results to the user.

[0062] The above is an introduction to the mathematical model solving system 100 provided in an embodiment of the present application. Among them, the services included in the above-mentioned mathematical model solving system 100 can all be configured on a 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 on at least one server. The specific details can be determined according to the actual situation and are 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 services related to CAE simulation 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 shown in Figure 2, the interaction between tenants and the cloud computing platform mainly includes: tenants log in to the cloud computing platform 200 through the client webpage, select and purchase cloud services related to CAE simulation (i.e., services related to CAE simulation) in the cloud computing platform 200. After 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 located 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 tenants purchase and use services related to CAE simulation, they mainly pay for the resources used. In other embodiments provided in this application, tenants can also select or purchase other numerical calculation solution services including parameter recommendation services in the cloud computing platform 200, enter information related to the system of linear equations on the configuration interface provided by the service, and call the parameter recommendation service and numerical calculation solution service to solve them. 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 on the cloud computing platform 200, after using CAE simulation-related services, the tenant can use the configuration interface provided by the cloud computing platform 200 or the interface for interacting with the tenant to complete the import of the geometric model, select the mesh type, and set boundary conditions based on the nature of the problem and the simulation type. Furthermore, the tenant can also use the configuration interface provided by the cloud computing platform 200 or the interface for interacting with the tenant to complete the settings such as whether to use the parameter recommendation service and which level of solution parameters to recommend. Once the tenant completes the settings, the cloud computing platform 200 can perform simulation calculations according to the tenant's 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 services provided by the cloud computing platform 200 through the CAE simulation service 110. After the CAE simulation service 110 calls the services provided by the cloud computing platform 200, the cloud computing platform 200 can perform parameter recommendations, numerical calculations, etc. to obtain the solution results, and then return the solution results 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, as well as 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] Exemplarily, FIG3 shows a flow chart of a mathematical model solving method provided by an embodiment of the present application. It is understood that the method can be executed by any device, equipment, platform, or device cluster with computing and processing capabilities. For example, it can be executed by the cloud computing platform 200 described in FIG2 above. For ease of description, the following description is based on the cloud computing platform 200 as the execution entity. Of course, the cloud computing platform can also be replaced by other execution entities, and the replaced solution is still within the scope of protection of this application. As shown in FIG3, the mathematical model solving method may include the following steps:

[0067] S301. The cloud computing platform obtains the matrix of the linear equation group and a solution parameter recommendation request. The solution parameter recommendation request is used to indicate the solution parameters that the user expects to be recommended. The solution parameters that the user expects to be recommended correspond to a parameter level. The solution parameters that the user expects to be recommended include: one or more of: a pre-processing method, an iterative method, parameters of the iterative method, a preprocessor, and parameters of the preprocessor. Among them, 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, iterative method, parameters of the iterative method, preprocessor, parameters of the 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. The client associated with the cloud computing platform can be a desktop application, a mobile application, a web application, or a web-based application, etc. 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 desires to recommend 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 that 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 be recommended. Then, the cloud computing platform can input the matrix of the linear equation system 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 equation system to obtain the values ​​of the solution parameters that the user expects to be recommended. For example, the name of the pre-processing method, the name of the iterative method, the name of the preprocessor, the parameters of the iterative method, the parameters of the preprocessor, or the sub-parameters contained in the parameters of the preprocessor, etc. 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 be recommended are located.

[0072] As a possible implementation, a user can select the recommended solution parameters on a client associated with a cloud computing platform without selecting a pre-processing method, an iterative method cluster, or a pre-processing sub-cluster. This 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. For example, the pre-processing method may include ordering or scaling, the iterative method cluster may include the generalized minimal residual (GMRES) cluster, the biconjugate gradient (BiCG) cluster, and the pre-processing sub-cluster may include the incomplete lower-upper (ILU) cluster or the multigrid (MG) cluster. In this case, 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 a first-level recommendation engine as the parameter recommendation engine for 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 first-level recommendation engine, the cloud computing platform can input the matrix of the linear equation group into the first-level recommendation engine to obtain one or more of the pre-processing method, iterative method cluster and 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-iterative 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 turning on of the parameter recommendation enhancement mode. In this case (i.e., when the parameter recommendation enhancement mode is turned on), the cloud computing platform can input the matrix of the linear equation group, the iterative method and 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 be recommended. 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, more fine-grained solution parameter values ​​can be automatically recommended to the user, reducing the difficulty of solving the mathematical model and improving the user experience.

[0074] As another possible implementation, a user can select an iterative method cluster and / or a preprocessing subcluster on a client associated with a cloud computing platform. When a 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 sub-iterative methods of the iterative method cluster and / or sub-preprocessing subcluster of the preprocessing subcluster. For example, when a user selects the 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, which can be used to configure the iterative method cluster and / or preprocessing subcluster. After receiving the parameter configuration instruction, the cloud computing platform can configure the iterative method cluster and / or preprocessing subcluster selected by the user, and use a secondary recommendation engine as the parameter recommendation engine at the corresponding level. The secondary recommendation engine can be used to recommend sub-iterative methods in the iterative method cluster and / or sub-preprocessing subcluster in the 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 methods 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-iterative method of the iterative method cluster and / or the parameters of the sub-preprocessor of the preprocessing subcluster. 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 turning on of the parameter recommendation enhancement mode. In this case (i.e., when the parameter recommendation enhancement mode is turned on), the cloud computing platform can input the matrix of the linear equation group, the sub-iterative 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 subcluster into the third-level recommendation engine to obtain the values ​​of the solution parameters that the user expects to be recommended. 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, it can automatically recommend the values ​​of the solution parameters of more fine-grainedness to the user, reducing the difficulty of solving the mathematical model and improving the user experience.

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

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

[0080] 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 efficiency of CAE simulation.

[0081] The above is an introduction to the mathematical model solving method provided in this embodiment. To facilitate understanding, the following examples are given to illustrate.

[0082] For example, as shown in FIG4 , when the user chooses not to recommend solution parameters, the user can select a preprocessing method, an iterative method (e.g., Krylov subspace methods (KSP)), and a preconditioner (PC). Finally, the matrix of the linear system of equations can be solved using the preprocessing 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 the parameter recommendation engine, and at least the matrix of the linear system of equations can be 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 can be, but is not limited to, the name of the pre-processing method, iterative method and / or pre-processor. Finally, the obtained pre-processing method, iterative method and / or pre-processor can be used to solve the matrix of the linear system of equations. Exemplarily, when solving, the default parameter values ​​of the pre-processing method, iterative method and / or pre-processor can be used for solving, but are not limited to. 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 more fine-grained solution parameter values ​​through the third-level recommendation engine.

[0084] When the user chooses to recommend solution parameters, if the user has fixed the iterative method cluster and / or preprocessor cluster, such as the GMRES cluster, but has not fixed a specific iterative method and / or preprocessor, then the secondary recommendation engine can be used as the parameter recommendation engine, and at least the matrix of the linear system of equations can be input into the secondary parameter recommendation engine to obtain the iterative method and / or preprocessor under the specific cluster. Exemplarily, the output of the secondary parameter recommendation engine can be, but is not limited to, the name of the iterative method and / or preprocessor. Finally, the iterative method and / or preprocessor under the obtained specific cluster can be used to solve the matrix of the linear system of equations. Exemplarily, when solving, the default parameter values ​​of the iterative method and / or preprocessor used can be used for solving, but is not limited to. 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 more fine-grained solution parameter values ​​through the tertiary recommendation engine.

[0085] When a user selects 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, the three-level recommendation engine can be used as the parameter recommendation engine, and at least the matrix of the linear system of equations can be 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 a user selects recommended solution parameters, if the user has fixed a specific iterative method and / or preprocessor, and fixed the specific parameters of the iterative 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 can be input into the four-level parameter recommendation engine to obtain the sub-parameter values ​​included in the parameters of the specific iterative method and / or preprocessor. Finally, the sub-parameter values ​​included in the obtained parameter values ​​of the iterative 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, iterative method, and pre-processing sub-processor. When the user selects any one or two, the cloud computing platform can use the system default to solve the remaining one or two. For example, when the user only selects the recommended pre-processing method, but does not set the iterative method and pre-processing sub-processor by himself, the cloud computing platform can recommend the pre-processing method to 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] Furthermore, the granularity of the solution parameters recommended by the cloud computing platform to users during 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 two-level recommendation engine to recommend KSPs for a specific cluster and a three-level recommendation engine to recommend parameter values ​​for a specific PC.

[0089] It should be understood that the order of execution of the steps in the above embodiments does not necessarily imply a specific order of execution. The order of execution of each process should be determined by its function and inherent logic, and should not constitute any limitation on the implementation process of the embodiments of this application. In addition, the various embodiments described above can be combined according to actual circumstances, and the combined solutions are still within the scope of protection of this 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] Exemplarily, FIG5 shows a schematic structural diagram of a mathematical model solving device provided in an embodiment of the present application. Exemplarily, the mathematical model solving device can be, but is not limited to, deployed on a cloud computing platform. As shown in FIG5 , the mathematical model solving device 500 includes: an acquisition module 501 and a processing module 502. Among them, the acquisition module 501 is used to obtain the matrix of the linear equation system and a 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 iterative method, the parameters of the iterative 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. Processing module 502 is configured to input the matrix of the linear system of equations into a parameter recommendation engine at a corresponding level, based on the parameter level corresponding to the solution parameters desired by the user, to obtain the values ​​of the solution parameters desired by the user. The parameter recommendation engine at the corresponding level is configured to recommend the values ​​of the solution parameters for the parameter level corresponding to the solution parameters desired by the user. Processing module 502 is further configured to solve the linear system of equations based on the values ​​of the solution parameters desired by the user, to obtain a solution result for the linear system of equations.

[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 into the parameter recommendation engine of the corresponding level to obtain the values ​​of the solution parameters that the user desires to be recommended, the processing module 502 is further configured to: when the solution parameter recommendation request indicates that the user desires 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 configured 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 sub-iterative methods of the iterative method cluster, and the parameters of the preprocessor include parameters of sub-preprocessors of the preprocessor cluster.

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

[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 configured to receive a first parameter configuration instruction, where the first parameter configuration instruction is used to configure the iterative method cluster and / or the preprocessing sub-cluster.

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

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

[0103] In some embodiments, before inputting the matrix into the parameter recommendation engine of the corresponding level, the processing module 502 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.

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

[0105] In some embodiments, the acquisition module 501 is further configured to: receive a third parameter configuration instruction, where the third parameter configuration instruction is used to configure a first parameter of a sub-iterative method in 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 the solution parameters that the user expects to recommend, the processing module 502 is specifically used to: input the system of 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 system of linear equations.

[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, both acquisition module 501 and processing module 502 shown in FIG5 can be implemented via software or hardware. For example, the implementation of acquisition module 501 will be described below using acquisition module 501 as an example. Similarly, the implementation of processing module 502 can refer to the implementation of acquisition module 501.

[0111] As an example of a software functional unit, the acquisition module 501 may include code running on a computing instance. The computing instance may include at least one of a physical host (computing device), a virtual machine, and a container. Furthermore, the 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 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 one data center or multiple geographically close data centers. Typically, a region may include multiple AZs.

[0112] Similarly, multiple hosts / virtual machines / containers running the code can be distributed within the same virtual private cloud (VPC) or across multiple VPCs. Typically, a VPC is set up within a region. Cross-region communication between two VPCs within the same region, or between VPCs in different regions, requires a communication gateway within each VPC to interconnect the VPCs.

[0113] As an example of a hardware functional unit, the acquisition module 501 may include at least one computing device, such as a server. Alternatively, the acquisition module 501 may be 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 acquisition module 501 can be distributed in the same region or in different regions. The multiple computing devices included in acquisition module 501 can be distributed in the same AZ or in different AZs. Similarly, the multiple computing devices included in acquisition module 501 can be distributed in the same VPC or in multiple VPCs. The multiple computing devices can be any combination of servers, ASICs, PLDs, CPLDs, FPGAs, GALs, and other computing devices.

[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. By respectively implementing different steps in the mathematical model solving method described in the above embodiment by the acquisition module 501 and the processing module 502, all the functions of the mathematical model solving device 500 shown in Figure 5 can be realized.

[0116] This application also provides a computing device 600. As shown in Figure 6, computing device 600 includes a bus 602, a processor 604, a memory 606, and a communication interface 608. Processor 604, memory 606, and communication interface 608 communicate with each other via bus 602. Computing device 600 can be a server or a terminal device. It should be understood that this application does not limit the number of processors and memories in computing device 600.

[0117] Bus 602 may be a Peripheral Component Interconnect (PCI) bus or an Extended Industry Standard Architecture (EISA) bus, among others. Buses may be classified as address buses, data buses, control buses, and the like. For ease of illustration, FIG6 shows a single bus line, but this does not imply a single bus or type of bus. Bus 604 may include a path for transmitting information between various components of computing device 600 (e.g., memory 606, processor 604, and communication interface 608).

[0118] The processor 604 may include any one or more processors such as 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 volatile memory, such as random access memory (RAM). The processor 604 may also include non-volatile memory, such as read-only memory (ROM), flash memory, hard disk drive (HDD), or solid state drive (SSD).

[0120] Memory 606 stores executable program code, which processor 604 executes to implement the functions of acquisition module 501 and processing module 502 shown in FIG5 , thereby implementing the mathematical model solving method described in the above embodiment. In other words, memory 606 stores instructions for executing the mathematical model solving method described in the above embodiment.

[0121] Alternatively, the memory 606 stores executable code, and the processor 604 executes the executable code to implement the functions of the mathematical model solving device 500 shown in FIG. 5 , thereby implementing the mathematical model solving method described in the above embodiment. In other words, 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] Embodiments of the present application also provide 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 smartphone.

[0124] As shown in Figure 7, 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 can store different instructions, each for executing part of the functions of the mathematical model solving apparatus 700 shown in FIG7 . In other words, 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 a computing device cluster may be connected via a network. The network may be a wide area network (WAN) or a local area network (LAN), among others. FIG. 8 illustrates a possible implementation. As shown in FIG. 8 , two computing devices 600A and 600B are connected via a network. Specifically, the connection to the network is achieved 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. Simultaneously, 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 the functionality of the computing device 600A shown in FIG8 may also be implemented by multiple computing devices 600. Similarly, the functionality of the computing device 600B may also be implemented by multiple computing devices 600.

[0129] The present application also provides another computing device cluster. The connection relationship between the computing devices in this computing device cluster can be similar to the connection method of the computing device cluster described in Figures 7 and 8. However, the memory 606 in one or more computing devices 600 in this computing device cluster can store the same instructions for executing the method described 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 some instructions for executing the aforementioned mathematical model solving method. In other words, the combination of one or more computing devices 600 can jointly execute the instructions for executing the aforementioned mathematical model solving method.

[0131] Based on the method in the above embodiment, an 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 contains one or more available media. The available medium can be a magnetic medium (for example, a floppy disk, a hard disk, a tape), an optical medium (for example, a DVD), or a semiconductor medium (for example, a solid-state drive), 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 may be 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, which 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 can be a general-purpose computer, a special-purpose computer, a computer network, or other programmable device. The computer instructions can be stored in a computer-readable storage medium or transmitted via the computer-readable storage medium. The computer instructions can be transmitted from one website, computer, server or data center to another website, computer, server or data center via a wired (e.g., coaxial cable, optical fiber, digital subscriber line (DSL)) or wireless (e.g., infrared, wireless, microwave, etc.) method. The computer-readable storage medium can 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 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 drive (SSD)).

[0136] It will be understood that the various numerical numbers involved in the embodiments of the present application are merely distinctions for the convenience of description and are not intended 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 them. 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 deviate the essence of the corresponding technical solutions 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 of the iterative method cluster and / or a sub-preprocessing sub-cluster of the preprocessing 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; The processing module inputs the matrix of the linear equation group into the parameter recommendation engine of the corresponding level to obtain the user's expected recommendation When solving for the value of the parameter, it is specifically used for: 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 of the iterative method cluster and / or a sub-preprocessing sub-cluster of the preprocessing 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 The computing device cluster executes the method according to any one of claims 1 to 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.

Images