Nonlinear equation set solving method and related equipment

Abstract

The embodiment of the invention discloses a nonlinear equation set solving method, and the method comprises the steps: enabling a neural network model to recognize the equation set feature information of a first nonlinear equation set during the ith iteration according to the input description information of the ith iteration during the ith iteration of the first nonlinear equation set, according to the method, the relatively appropriate first convergence strategy of the first nonlinear equation set in the current iteration process is efficiently determined, so that the target convergence strategy is determined according to the first convergence strategy, and iteration solution is efficiently and accurately performed on the first nonlinear equation set based on the target convergence strategy. The iterative solution performance of the nonlinear equation set is improved (for example, the solution speed is improved, and the solution time consumption is reduced), and the generalization problem caused by a convergence strategy determined based on expert experience and a default convergence strategy is avoided. The problem that convergence strategies determined in different scenes are poor in effect and difficult to converge when the nonlinear equation set is solved is solved.

Description

[0001] This application claims priority to the Chinese patent application filed with the State Intellectual Property Office on September 26, 2023, with Chinese application number 202311253320.3 and invention name “A mathematical solution method, device and system”, the entire contents of which are incorporated by reference in this application. Technical Field

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

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

[0004] In the CAE simulation process, the most important and time-consuming task is usually solving a set of equations. In many CAE simulation scenarios, a large number of nonlinear equations are involved.

[0005] Currently, when solving a system of nonlinear equations, an iterative solution is usually performed using a default convergence strategy, or a convergence strategy is set using manual experience.

[0006] However, fixed convergence strategies are difficult to achieve good results in solving various nonlinear problems, and strategies cannot be adjusted during iterations. Artificial experience usually requires a long time to accumulate and cannot be quickly acquired. In addition, the participation of relevant experts is required during the solution process, which affects processing efficiency.

[0007] It can be seen that there is an urgent need for a method that can efficiently and quickly determine the appropriate convergence strategy when iteratively solving a system of nonlinear equations. Summary of the invention

[0008] The embodiment of the present application provides a method for solving a nonlinear system of equations, which can efficiently and quickly determine a suitable convergence strategy when iteratively solving a nonlinear system of equations. The present application also provides corresponding devices, equipment, computer-readable storage media, and computer program products.

[0009] A first aspect of the present application provides a method for solving a nonlinear system of equations, which is applied to a computing device cluster, and the method includes: obtaining a first nonlinear system of equations; based on the first nonlinear system of equations, obtaining description information of the i-th iteration of the first nonlinear system of equations, wherein the description information of the i-th iteration is used to describe characteristic information of the first nonlinear system of equations at the i-th iteration, and i is a positive integer; inferring the description information of the i-th iteration of the first nonlinear system of equations through a neural network model to obtain at least one first convergence strategy for the i-th iteration; determining a target convergence strategy based on the at least one first convergence strategy, and using the target convergence strategy to perform an i-th iteration solution on the first nonlinear system of equations to obtain a target solution to the first nonlinear system of equations.

[0010] In the first aspect, during the i-th iteration of the first nonlinear equation group, the neural network model can identify the characteristics of the first nonlinear equation group and the characteristics of the current iteration parameters and other characteristic information of the first nonlinear equation group at the i-th iteration based on the input description information of the i-th iteration, so as to efficiently determine a first convergence strategy that is more suitable for the first nonlinear equation group in the current iteration process, thereby determining a target convergence strategy based on the first convergence strategy, and iteratively solving the first nonlinear equation group efficiently and accurately based on the target convergence strategy, thereby improving the iterative solution performance of the nonlinear equation group (for example, improving the solution speed and reducing the solution time), and avoiding the generalization problems brought about by the convergence strategy determined based on expert experience and the default convergence strategy, and solving the problem that the convergence strategy determined in different scenarios when solving the nonlinear equation group is not effective and difficult to converge.

[0011] In a possible implementation manner of the first aspect, the description information of the i-th iteration includes at least one of the first nonlinear equation group, the Jacobian matrix of the i-th iteration, the right-hand side term of the i-th iteration, and the current solution of the i-th iteration.

[0012] In this possible implementation, the description information of the i-th iteration may include a mathematical expression of the first linear equation group, and / or iteration parameter information of the i-th iteration, and the iteration parameter information may include at least one of the Jacobian matrix of the iterative equation group corresponding to the first nonlinear equation group, the right-hand side term, and the current solution of the i-th iteration.

[0013] In a possible implementation manner of the first aspect, the target convergence strategy includes one or more of the following strategies: a convergence algorithm, a step size strategy, and a direction strategy.

[0014] In this possible implementation, the target convergence strategy may include a single strategy or a combination of multiple strategies, thereby determining a better iterative search path in the process of solving a nonlinear system of equations from one or more aspects to improve iterative performance.

[0015] In a possible implementation of the first aspect, the description information of the i-th iteration also includes information about a physical problem to be solved, and the first set of nonlinear equations is obtained by numerically simulating the information about the physical problem to be solved, and the information about the physical problem to be solved includes at least one of the following: boundary conditions, grid information, and physical equations.

[0016] In this possible implementation, the physical problem information is the upper-level scene information involved in constructing the first nonlinear equation group, and is strongly related to the constructed first nonlinear equation group. Therefore, the description information of the i-th iteration can include the physical problem information associated with the first nonlinear equation group, so that in the subsequent processing process, the above physical problem information is used as the input of the neural network model, which facilitates the neural network model to mine useful scene feature information and feature information of the first nonlinear equation group itself from the physical problem information.

[0017] In a possible implementation of the first aspect, a target convergence strategy is determined according to at least one first convergence strategy, and the target convergence strategy is used to perform an i-th iteration to solve the first nonlinear equation group to obtain a target solution to the first nonlinear equation group, including: obtaining first configuration information, the first configuration information is used to indicate the use of a recommended convergence strategy set, and / or, at least one of a historical convergence strategy set, a user-defined convergence strategy set, and a default convergence strategy set as a convergence strategy set, the recommended convergence strategy set includes at least one first convergence strategy, and at least one of the historical convergence strategy set, the user-defined convergence strategy set, and the default convergence strategy set includes at least one second convergence strategy; according to the first configuration information, multiple convergence strategies for the i-th iteration are determined, the multiple convergence strategies include at least one first convergence strategy and / or at least one second convergence strategy; the target convergence strategy is selected from the multiple convergence strategies; and the target convergence strategy is used to perform an i-th iteration to solve the first nonlinear equation group to obtain a target solution to the first nonlinear equation group.

[0018] In this possible implementation, considering that different convergence strategies may be applicable to different application scenarios, such as physical problems in different physical scenarios, multiple convergence strategies may be provided according to the first configuration information. In this way, the adaptability of different convergence strategies in different application scenarios (such as different physical problems) can be fully considered, and a more suitable target convergence strategy in the current scenario can be selected from multiple convergence strategies, thereby improving the quality of the target convergence strategy finally obtained, and thus improving the solution performance of the iterative solution process of the first nonlinear equation group.

[0019] In a possible implementation of the first aspect, a target convergence strategy is screened out from multiple convergence strategies, including: obtaining second configuration information, the second configuration information including a performance evaluation indicator, or including a performance evaluation indicator and a weight corresponding to each performance evaluation indicator; and screening out the target convergence strategy from the multiple convergence strategies based on the second configuration information and performance parameter information of each convergence strategy in the multiple convergence strategies.

[0020] In this possible implementation, any performance evaluation index can be used to evaluate the iterative performance of the corresponding convergence strategy when it is used as the convergence strategy for the i-th iteration. The user can flexibly configure the performance evaluation index according to the actual scenario needs (for example, in some examples, multiple performance evaluation indicators can be flexibly set from multiple dimensions to screen the convergence strategy from multiple dimensions), so as to flexibly set the screening method of the target convergence strategy. In this way, the corresponding target convergence strategy with better iterative performance can be screened out from the multiple convergence strategies for the i-th iteration based on the performance evaluation index and related weights and other information, so that the first nonlinear equation group can be solved for the i-th iteration based on the target convergence strategy, so that the solution performance meets the requirements of the current scenario.

[0021] In a possible implementation of the first aspect, the performance evaluation indicators include one or more of the following: nonlinear evaluation, and / or linear evaluation; wherein the nonlinear evaluation is based on the first nonlinear equation group and the performance parameter information of each convergence strategy in multiple convergence strategies, and the linear evaluation is based on the iterative equation group corresponding to the first nonlinear equation group and the performance parameter information of each convergence strategy in multiple convergence strategies; wherein the nonlinear evaluation includes one or more of the following: convergence evaluation, solution speed evaluation, accuracy evaluation; the linear evaluation includes one or more of the following: convergence evaluation, solution speed evaluation, accuracy evaluation.

[0022] In this possible implementation, the user can flexibly set the screening method of the target convergence strategy from the dimensions of nonlinear evaluation and / or linear evaluation according to the actual scenario needs, so as to screen out the target convergence strategy with better iteration performance that meets the requirements of the current scenario from multiple convergence strategies of the i-th iteration.

[0023] In a possible implementation of the first aspect, a neural network model is obtained by training based on a data set, the data set includes first training data and a label of the first training data, the first training data includes description information of a second nonlinear set of equations, the description information of the second nonlinear set of equations is used to describe characteristic information of the second nonlinear set of equations during a historical iteration process, and the label of the first training data includes a third convergence strategy corresponding to the second nonlinear set of equations.

[0024] In this possible implementation, the neural network model may be a trained model. The neural network model may be trained in a computing device cluster, or may be trained in other devices and then transmitted and deployed to the computing device cluster.

[0025] The second convergence strategy can be considered as the optimal convergence strategy for solving the second nonlinear equation group. In some examples, for a second nonlinear equation group, the second convergence strategy of the second nonlinear equation group can be fixed. In other examples, for a second nonlinear equation group, the second convergence strategy of the second nonlinear equation group can be flexibly adjusted according to user configuration.

[0026] In a possible implementation manner of the first aspect, the first training data corresponds to multiple groups of candidate convergence strategies and performance parameter information corresponding to each group of candidate convergence strategies; the method also includes: receiving third configuration information input by a user, the third configuration information including performance evaluation indicators, or including performance evaluation indicators and weights corresponding to each performance evaluation indicator; according to the third configuration information and the performance parameter information of each group of candidate convergence strategies corresponding to the first training data, determining the third convergence strategy in the label of the first training data from the multiple groups of candidate convergence strategies corresponding to the first training data.

[0027] In this possible implementation, the performance evaluation index is used to evaluate the solution performance of the candidate convergence strategy. Exemplarily, the performance evaluation index in the third configuration information may include one or more of the following evaluation indicators: solution accuracy, solution time, and number of iterations.

[0028] In this way, users can flexibly adjust the optimal convergence strategy required in the current scenario by configuring performance evaluation indicators, or including performance evaluation indicators and the weights corresponding to each performance evaluation indicator, according to the needs of the actual application scenario, so that the convergence strategy recommendation method learned by the trained neural network model can meet the needs of the current scenario.

[0029] In a possible implementation of the first aspect, the method also includes: receiving fourth configuration information input by a user, the fourth configuration information being used to indicate a strategy range to which a candidate convergence strategy belongs, the strategy range including one or more of the following: one or more convergence algorithms, one or more step size strategies, and one or more direction strategies; according to the fourth configuration information, obtaining multiple groups of candidate convergence strategies corresponding to each first training data.

[0030] In this possible implementation, the user can configure the selectable range of candidate convergence strategies on one or more strategy dimensions (e.g., convergence algorithm, step size strategy and / or direction strategy), thereby limiting the candidate convergence strategies corresponding to the second training data within a specified range (e.g., the range of convergence strategies executable by the nonlinear iterative solution service), that is, limiting the second convergence strategy in the label of the second training data within a specified range, so that the convergence strategy recommendations that can be learned by the trained neural network model are limited to a specified range, so that in the inference stage, the convergence strategy output by the neural network model is executable.

[0031] In a possible implementation of the first aspect, the method further includes: generating second training data and a label of the second training data, the second training data including description information of the i-th iteration, and the label of the second training data including a target convergence strategy; training the neural network model according to the second training data to obtain an optimized neural network model.

[0032] In this possible implementation, the neural network model can be continuously iterated and updated as the data distribution and scale of users in the actual application scenario change, thereby continuously optimizing the model so that the optimized neural network model is more adaptable to the current scenario needs and can generate better target convergence strategies for the iterative process of the nonlinear equation group in different scenarios, thereby improving the solution performance.

[0033] The second aspect of the present application provides a device for solving a nonlinear system of equations, which has the function of implementing the method of the first aspect or any possible implementation of the first aspect. The function can be implemented by hardware, or by hardware executing corresponding software. The hardware or software includes one or more modules corresponding to the above functions, such as an interface module and a processing module.

[0034] A third aspect of the present application provides a computing device cluster, which includes at least one computing device, each computing device including a processor and a memory, and the memory of at least one computing device stores computer execution instructions that can be run on the processor. When the computer execution instructions are executed by the processor, the processor executes the method as described in the first aspect or any possible implementation method of the first aspect.

[0035] A fourth aspect of the present application provides a computer-readable storage medium storing one or more computer-executable instructions. When the computer-executable instructions are executed by a computing device cluster, the computing device cluster executes a method as described in the first aspect or any possible implementation of the first aspect.

[0036] In a fifth aspect, the present application provides a computer program product storing one or more computer execution instructions. The computer program product includes computer execution instructions. When the computer execution instructions are executed by a computing device cluster, the computing device cluster executes a method as described in the first aspect or any possible implementation of the first aspect.

[0037] In a sixth aspect of the present application, a chip system is provided, which includes a processor for supporting a computing device cluster to implement the functions involved in the first aspect or any possible implementation of the first aspect. In a possible design, the chip system may also include a memory, which is used to store necessary program instructions and data. The chip system may be composed of a chip, or may include a chip and other discrete devices.

[0038] Among them, the technical effects brought about by the second to sixth aspects or any possible implementation methods thereof can refer to the technical effects brought about by the first aspect or the relevant possible implementation methods of the first aspect, and will not be repeated here. BRIEF DESCRIPTION OF THE DRAWINGS

[0039] Figure 1 is an exemplary flow chart of CAE simulation provided by an embodiment of the present application;

[0040] Figure 2 is an exemplary schematic diagram of a data center provided in an embodiment of the present application;

[0041] Figure 3 This is an exemplary schematic diagram of performing CAE simulation-related tasks through a cloud management platform provided in an embodiment of the present application;

[0042] Figure 4 It is a schematic diagram of an embodiment of a method for solving a nonlinear system of equations provided in an embodiment of the present application;

[0043] Figure 5 is an exemplary schematic diagram of the model training provided in the embodiment of the present application;

[0044] Figure 6 It is an exemplary schematic diagram of iteratively solving the first nonlinear equation group based on the convergence strategy optimization module provided in an embodiment of the present application;

[0045] Figure 7 is a schematic diagram of an exemplary processing flow provided in an embodiment of the present application;

[0046] Figure 8 It is an exemplary schematic diagram of executing a nonlinear equation solving task through a cloud management platform provided in an embodiment of the present application;

[0047] Fig. 9is an exemplary schematic diagram of a computer model of a solenoid valve provided in an embodiment of the present application;

[0048] Fig.10 It is a schematic diagram of an embodiment of a nonlinear equation solving device provided in an embodiment of the present application;

[0049] Fig.11 is a schematic diagram of a structure of a computing device provided in an embodiment of the present application;

[0050] Fig.12 is a schematic diagram of a structure of a computing device cluster provided in an embodiment of the present application;

[0051] Fig.13 It is a structural diagram of a computing device cluster provided in an embodiment of the present application. DETAILED DESCRIPTION

[0052] The following describes the embodiments of the present application in conjunction with the drawings in the embodiments of the present application. The terms used in the implementation method section of the present application are only used to explain the specific embodiments of the present application, and are not intended to limit the present application.

[0053] Those skilled in the art may appreciate that, with the development of technology and the emergence of new scenarios, the technical solutions provided in the embodiments of the present application are also applicable to similar technical problems.

[0054] In the present application, "at least one" means one or more, and "plurality" means two or more. "And / or" describes the association relationship of associated objects, indicating that three relationships may exist. For example, A and / or B can represent: A exists alone, A and B exist at the same time, and B exists alone, where A and B can be singular or plural. The character " / " generally indicates that the objects associated before and after are in an "or" relationship. "At least one of the following" or similar expressions refers to any combination of these items, including any combination of singular or plural items. The terms "first", "second", etc. in the specification and claims of this application and the above-mentioned drawings are used to distinguish similar objects, and do not have to be used to describe a specific order or sequence. It should be understood that the terms used in this way can be interchangeable where appropriate, and this is merely a description of the way in which objects with the same attributes are described in the embodiments of the present application. Furthermore, the terms "comprises," "comprising," and "having," and any variations thereof, are intended to cover a non-exclusive inclusion, so that a process, method, system, product, or apparatus that comprises a list of elements is not necessarily limited to those elements but may include other elements not expressly listed or inherent to such process, method, product, or apparatus.

[0055] Before introducing the embodiments of the present application, some concepts involved in the embodiments of the present application are first explained.

[0056] 1. CAE simulation.

[0057] CAE simulation refers to the process of analyzing and solving engineering problems through numerical calculation and simulation using computer-aided engineering technology. CAE simulation is an engineering analysis method based on computer technology. It can conduct virtual testing of products during the design phase to evaluate product performance, reliability, and safety, thereby reducing the cost and time of actual testing. CAE simulation can be applied to various engineering fields, such as machinery, electronics, aerospace, automobiles, and construction, and can simulate various physical phenomena, such as structural mechanics, fluid mechanics, and heat conduction.

[0058] like Figure 1 The figure shows an exemplary process flow diagram of CAE simulation.

[0059] Figure 1 In the simulation process shown, first, computer-aided design (CAD) modeling can be performed on the physical problem to obtain a computer model. The computer model can be a digital model obtained by using a specified software in a computer, and can virtually describe the physical structure. The computer model can be newly created by using CAD, or can be obtained and imported from other means (such as other equipment).

[0060] Then, the computer model obtained after modeling can be subjected to geometric pre-processing, for example, threads and slits in the computer model can be removed, and the thin slices can be subjected to dimensionality reduction processing, etc. Then, one or more of the materials, domain equations, boundary conditions, loads, and initial conditions of the computer model can be set, and then the computer model can be meshed. After the meshing is completed, physical equations can be generated according to the physical problem to be solved, and a group of partial differential equations can be constructed to obtain a group of equations to be solved.

[0061] After obtaining the system of equations to be solved (for example Figure 1 After that, the system of equations can be solved (for example, by Figure 1 After obtaining the solution, the corresponding physical problem can be solved according to the solution to obtain the simulation result. Figure 1 In the example shown, after obtaining the solution to the linear equations, three-dimensional drawings, cross-sectional diagrams, and derived values ​​of the computer model can be calculated based on the solution results, for example, integrating a volume, surface, or variable, or calculating the value of an expression along an edge or point, etc.

[0062] After obtaining the simulation results, simulation post-processing can be performed. For example, the defects of the design scheme in the project can be located according to the simulation results, and improvement analysis can be performed. In addition, the design scheme can be updated and iterated. For example, a simulation report can be written according to the simulation results to guide the update of the corresponding design scheme.

[0063] CAE simulation can be used to solve a variety of physical problems, such as Figure 1 As shown in the figure, CAE simulation is widely used in various practical engineering application scenarios in the industrial field.

[0064] 2. Numerical calculation.

[0065] exist Figure 1 In the example shown, after the system of equations to be solved is obtained, the system of equations can be solved by numerical calculation to obtain corresponding solution results.

[0066] Numerical computing refers to a method of using computers to solve mathematical problems, such as solving equations, solving calculus problems, and optimization problems. The basic idea of ​​numerical computing is to convert mathematical problems into numerical computing problems that can be processed by computers, and then use computers to perform calculations to obtain numerical solutions. Numerical computing includes numerical approximation, numerical integration, numerical differentiation, numerical algebra, numerical equation solving, and numerical optimization. Numerical computing has a wide range of applications in scientific computing, engineering computing, financial computing, statistical computing, and other fields.

[0067] There are many methods for numerical calculation, for example, nonlinear iteration method and linear iteration method.

[0068] Since the embodiments of the present application involve a nonlinear iterative method, the nonlinear iterative method is introduced below.

[0069] 3. Nonlinear iterative method.

[0070] Nonlinear iteration method is an iterative method for solving nonlinear equations. Nonlinear iteration method refers to obtaining approximate solutions to nonlinear equations through a finite number of iterations. For example, Newton iteration method can be used to continuously solve linear problems and iteratively update the solution results, thereby gradually approaching the true solution of nonlinear problems.

[0071] Specifically, when solving a nonlinear system of equations, the nonlinear system of equations can be converted into an iterative system of equations, which includes one or more iterative equations, wherein the one or more iterative equations can include a Jacobian matrix and a right-hand side term, so as to form a thread equation through the Jacobian matrix, the right-hand side term and the variable. In this way, the linear problem can be continuously solved and the solution result can be iteratively updated through the iterative system of equations, so as to gradually approach the real solution of the nonlinear problem.

[0072] In the CAE simulation process, the more important and time-consuming task is usually solving the system of equations.

[0073] In many CAE simulation scenarios, a large number of nonlinear equations are involved, such as fluid simulation analysis of automobile air-conditioning systems to guide air-conditioning system product design and optimization, simulation analysis of nonlinear materials in structural mechanics problem simulation, and collision analysis in automobile R&D.

[0074] If the software function module for solving nonlinear equations is called a nonlinear solver, then in practical applications, when iteratively solving nonlinear equations, the nonlinear solver can be based on nonlinear iterative methods such as the Newton iteration method. In each iteration process, the linear solver calculation is called to support the solution of the Jacobian matrix of the free matrix, which is used to solve nonlinear mechanics, materials, and contact problems in various engineering scenarios such as structures, fluids, electromagnetics, and multi-physics field coupling. Commonly used nonlinear iterative methods include Newton's method, quasi-Newton's method, inexact Newton's method, etc. In addition, in the solution process, it is also necessary to cooperate with the convergence strategy to iterate.

[0075] 4. Convergence strategy.

[0076] In the scenario of solving a nonlinear system of equations, the convergence strategy is used to obtain the convergence path of the iterative solution process of the nonlinear system of equations.

[0077] Specifically, the convergence strategy may include a convergence algorithm, a direction strategy, a step size strategy, or a combination thereof.

[0078] The convergence algorithm may include line search, trust region, etc. The direction strategy is used to obtain the iteration direction, and the step size strategy is used to obtain the iteration step size.

[0079] It can be understood that the solution performance of the iterative solution process of the nonlinear equation system is affected by the number of iterations and the single iteration time, and different convergence strategies can obtain different directions and step sizes, that is, different iterative search paths, resulting in different computational costs.

[0080] If the convergence algorithm is not properly selected, it may cause oscillation or divergence during the iteration process, making it impossible to converge. If the step size is too large or too small or the direction is wrong, it may require more iterations to converge to the true solution, which will increase the calculation time. It can be seen that a good set of convergence strategies can significantly reduce the number of iterations in the solution process, thereby reducing the solution time for nonlinear equations.

[0081] Currently, when solving a system of nonlinear equations, an iterative solution is usually performed using a default convergence strategy, or a convergence strategy is set based on human experience according to the current scenario.

[0082] However, in actual CAE simulation scenarios, there are many types of physical problems involved. Different types of physical problems derive different properties of the nonlinear equations to be solved; and, although the structures of the nonlinear equations derived from the same type of physical problems are similar, the properties and scale of the matrices are changing. Therefore, a fixed convergence strategy is difficult to achieve good results in solving various nonlinear problems, and the strategy cannot be adjusted during the iteration process.

[0083] However, manual experience usually requires a long period of accumulation and cannot be acquired quickly. In addition, the participation of relevant experts is required in the solution process, which affects processing efficiency.

[0084] In summary, there is an urgent need for a method that can efficiently and quickly determine a suitable convergence strategy when iteratively solving a system of nonlinear equations.

[0085] The method of the embodiment of the present application may be applied to a computing device cluster, which may include one or more computing devices.

[0086] The type of any computing device is not limited herein. Exemplarily, any computing device may be a terminal device, or a server, a container, or a virtual machine.

[0087] In one example, the computing device cluster can be used to implement a cloud management platform. In other words, the embodiments of the present application can be applied to a cloud management platform.

[0088] The cloud management platform is used to manage the infrastructure that provides cloud services, and can provide computing, network and storage capabilities based on services of hardware resources and software resources. Exemplarily, the cloud management platform and infrastructure can be located in one or more data centers to provide cloud resources through one or more data centers.

[0089] Combine the following Figure 2 An architectural diagram shown is an exemplary introduction to a data center.

[0090] Figure 2 In the cloud management platform, the cloud management platform communicates with one or more servers (such as Figure 2 The server 1 and server 2 in the server exchange information. The server includes a hardware layer and a software layer. The hardware layer includes the hardware configured by the server, wherein the PCI device may be, for example, a network card, a graphics processing unit (GPU), an offload card, etc., which can be inserted into the peripheral component interconnect standard (PCI) or peripheral component interconnect express (PCIe) slot of the server. The software layer includes an operating system installed and running on the server (relative to the operating system of the virtual machine, it can be called the host operating system). The host operating system is provided with a virtual machine manager (also called a hypervisor). The role of the virtual machine manager is to realize the computing virtualization, network virtualization and storage virtualization of the virtual machine, and is responsible for managing the virtual machine. Among them, a virtual machine (virtual machine) refers to a complete computer system with complete hardware system functions simulated by software and running in a completely isolated environment. Figure 2 In the system architecture shown, multiple servers are set up in the infrastructure, and the servers can be used to run virtual machines. The specifications of each virtual machine can be the same or different. Among them, the virtual machine can also be called a cloud server (elastic compute service, ECS), elastic instance, etc. Different cloud service providers may have different names.

[0091] In one example of the embodiment of the present application, the cloud management platform can be a public cloud platform. In this case, cloud service providers such as individuals or software developers with cloud resource development capabilities can provide cloud services to users. Users obtain cloud services through the Internet but do not own cloud computing resources. In other embodiments of the present application, the cloud management platform can be a private cloud platform or a hybrid cloud platform, and the present application does not limit this.

[0092] Specifically, in Figure 2 In the example shown, the cloud management platform can provide an access interface (such as an interface or application programming interface (API)). Users of the cloud management platform and cloud service providers can operate the client remote access access interface to register a cloud account and password on the cloud management platform, and log in to the cloud management platform after the cloud management platform successfully authenticates the cloud account and password, thereby creating, managing, logging in and operating virtual machines in the cloud data center.

[0093] For example, when there is a need to perform a task of solving the first nonlinear equation group, some enterprises, organizations or individuals can purchase cloud services, thereby performing the relevant first nonlinear equation group solving task through the cloud resources of the cloud management platform, and obtaining the corresponding solution results from the cloud management platform.

[0094] Of course, the cloud management platform may also be other types of cloud management platforms, which is not limited in the embodiments of the present application.

[0095] In some examples, the cloud management platform can provide users with convergence strategy recommendation services and nonlinear iterative solution services for solving the first nonlinear equation group. In addition, it can also provide numerical calculation solution services and CAE simulation services, etc. In this way, users can perform CAE simulation tasks through the cloud management platform, and in the process of performing CAE simulation tasks, generate the first nonlinear equation group, and then perform the first nonlinear equation group solution task through the cloud management platform.

[0096] like Figure 3 The figure shows an exemplary schematic diagram of executing CAE simulation tasks through a cloud management platform.

[0097] Among them, the user can send configuration information to the CAE simulation service of the cloud management platform to configure the called service, and can trigger the CAE simulation service to send a numerical calculation request to the numerical calculation solution service. The numerical calculation request is used to request numerical calculations related to the nonlinear equation group. Then, the numerical calculation solution service can select a nonlinear iterative method to solve the nonlinear equation group based on the user's configuration information, etc., so that the nonlinear iterative solution service can be called. During each iteration process, the nonlinear iterative solution service can obtain a convergence strategy recommendation service that can be called, based on the relevant description information of the nonlinear equation group in the current iteration process (for example Figure 3 In the example shown, the target convergence strategy is obtained from the nonlinear equation group obtained from the numerical calculation solution service and the iteration parameter information (at least one of the Jacobian matrix of the i-th iteration, the right-hand term of the i-th iteration, and the current solution of the i-th iteration) obtained from the nonlinear iterative solution service, and the target convergence strategy is transmitted to the nonlinear iterative solution service for iterative solution to obtain the solution result. The final solution result can be fed back to the CAE simulation service so that the CAE simulation service can obtain the simulation result and output the simulation result to the user.

[0098] It should be noted that Figure 3 The services mentioned are only examples of services provided by the cloud management platform and are not limiting.

[0099] For example, in some other examples, the cloud management platform does not provide CAE simulation services. Users perform CAE simulations through the client to obtain corresponding computer models and other information. Then, users can directly send numerical calculation requests to the numerical calculation solver service of the cloud management platform through the client to request numerical calculations related to linear equations. In other embodiments provided in this application, the service can be deployed as a whole in the customer's server cluster, and this application does not limit this. In addition, in some other examples, the functional division of each service can be different from Figure 3 The services shown are different, and the deployment methods of each service can be different. Each service can provide services independently, or be embedded in other services, or multiple services can be deployed in combination.

[0100] Based on the above computing device cluster, refer to Figure 3 The cloud management platform architecture shown in Figure 4 As shown, in an embodiment of the present application, a target convergence strategy can be determined based on a neural network model through a computing device cluster, thereby iteratively solving a nonlinear equation group through the target convergence strategy.

[0101] Specifically, a method for solving a nonlinear system of equations provided in an embodiment of the present application may include steps 401-404.

[0102] Step 401, obtaining a first nonlinear equation group.

[0103] The first nonlinear system of equations includes one or more nonlinear equations.

[0104] Exemplarily, the first set of nonlinear equations may be obtained by a computing device cluster through CAE simulation, by numerical simulation based on information of the physical problem to be solved; alternatively, the first set of nonlinear equations may be pre-stored in a memory or hard disk of the computing device cluster and read from the memory or hard disk; alternatively, the first set of nonlinear equations may also be obtained by the computing device cluster from other devices (e.g., client devices).

[0105] Step 402: Based on the first nonlinear equation group, obtain description information of the i-th iteration of the first nonlinear equation group.

[0106] The description information of the i-th iteration is used to describe the characteristic information of the first nonlinear equation group at the i-th iteration, and i is a positive integer.

[0107] In an embodiment of the present application, step 402 and subsequent steps can be triggered to execute during one or more iterations in the process of solving the first nonlinear equation group, so as to adopt the method in the embodiment of the present application to obtain the target convergence strategy of the iteration, and iteratively solve the first nonlinear equation group according to the target convergence strategy of the iteration.

[0108] For example, Figure 3 In the example shown, before each iteration, the nonlinear iterative solution service can transmit the description information of the iteration to the convergence strategy recommendation service, or instruct the convergence strategy recommendation service to obtain the description information of the iteration from other services or devices, so that the convergence strategy recommendation service obtains the target convergence strategy of the iteration based on the description information of the iteration and provides feedback to the nonlinear iterative solution service. The nonlinear iterative solution service can perform the iterative solution according to the target convergence strategy of the iteration.

[0109] The i-th iteration may be any iteration in the process of solving the first nonlinear equation set, for example, the first iteration or a subsequent iteration.

[0110] The description information of the i-th iteration is used to describe the characteristic information of the first nonlinear equation group at the i-th iteration. In addition, in some examples, the description information of the i-th iteration also includes information of the physical problem to be solved. When the value of i is different, the description information of the i-th iteration of the i-th iteration may be different.

[0111] The following is an exemplary introduction to the specific contents that the description information of the i-th iteration may include.

[0112] 1. The first nonlinear system of equations.

[0113] The first nonlinear equation group included in the description information of the i-th iteration may be a mathematical expression of the first linear equation group (for example, a mathematical expression including operators, cos, sin, powers, etc.), or may include information such as variables and coefficients of variables in the first linear equation group.

[0114] 2. Iteration parameter information of the i-th iteration.

[0115] The iteration parameter information of the i-th iteration is used to describe the initial state of the i-th iteration.

[0116] In some embodiments, the iteration parameter information of the i-th iteration includes but is not limited to at least one of the following information:

[0117] Information of the iterative equation system corresponding to the first nonlinear equation system, and the current solution of the i-th iteration.

[0118] The iterative equation group corresponding to the first nonlinear equation group is obtained by transforming the first nonlinear equation group, for example, it can be obtained by transforming according to a nonlinear iterative method.

[0119] When solving the first nonlinear equation group, the first nonlinear equation group can be converted into a corresponding iterative equation group, which includes one or more iterative equations, wherein the one or more iterative equations can include a Jacobian matrix and a right-hand side term, so as to form a linear equation form through the Jacobian matrix, the right-hand side term and the variable. In this way, the linear problem can be continuously solved and the solution result can be iteratively updated through the iterative equation group, so as to gradually approach the true solution of the nonlinear equation group.

[0120] That is, the description information of the i-th iteration may include the Jacobian matrix of the i-th iteration and / or the right-hand term of the i-th iteration.

[0121] The current solution of the i-th iteration is related to the value of i.

[0122] Specifically, when i is 1, the current solution of the i-th iteration is the initial solution when solving the first nonlinear equation system.

[0123] When i is a positive integer greater than 1, the current solution of the i-th iteration is the solution obtained after solving the i-1-th iteration.

[0124] In addition, in some other examples, the iteration parameter information of the i-th iteration may also include other information, for example, may include performance parameters of the current solution of the i-th iteration.

[0125] Exemplarily, the performance parameters of the current solution of the i-th iteration may include one or more of the following parameters:

[0126] The error of the current solution of the i-th iteration, the solution time of the i-1-th iteration, and the current number of iterations (e.g., the value of i).

[0127] Specifically, when i is 1, the current solution of the i-th iteration is the initial solution when solving the nonlinear equation system. At this time, the performance parameters of the current solution of the i-th iteration may include the error of the initial solution and / or the value of i, but since the iteration has not started, the solution time of the i-1-th iteration is not included.

[0128] When i is a positive integer greater than 1, the performance parameters of the current solution of the i-th iteration may include the error of the solution obtained in the i-1-th iteration, the solution time of the i-1-th iteration, and the value of i.

[0129] 3. Information about the physical problem to be solved.

[0130] Physical problem information is used to describe the physical problems to be solved in industrial application scenarios.

[0131] The specific field of the industrial application scenario is not limited here. For example, the industrial application scenario can be a scenario in an engineering field such as machinery, electronics, aerospace, automobile or construction.

[0132] In some examples, the physical problem information can be described by corresponding CAE simulation scenarios. Figure 1 In the process shown, in the CAE simulation scenario, after steps such as geometric preprocessing, setting boundary conditions, meshing, and setting physical equations, one or more of the boundary conditions, mesh information, and corresponding physical equations of the corresponding computer model can be obtained, thereby obtaining the physical problem information associated with the set of linear equations.

[0133] The physical problem information includes at least one of the following information:

[0134] Boundary conditions, mesh information, physical equations.

[0135] For example, in one example, the physical problem information may include mesh information and physical equations.

[0136] Among them, boundary conditions are used to describe the boundary conditions of the computer model in the corresponding CAE simulation. Figure 1 In the process shown, the boundary conditions can be generated after the geometric pre-processing. There are many ways to describe the boundary conditions. For example, they can be described by grid point information; or they can be described in the form of equations (such as Dirichlet conditions, Neumann conditions, etc.).

[0137] The grid information is used to describe the grid division method of the corresponding computer model. Specifically, the grid division method refers to the division method of dividing the computer model into multiple grid units. Figure 1 In the process shown, the grid information is completed in the grid generation stage. The grid information includes one or more of the grid point coordinates, grid division accuracy, etc. Among them, exemplarily, the coordinates of multiple grid points can be described in the form of a matrix.

[0138] The physical equation is determined according to the physical problem to be solved. The number of physical equations involved in the description information of the i-th iteration is not limited here, and it can be one physical equation or a physical equation group including multiple physical equations.

[0139] Exemplarily, the physical equation may include one or more of the following:

[0140] 1) Physical equations in mathematical form such as partial differential equations, such as Poisson's equation for electric potential and Poisson's equation for pressure.

[0141] 2) Physical parameter values ​​in physical equations. For example, in physical problems related to charge distribution, the physical parameter values ​​may include physical parameters such as the capacitance of a grid point.

[0142] The first nonlinear equation group is obtained by numerical simulation of the physical problem information to be solved. It can be seen that the first nonlinear equation group is constructed based on the physical problem information, that is to say, the above physical problem information will affect the first nonlinear equation group generated subsequently. The above physical problem information, as the upper-level scene information of the first nonlinear equation group generated subsequently, will affect the specific form and scale of the first nonlinear equation group generated subsequently.

[0143] It can be understood that in the embodiments of the present application, the data form of the physical problem information to be solved may include one or more forms such as matrix, equation, vector, numerical value, etc.

[0144] It can be seen that in the embodiment of the present application, the physical problem information, as the upper-level scene information involved in constructing the first nonlinear equation group, is strongly related to the constructed first nonlinear equation group. Therefore, the description information of the i-th iteration can include the physical problem information associated with the first nonlinear equation group, so that in the subsequent processing process, the above physical problem information is used as the input of the neural network model, which facilitates the neural network model to mine useful scene feature information and feature information of the first nonlinear equation group itself from the physical problem information.

[0145] There may be multiple ways to obtain the description information of the i-th iteration, and the ways to obtain different contents in the description information of the i-th iteration may be the same or different, which is not limited here.

[0146] In one example, a user logs in to a cloud management platform through a client, and sends the first nonlinear equation group and physical problem information to be solved in the description information of the i-th iteration to the convergence strategy recommendation service of the cloud management platform through the client, and the first nonlinear equation group can be processed.

[0147] In this example, the user can obtain a computer model such as CAE simulation through the client, obtain physical problem information through the computer model, and generate a first nonlinear equation group to be solved based on the physical problem information. Then, the first nonlinear equation group information and related physical problem information can be sent to a computing device cluster that implements a cloud management platform through the client.

[0148] In addition, in this example, the convergence strategy recommendation service of the cloud management platform can obtain the iteration parameter information of the i-th iteration through the nonlinear iterative solution service of the cloud management platform, for example, obtain at least one of the Jacobian matrix of the i-th iteration, the right-hand side term of the i-th iteration, and the current solution of the i-th iteration.

[0149] In another example, the user may obtain description information of the i-th iteration through cloud resources of the cloud management platform.

[0150] In this example, the user not only performs the task of solving the nonlinear equations through the cloud resources of the cloud management platform, but also constructs a computer model for CAE simulation through the first cloud resources of the cloud management platform. In this way, the corresponding physical problem information and the first nonlinear equations constructed according to the physical problem information can be obtained from the first cloud resource through the convergence strategy recommendation service of the cloud management platform, and the iteration parameter information of the i-th iteration can be obtained from the nonlinear iterative solution service during the solution process, for example, at least one of the Jacobian matrix of the i-th iteration, the right-hand side term of the i-th iteration, and the current solution of the i-th iteration can be obtained.

[0151] Step 403: Inferring the description information of the i-th iteration of the first nonlinear equation group through the neural network model to obtain at least one first convergence strategy of the i-th iteration.

[0152] The neural network model can be an existing or subsequently developed model, and is not limited in the embodiments of the present application. For example, the neural network model can be a general model such as a physics-informed neural network (PINN) or a CNN; or the neural network model can also be a model that can solve partial differential equations (PDE), for example, the neural network model can be a deeponet, and both training and reasoning are used as the solution process.

[0153] For different neural network models, the processing of the description information of the i-th iteration may be different based on the processing capabilities and requirements of the different neural network models themselves. For example, if the neural network model is PINN, and the PINN cannot directly process input data in the form of matrices and physical equations, then feature engineering can be performed on the description information of the i-th iteration including matrices and physical equations, for example, encoding the description information of the i-th iteration through a feature extraction model, or converting the description information of the i-th iteration into data form (for example, converting it into vector form) before inputting it into PINN. If the neural network model is deeponet, the description information of the i-th iteration in the form of matrices and / or physical equations can be received as input data.

[0154] In the embodiment of the present application, the neural network model may be a trained model. The neural network model may be trained in a computing device cluster, or may be trained in other devices and then transmitted and deployed to the computing device cluster.

[0155] The following is an exemplary introduction to the training process of the neural network model.

[0156] In the embodiment of the present application, the training process may include one or more of the following steps:

[0157] 1. Obtain a data set, where the data set includes multiple first training data and a label for each first training data.

[0158] Among them, each first training data includes description information of the corresponding second nonlinear equation group, the description information of the second nonlinear equation group is used to describe the characteristic information of the second nonlinear equation group during the historical iteration process, and the label of the first training data includes the second convergence strategy corresponding to the corresponding second nonlinear equation group.

[0159] The data set collection method is not limited here. For example, the data set can be obtained from an open source data set, or the data set can be generated by manually collecting information on iterative solutions of nonlinear equations in various scenarios.

[0160] In the data set, the second nonlinear equation groups corresponding to different first training data may be the same or different. The second nonlinear equation group may be the same as or different from the first nonlinear equation group.

[0161] Below, taking any first training data as an example, the description information of the second nonlinear equation group and the corresponding labels are exemplarily introduced.

[0162] The description information of the second nonlinear equation group may include at least one of the second nonlinear equation group, the Jacobian matrix of the iterative equation group corresponding to the second equation group, the right-hand side term of the iterative equation group corresponding to the second equation group, and the current solution of the second equation group during the historical iteration process.

[0163] The second nonlinear equation group may specifically be a mathematical expression of the second nonlinear equation group.

[0164] The historical iteration process of the second nonlinear equation group may include the jth iteration process in the solution process of the second nonlinear equation group collected in advance, and at this time, the third convergence strategy in the label of the first training data may be a better convergence strategy for the jth iteration. j is a positive integer.

[0165] For example, when j is 1, the current solution of the second system of equations in the historical iteration process may be the initial solution of the second system of nonlinear equations.

[0166] When j is greater than 1, the current solution of the second system of equations in the historical iteration process may be the solution obtained in the j-1th iteration of the second system of nonlinear equations.

[0167] Alternatively, the historical iteration process of the second nonlinear equation group may also be an end-to-end solution process of the second nonlinear equation group, for example, it may include an initial solution when solving the second nonlinear equation group. In this case, the third convergence strategy in the label of the first training data may be a better convergence strategy for the end-to-end solution process.

[0168] The second convergence strategy can be considered as the optimal convergence strategy for solving the second nonlinear equation system.

[0169] In some examples, for a second nonlinear system of equations, a second convergence strategy of the second nonlinear system of equations may be fixed.

[0170] In other examples, for a second nonlinear equation group, the second convergence strategy of the second nonlinear equation group can be flexibly adjusted according to user configuration.

[0171] There are many specific ways to determine the second convergence strategy.

[0172] For example, in some embodiments, each first training data corresponds to a plurality of groups of candidate convergence strategies and performance parameter information corresponding to each group of candidate convergence strategies;

[0173] The method further includes:

[0174] Receive third configuration information input by a user, where the third configuration information includes performance evaluation indicators, or includes performance evaluation indicators and a weight corresponding to each performance evaluation indicator;

[0175] According to the third configuration information and the performance parameter information of each group of candidate convergence strategies corresponding to the first training data, the third convergence strategy in the label of the first training data is determined from the multiple groups of candidate convergence strategies corresponding to the first training data.

[0176] In the embodiment of the present application, the performance parameter information corresponding to each group of candidate convergence strategies is used to indicate the solution performance of the corresponding candidate convergence strategy when used in the solution process of the corresponding second nonlinear equation group.

[0177] Exemplarily, the performance parameter information corresponding to each group of candidate convergence strategies may include corresponding solution accuracy, solution time, number of iterations, etc.

[0178] like Figure 5In the example shown, the computing device cluster can provide a third configuration interface, which displays multiple candidate evaluation indicators. The user can use the third configuration interface to determine one or more performance evaluation indicators from the multiple candidate evaluation indicators, and can also determine the weight corresponding to each performance evaluation indicator.

[0179] In this way, the third convergence strategy in the label of the first training data can be determined from multiple groups of candidate convergence strategies corresponding to the first training data according to the third configuration information input by the user and the performance parameter information of each group of candidate convergence strategies corresponding to the first training data.

[0180] Performance evaluation indicators are used to evaluate the solution performance of candidate convergence strategies.

[0181] The number of the performance evaluation indicators can be one or more, and the number of the performance evaluation indicators is not limited here.

[0182] Furthermore, the specific content of the performance evaluation index is not limited here.

[0183] Exemplarily, the performance evaluation indicator in the third configuration information may include one or more of the following evaluation indicators:

[0184] Solution accuracy, solution time, and number of iterations.

[0185] In this way, users can flexibly adjust the optimal convergence strategy required in the current scenario by configuring performance evaluation indicators, or including performance evaluation indicators and the weights corresponding to each performance evaluation indicator, according to the needs of the actual application scenario, so that the convergence strategy recommendation method learned by the trained neural network model can meet the needs of the current scenario.

[0186] For example, the candidate convergence strategies corresponding to the first training data include an accelerated convergence method and a global convergence method.

[0187] Among them, the accelerated convergence method aims to speed up the convergence speed of iteration. For example, the Aitken acceleration method in the accelerated convergence method improves the convergence speed by performing linear interpolation on the iterative sequence. It can be seen that the solution speed of the accelerated convergence method is faster.

[0188] The global convergence method guarantees that the solution of the system of equations is found near a reasonable initial point. For example, the Broyden method and the Anderson hybrid method in the global convergence method are globally convergent. It can be seen that the solution accuracy of the global convergence method is high.

[0189] If the current scenario requires a high level of solution accuracy, then the performance evaluation index may include solution accuracy, and a larger weight may be set for the performance evaluation index of solution accuracy. The third convergence strategy determined based on the performance evaluation index and the corresponding weight may be a convergence strategy with higher solution accuracy, such as the global convergence method described above. This allows the trained neural network model to learn a convergence strategy that recommends a convergence strategy with higher solution accuracy.

[0190] If the current scenario requires a higher solution speed, the performance evaluation indicator can be determined to include the solution time, and the weight corresponding to the performance evaluation indicator of the solution time can be set to be larger. At this time, the third convergence strategy is a convergence strategy with a faster solution speed. For example, it can be the above-mentioned global convergence method, so that the convergence strategy recommendation method that can be learned by the trained neural network model is to recommend a convergence strategy that results in a shorter solution time (that is, a faster solution speed).

[0191] In addition, in some embodiments, the user can also configure the strategy range to which each candidate convergence strategy belongs, that is, limit the candidate convergence strategy corresponding to the second training data within a specified range, that is, limit the second convergence strategy in the label of the second training data within a specified range, so that the convergence strategy recommendation method that can be learned by the trained neural network model is limited to a specified range, so that in the inference stage, the convergence strategy output by the neural network model can be executed.

[0192] Specifically, the method further includes:

[0193] Receive fourth configuration information input by a user, where the fourth configuration information is used to indicate a strategy range to which the candidate convergence strategy belongs, where the strategy range includes one or more of the following: one or more convergence algorithms, one or more step size strategies, and one or more direction strategies;

[0194] According to the fourth configuration information, multiple groups of candidate convergence strategies corresponding to each first training data are obtained.

[0195] In an embodiment of the present application, each first training data corresponds to multiple groups of preset convergence strategies. The user can configure the strategy range to which the candidate convergence strategies belong to filter out candidate convergence strategies from the multiple groups of preset convergence strategies to limit the candidate convergence strategies corresponding to the second training data within a specified range, that is, to limit the second convergence strategy in the label of the second training data within the specified range.

[0196] The policy scope to which the candidate convergence policy belongs may be determined according to possible policy dimensions of the candidate convergence policy.

[0197] For example, candidate convergence strategies include one or more of the following strategies:

[0198] Convergence algorithm, step size strategy, direction strategy.

[0199] Exemplarily, the convergence algorithm may be a line search algorithm or a trust region algorithm.

[0200] The direction strategy determines which direction is selected for updating during the iteration process. Exemplarily, in solving a nonlinear system of equations, one or more of the following direction strategies can be used:

[0201] Newton method direction: Based on the inverse matrix of the Jacobian matrix, the direction is selected by linearization;

[0202] Gradient descent direction: Update the approximate solution according to the gradient direction of the objective function;

[0203] Conjugate Gradient Direction: Used for quadratic optimization problems, the solution is updated through a series of conjugate directions.

[0204] Of course, the direction strategy may not be limited to the above strategies. For example, the direction strategy may also be: memory-constrained Broyden-Fletcher-Goldfard-Shanno (LBFGS) algorithm, steepest descent method, and dogleg method.

[0205] The step size strategy may be an adaptive step size strategy, so that the step size can be automatically adjusted according to the situation during the iteration process. Among them, the adaptive step size can improve the convergence speed and avoid excessively large or too small step sizes.

[0206] The user can configure the selectable range of candidate convergence strategies on the one or more strategy dimensions, thereby limiting the candidate convergence strategies corresponding to the second training data within a specified range, that is, limiting the second convergence strategy in the label of the second training data within a specified range (for example, the range of convergence strategies executable by the nonlinear iterative solution service), so that the convergence strategy recommendation method that can be learned by the trained neural network model is limited to a specified range, and the convergence strategy output by the neural network model is executable.

[0207] The configurable policy range of the candidate convergence policy in each policy dimension is not limited here.

[0208] like Figure 5 In the example shown, the computing device cluster may provide a fourth configuration interface, on which is displayed the configurable policy ranges of the candidate convergence policies in three policy dimensions: convergence algorithm, step size policy, and direction policy.

[0209] like Figure 5As shown, in the fourth configuration interface, the configurable ranges of the candidate convergence strategy in the three strategy dimensions of convergence algorithm, step size strategy and direction strategy are as follows:

[0210] 1. The configurable range of the convergence algorithm:

[0211] Line search algorithm, trust region algorithm.

[0212] 2. Configurable range of direction strategy:

[0213] Newton's method, Broyden's algorithm (a quasi-Newton method), nonlinear conjugate gradient descent (nonlinear CG), LBFGS algorithm, steepestdescent, dogleg.

[0214] 3. The configurable range of step size strategy:

[0215] Full-step strategy, morethuente strategy, backtracking, polynomial algorithm.

[0216] The user may consider the convergence strategies that can be executed in the current nonlinear iterative solution service, and thereby determine the strategy range to which the candidate convergence strategy belongs from the configurable ranges in the three strategy dimensions through the fourth configuration interface.

[0217] The user can select the strategy range to which the candidate convergence strategy belongs from the configurable range in the fourth configuration interface. For example, the user can select the strategy range to which the convergence algorithm of the candidate convergence strategy belongs as trust region, the strategy range to which the direction strategy belongs as Newton method, Broyden algorithm and nonlinear CG, and the strategy range to which the step size strategy belongs as backtrack and polynomial.

[0218] Then, the candidate convergence strategy corresponding to the first training data may be determined according to the strategy range to which the candidate convergence strategy configured by the user belongs, for example: Figure 5 The example shown includes candidate convergence strategies 1-candidate convergence strategies m.

[0219] 2. Preprocess the training data of the dataset.

[0220] The preprocessing method is not limited here. Exemplarily, the preprocessing may include one or more of the following methods:

[0221] Data cleaning, data integration (for example, merging multiple data sources into one data set), data transformation (for example, standardizing, normalizing, discretizing, etc.), data reduction (which can be achieved through methods such as clustering, sampling, and feature extraction), and feature engineering.

[0222] 3. Classify the data set and divide it into training set and validation set.

[0223] 4. Train one or more models to be trained according to the training set to obtain a trained model.

[0224] When there are multiple models to be trained, the types and structures of different models to be trained can be the same, similar, or different.

[0225] During the training process, the parameters of the model to be trained can be updated according to the loss function.

[0226] The loss function is used to evaluate the difference between the convergence strategy output by the to-be-trained model during the training process and the third convergence strategy in the label of the corresponding first training data.

[0227] The specific form of the loss function is not limited here. Exemplarily, the loss function can be a cross entropy function or the like.

[0228] In this way, one or more trained models can be obtained according to the training set and the loss function.

[0229] 5. Use the validation set to validate one or more trained models and select the best model as the neural network model.

[0230] 6. Deploy the obtained neural network model to a computing device cluster.

[0231] like Figure 5 As shown, according to the first training data and the label corresponding to the first training data, after training and verifying the model to be trained based on the specified loss function, a neural network model can be obtained, and the neural network model can be applied to the convergence strategy recommendation service.

[0232] After the obtained neural network model is deployed to the computing device cluster, the description information of the i-th iteration can be processed by the neural network model to obtain at least one first convergence strategy of the i-th iteration.

[0233] The description information of the i-th iteration may be preprocessed such as data conversion and / or feature engineering, and then input into a neural network model, so as to output a first convergence strategy of the i-th iteration through the neural network model.

[0234] The first convergence strategy may have one or more groups, and the number of the first convergence strategies is not limited here.

[0235] In some examples, the output result of the neural network model includes multiple groups of convergence strategies and the confidence corresponding to each group of convergence strategies. A group of convergence strategies with the highest confidence can be obtained from the output result of the neural network model as the first convergence strategy; or, N groups of convergence strategies with the highest confidence can be obtained from the output result of the neural network model as N groups of first convergence strategies, where N can be a positive integer greater than 1.

[0236] Step 404: determine a target convergence strategy according to at least one first convergence strategy, and use the target convergence strategy to perform an i-th iteration to solve the first nonlinear equation group to obtain a target solution to the first nonlinear equation group.

[0237] The target convergence strategy may include convergence strategies on one or more strategy dimensions.

[0238] In some embodiments, the target convergence strategy includes one or more of the following strategies:

[0239] Convergence algorithm, step size strategy, direction strategy.

[0240] The convergence algorithm, step size strategy and direction strategy may be existing strategies or strategies to be developed later, and are not limited here.

[0241] Exemplarily, in the target convergence strategy, the convergence algorithm can be a line search algorithm or a trust region algorithm; the direction strategy can be: Newton method, quasi-Newton method (such as Broyden algorithm), nonlinearCG, LBFGS, steepestdescent or dogleg; the step size strategy can be fullstep, morethuente, backtrack or polynomial.

[0242] It can be seen that the target convergence strategy may include a single strategy or a combination of multiple strategies, thereby determining a better iterative search path in the process of solving a nonlinear system of equations from one or more aspects and improving iterative performance.

[0243] In this way, by using the target convergence strategy to perform the i-th iterative solution on the first nonlinear equation group, the first nonlinear equation group can be converged during the iterative process to obtain the target solution of the first nonlinear equation group.

[0244] The target solution can be considered as the solution of the first nonlinear equation group obtained through the i-th iteration process, and can also be considered as the solution result obtained by solving the first nonlinear equation group through a nonlinear iteration method.

[0245] In an embodiment of the present application, during the i-th iteration of the first nonlinear equation group, the neural network model can identify characteristic information of the first nonlinear equation group at the i-th iteration, such as characteristics of the first nonlinear equation group and current iteration parameters, based on the input description information of the i-th iteration, so as to efficiently determine a first convergence strategy that is more suitable for the first nonlinear equation group in the current iteration process, thereby determining a target convergence strategy based on the first convergence strategy, and iteratively solving the first nonlinear equation group efficiently and accurately based on the target convergence strategy, thereby improving the iterative solution performance of the nonlinear equation group (for example, improving the solution speed and reducing the solution time), and avoiding the generalization problems brought about by the convergence strategy determined based on expert experience and the default convergence strategy, and solving the problem that the convergence strategy determined in different scenarios when solving the nonlinear equation group is not effective and difficult to converge.

[0246] In an embodiment of the present application, after obtaining the first convergence strategy, the first convergence strategy can be used as the target convergence strategy for the i-th iteration of the first nonlinear equation group, so as to perform the i-th iteration solution on the first nonlinear equation group and obtain the i-th iteration solution result; or, after obtaining the first convergence strategy, a better target convergence strategy can be queried according to the first convergence strategy, so as to perform the i-th iteration solution on the first nonlinear equation group according to the better target convergence strategy and obtain the solution result.

[0247] In this example, the functional module that implements the convergence strategy screening process in the computing device cluster is called a convergence strategy optimization module.

[0248] like Figure 6 As shown, it is an exemplary schematic diagram of iteratively solving the first nonlinear equation group based on the convergence strategy optimization module.

[0249] The convergence strategy recommendation service can obtain the description information of the first nonlinear equation group from user data and / or nonlinear iterative solution service. When the value of i is 1, it indicates that the first nonlinear equation group has not been iteratively solved. At this time, the description information can include the initial solution; and when i is greater than 1, the description information can include the solution obtained by the nonlinear iterative solution service through the i-1th iteration. The convergence recommendation service can obtain the first convergence strategy based on the description information of the first nonlinear equation group through the neural network model, and then, through the convergence strategy optimization module, a better target convergence strategy can be queried based on the first convergence strategy.

[0250] Below Figure 6Taking the convergence strategy optimization module as an example, the further convergence strategy screening process after obtaining the first convergence strategy is described. In the actual implementation process, the convergence strategy optimization module can be implemented by one or more cloud services of the cloud management platform, which is not limited in the embodiments of the present application.

[0251] Specifically, the convergence strategy screening process may include one or more combinations of the following steps:

[0252] 1. Obtain a convergence strategy set to select a target convergence strategy from the convergence strategy set.

[0253] In some embodiments, the above step 404 includes:

[0254] Obtaining first configuration information, where the first configuration information is used to indicate the use of a recommended convergence strategy set, and / or at least one of a historical convergence strategy set, a user-defined convergence strategy set, and a default convergence strategy set as a convergence strategy set, where the recommended convergence strategy set includes at least one first convergence strategy, and at least one of the historical convergence strategy set, the user-defined convergence strategy set, and the default convergence strategy set includes at least one second convergence strategy;

[0255] Determine, according to the first configuration information, a plurality of convergence strategies for the i-th iteration, the plurality of convergence strategies including at least one first convergence strategy and / or at least one second convergence strategy;

[0256] Select a target convergence strategy from multiple convergence strategies;

[0257] The target convergence strategy is used to iterate and solve the first nonlinear equation group for the i-th time to obtain the target solution of the first nonlinear equation group.

[0258] In the embodiment of the present application, the cloud management platform may provide a first configuration interface, on which a plurality of candidate convergence strategy sets are displayed. The user may select one or more convergence strategy sets from the first configuration interface and confirm. In this way, the user may input the first configuration information to the cloud management platform, that is, the first configuration information is configured and input by the user.

[0259] Alternatively, the cloud management platform may also be pre-configured with multiple candidate convergence strategy sets in the cloud services provided to users by developers based on expert experience, etc. That is, in this example, the first configuration information may be pre-configured by developers in the relevant cloud services.

[0260] The specific content of the convergence strategy set is not limited here.

[0261] For example, in Figure 6 In the example shown, the convergence strategy set may include one or more of the following:

[0262] 1) Recommend a set of convergence strategies;

[0263] The recommended convergence strategy set includes at least one first convergence strategy generated based on the above steps 401-403;

[0264] 2) Historical convergence strategy set;

[0265] Exemplarily, the historical convergence strategy set includes at least one convergence strategy of a historical iteration (e.g., the i-1th iteration) of the first nonlinear equation system as the second convergence strategy;

[0266] 3) User-defined convergence strategy set;

[0267] The user-defined convergence strategy set includes one or more convergence strategies input by a user as a second convergence strategy;

[0268] 4) Default convergence strategy set;

[0269] The default convergence strategy set includes one or more default convergence strategies in the convergence strategy optimization module as the second convergence strategy.

[0270] That is, the recommended convergence strategy set includes at least one first convergence strategy, and at least one of the historical convergence strategy set, the user-defined convergence strategy set, and the default convergence strategy set includes at least one second convergence strategy.

[0271] In the embodiment of the present application, considering that different convergence strategies may be applicable to different application scenarios, such as physical problems in different physical scenarios, multiple convergence strategies may be provided according to the first configuration information. In this way, the degree of adaptation of different convergence strategies in different application scenarios (such as different physical problems) can be fully considered, and a more suitable target convergence strategy in the current scenario can be selected from multiple convergence strategies, thereby improving the quality of the target convergence strategy finally obtained, and thus improving the solution performance of the iterative solution process of the first nonlinear equation group.

[0272] 2. Filter out the target convergence strategy from multiple convergence strategies.

[0273] In some embodiments, selecting a target convergence strategy from a plurality of convergence strategies includes:

[0274] Acquire second configuration information, where the second configuration information includes performance evaluation indicators, or includes performance evaluation indicators and a weight corresponding to each performance evaluation indicator;

[0275] A target convergence strategy is selected from the multiple convergence strategies according to the second configuration information and the performance parameter information of each convergence strategy in the multiple convergence strategies.

[0276] In some examples, the cloud management platform may provide a second configuration interface, on which a plurality of preset evaluation indicators are displayed. The user may select at least one evaluation indicator from the second configuration interface and confirm it as a performance evaluation indicator. In this way, the user may input the second configuration information to the cloud management platform, that is, the second configuration information is configured by the user.

[0277] In this example, the user can flexibly configure the performance evaluation index based on the current scenario needs through the second configuration interface, so as to determine the target convergence strategy that better meets the needs of the current scenario according to the configured performance evaluation index.

[0278] In other examples, the cloud management platform may also be pre-configured with performance evaluation indicators in the cloud services provided to users by developers based on experience, etc. That is, in this example, the second configuration information may be pre-configured by developers in the relevant cloud services.

[0279] The second configuration information may carry an identifier of the performance evaluation indicator, and may also carry the content of the performance evaluation indicator, for example, a specific evaluation method of the evaluation indicator (for example, a related evaluation formula, etc.).

[0280] The number and type of the performance evaluation indicators are not limited here.

[0281] like Figure 6 In the example shown, the performance evaluation index may include nonlinear evaluation and / or linear evaluation, wherein the nonlinear evaluation includes one or more of convergence evaluation, solution speed evaluation or accuracy evaluation, and / or the linear evaluation includes one or more of convergence evaluation, solution speed evaluation or accuracy evaluation.

[0282] The following is an exemplary introduction to possible types of performance evaluation indicators.

[0283] In some examples, the performance evaluation index may include one or more performance indicators, such as one or more of convergence evaluation, solution speed evaluation, or accuracy evaluation.

[0284] In this example, each performance indicator may be evaluated based on performance parameter information of each convergence strategy among multiple convergence strategies.

[0285] The performance parameter information of each convergence strategy is used to indicate the solution performance of the corresponding convergence strategy when it is used in the solution process of the first nonlinear equation group.

[0286] Exemplarily, the performance parameter information of each convergence strategy may include corresponding solution accuracy, solution time, number of iterations, etc.

[0287] The specific method for obtaining the performance parameter information of each convergence strategy is not limited here.

[0288] Exemplarily, for the first convergence strategy, the performance parameter information of the first convergence strategy is used to describe the performance of the solution of the i-1th iteration, for example, the accuracy of the solution of the i-1th iteration, the solution speed and / or the current number of iterations can be described. Exemplarily, the performance parameters of the solution obtained by the i-1th iteration may include one or more of the following parameters: the error of the solution obtained by the i-1th iteration, the solution time duration of the i-1th iteration, and the value of i (used to reflect the current number of iterations).

[0289] For the second convergence strategy among the multiple convergence strategies of the i-th iteration (for example, a convergence strategy pre-configured by the user or a default convergence strategy, etc.), the performance parameter information of the other convergence strategies can be obtained in advance through experience or testing, etc., or can be derived based on the relevant information of the second convergence strategy and the first nonlinear equation group (for example, a related iterative equation group, etc.).

[0290] The following is an exemplary introduction to each performance indicator.

[0291] 1. Convergence evaluation.

[0292] Convergence evaluation refers to the property of the numerical method solution approaching the true solution when the discretization step size approaches zero. If the numerical method converges to the true solution when the step size is small enough, and the convergence speed is as expected, then we can consider that the numerical method has good convergence.

[0293] There are two common ways to evaluate convergence: convergence theory and convergence test. Convergence theory is to derive the error estimate and convergence rate of numerical methods by analyzing the discretization error and truncation error of numerical methods. Convergence test is to analyze the gap between numerical solutions and true solutions by comparing the solution results of numerical methods under discretization steps.

[0294] In the process of solving the first nonlinear equation group, the numerical method adopted is the nonlinear iteration method. At this time, the convergence can be evaluated by parameters such as the solution error in the performance parameters of the i-th iteration and / or the value of i (describing the current iteration step).

[0295] For the first convergence strategy, the error in the performance parameter of the i-th iteration may be the error of the solution obtained in the i-1-th iteration (when i is greater than 1), or the error of the initial solution of the first nonlinear equation group (when i is 1). The performance parameters such as the error of the second convergence strategy among the multiple convergence strategies may be collected based on a pre-test and included in the second configuration information, or may be obtained by theoretical deduction based on the corresponding convergence strategy and the first nonlinear equation group.

[0296] 2. Evaluation of solution speed.

[0297] The solution speed evaluation is used to evaluate the solution time when performing iterative solution based on each convergence strategy among multiple convergence strategies.

[0298] Specifically, the solution speed can be evaluated by using parameters such as the solution time in the performance parameters of the i-th iteration.

[0299] For the first convergence strategy, when i is 1, the current solution of the i-th iteration is the initial solution when solving the first nonlinear equation group. At this time, the performance parameters of the i-th iteration do not include the solution time, so the solution speed evaluation cannot be performed; and when i is greater than 1, the solution time in the performance parameters of the i-th iteration can be the solution time of the i-1-th iteration. The performance parameters such as the solution time of the second convergence strategy in the multiple convergence strategies can be collected based on a pre-experiment and included in the second configuration information, or can be obtained by theoretical derivation based on the corresponding convergence strategy and the first nonlinear equation group.

[0300] 3. Accuracy assessment.

[0301] The accuracy assessment is used to assess the accuracy of the solution results obtained by iteratively solving each of multiple convergence strategies.

[0302] The accuracy can describe the difference between the solution obtained by iterative solution and the exact solution.

[0303] Specifically, the accuracy can be evaluated by using parameters such as the error in the performance parameters of the i-th iteration.

[0304] For the first convergence strategy, the error in the performance parameter of the i-th iteration may be the error of the i-1-th iteration. The performance parameters such as the error of the second convergence strategy among the multiple convergence strategies may be collected based on a pre-experiment and included in the second configuration information, or may be obtained by theoretical derivation based on the corresponding convergence strategy and the first nonlinear equation group.

[0305] In some examples, the performance evaluation index may be evaluated from one or more aspects of nonlinearity and linearity.

[0306] In this example, the performance evaluation indicators include one or more of the following:

[0307] Non-linear evaluation, and / or, linear evaluation.

[0308] They are introduced below one by one.

[0309] 1. Nonlinear evaluation.

[0310] The nonlinear evaluation is performed based on the first nonlinear equation set and performance parameter information of each convergence strategy in the plurality of convergence strategies.

[0311] In the nonlinear evaluation, one or more performance indicators may be specifically included, that is, the nonlinear evaluation may be based on one or more performance parameters and perform nonlinear evaluation on one or more performances.

[0312] The performance parameter information of each convergence strategy is used to indicate the solution performance of the corresponding convergence strategy when it is used in the solution process of the first nonlinear equation group.

[0313] Exemplarily, the performance parameter information of each convergence strategy may include corresponding solution accuracy, solution time, number of iterations, etc.

[0314] In some examples, the nonlinear evaluation specifically includes one or more of the following performance indicators:

[0315] Convergence evaluation, solution speed evaluation, and accuracy evaluation.

[0316] Wherein, when performing convergence evaluation, solution speed evaluation and / or accuracy evaluation, the evaluation may be performed based on the first nonlinear equation group.

[0317] For example, convergence evaluation and / or accuracy evaluation may be performed based on the gap between the solution in the performance parameter information of each of the multiple convergence strategies in the i-th iteration and the true solution of the first nonlinear equation group.

[0318] 2. Linear evaluation.

[0319] The linear evaluation is performed based on the iterative equation group corresponding to the first nonlinear equation group and the performance parameter information of each convergence strategy in the plurality of convergence strategies.

[0320] In the linear evaluation, one or more performance indicators may be specifically included, that is, the linear evaluation may be performed on one or more performances based on one or more performance parameters.

[0321] In some examples, the linearity evaluation specifically includes one or more of the following performance indicators:

[0322] Convergence evaluation, solution speed evaluation, and accuracy evaluation.

[0323] When performing convergence evaluation, solution speed evaluation and / or accuracy evaluation, the evaluation may be performed based on a system of linear equations.

[0324] For example, convergence evaluation and / or accuracy evaluation may be performed based on the gap between the solution in the performance parameter information of each of the multiple convergence strategies in the i-th iteration and the numerical solution to the linear equation system.

[0325] It can be seen that in this example, the user can flexibly set the screening method of the target convergence strategy from the dimensions of nonlinear evaluation and / or linear evaluation according to the actual scenario needs, and screen out the target convergence strategy with better iterative performance that meets the requirements of the current scenario from multiple convergence strategies of the i-th iteration, and transmit the target convergence strategy to the nonlinear iterative solution service to perform the i-th iterative solution of the first nonlinear equation group.

[0326] In the embodiment of the present application, the weight corresponding to each performance evaluation indicator can be configured by the user or pre-configured by a developer or the like.

[0327] It can be understood that any performance evaluation index can be used to evaluate the iterative performance of the corresponding convergence strategy when it is used as the convergence strategy for the i-th iteration. The user can flexibly configure the performance evaluation index according to the actual scenario needs (for example, in some examples, multiple performance evaluation indicators can be flexibly set from multiple dimensions to screen the convergence strategy from multiple dimensions), so as to flexibly set the screening method of the target convergence strategy. In this way, the corresponding target convergence strategy with better iterative performance can be screened out from the multiple convergence strategies for the i-th iteration based on the performance evaluation index and related weights and other information, so that the first nonlinear equation group can be solved for the i-th iteration based on the target convergence strategy.

[0328] According to the method for solving a nonlinear equation group according to any of the above-mentioned embodiments, the first nonlinear equation group can be solved iteratively multiple times until the iteration termination condition is reached, for example, until the number of iterations reaches a specified number threshold, or until the solution result of the iterative solution converges to a specified condition, and the target solution result of the first nonlinear equation group can be obtained and output.

[0329] In addition, in some embodiments, after performing multiple iterative solutions to the first nonlinear equation group according to the method for solving a nonlinear equation group according to any of the above embodiments to obtain the target solution of the first nonlinear equation group, the neural network model can also be optimized based on relevant data of the solution process to improve the performance of the neural network model so that the neural network model can better meet the needs of actual application scenarios.

[0330] Specifically, in some embodiments, the method further includes:

[0331] Generate second training data and a label of the second training data, the second training data including description information of the i-th iteration, and the label of the second training data including a target convergence strategy;

[0332] The neural network model is trained according to the second training data to obtain an optimized neural network model.

[0333] In some examples, the second training data can be added to the data set to serve as training data for retraining the neural network model.

[0334] In an embodiment of the present application, the target convergence strategies corresponding to different sets of nonlinear equations can be continuously collected during the reasoning process. In addition, relevant performance data of the actual iterative solution results can also be obtained in some examples, so as to judge whether the corresponding target convergence strategy is a suitable convergence strategy and generate corresponding second training data.

[0335] Then, the neural network model can be trained according to the second training data to obtain an optimized neural network model, and then the subsequent nonlinear equation solving method is executed according to the optimized neural network model.

[0336] In this way, the neural network model can be continuously iterated and updated as the data distribution and scale of users in actual application scenarios change, thereby continuously optimizing, making the optimized neural network model more adaptable to the needs of the current scenario, and able to generate better target convergence strategies for the iterative process of nonlinear equations in different scenarios, thereby improving the solution performance.

[0337] like Figure 7 The figure shows an exemplary processing flow diagram of an embodiment of the present application.

[0338] Before iteratively solving the first nonlinear equation group, each first training data and the corresponding label in the data set can be obtained through the third configuration information and the fourth configuration information. The label can be a better convergence strategy that is flexibly determined based on the third configuration information and the fourth configuration information and meets the needs of the current scenario.

[0339] Then, the training model can be trained through the training module according to the data set, and after the training is completed, a neural network model is obtained. The neural network model can be used for convergence strategy recommendation service.

[0340] In this example, the convergence strategy recommendation service can be enabled based on the user's initial configuration.

[0341] When performing the i-th iteration solution to the first nonlinear equation group, the convergence strategy recommendation service may obtain the description information of the first nonlinear equation group from the user data and / or the nonlinear iterative solution service, for example, obtaining the nonlinear equation group from the numerical calculation solution service and obtaining the iteration parameter information (at least one of the Jacobian matrix of the i-th iteration, the right-hand side term of the i-th iteration, and the current solution of the i-th iteration) from the nonlinear iterative solution service. When the value of i is 1, it indicates that the first nonlinear equation group has not been iteratively solved. At this time, the current solution of the i-th iteration in the description information may be the initial solution; and when i is greater than 1, the current solution of the i-th iteration in the description information may be the solution obtained by the nonlinear iterative solution service through the i-1-th iteration.

[0342] The convergence recommendation service can obtain the first convergence strategy based on the description information of the first nonlinear equation group through the neural network model provided by the convergence strategy training module. Then, the first convergence strategy can be used as the target convergence strategy, or a better target convergence strategy can be queried based on the first convergence strategy through the convergence strategy optimization module.

[0343] Among them, the optimization method of the convergence strategy optimization module can be determined according to the first configuration information and the second configuration information input by the user, and the convergence strategy optimization module is used to perform convergence strategy optimization to obtain the target convergence strategy, and the target convergence strategy is passed to the nonlinear iterative solution service to perform the i-th iterative solution on the first nonlinear equation group to obtain the solution result, and the final solution result can be the target solution.

[0344] In addition, in this example, the second training data can be obtained based on the target convergence strategy, the corresponding performance parameter information, and the description information of the i-th iteration, so that the neural network model can be trained based on the second training data to obtain an optimized neural network model, so that the neural network model can be continuously iterated and updated as the data distribution and scale of users in actual application scenarios change, and then the subsequent nonlinear equation solving method is executed according to the updated neural network model.

[0345] It can be seen that based on the introduction of the above embodiments, Figure 3 An exemplary specific implementation of the convergence strategy recommendation service and the nonlinear iterative solution service is shown in Figure 8 shown.

[0346] exist Figure 8In the example shown, after the convergence strategy recommendation service obtains the description information of the i-th iteration of the nonlinear equation group to be solved (for example, the first nonlinear equation group), it can call the neural network model in the neural network model service through an inference request to process the description information to obtain the first convergence strategy. Then, the convergence strategy optimization module can filter out the target convergence strategy based on the convergence strategy set including the first convergence strategy. Next, the convergence strategy recommendation service can send the target convergence strategy to the nonlinear iterative solution service, so that the nonlinear iterative solution service calls the resources of the high-performance computing base through the data computing platform, and performs the i-th iteration solution of the nonlinear equation group according to the target convergence strategy to obtain the solution result of the i-th iteration. After performing multiple iterations based on the above process and reaching the iteration termination condition, the nonlinear iterative solution service can obtain the final solution result of the nonlinear equation group to be solved, and feedback the final solution result to the numerical calculation solution service, so that the CAE simulation service can perform the simulation task according to the final solution result.

[0347] Below, an example is used to illustrate the specific application process of the method for solving a system of nonlinear equations according to an embodiment of the present application in the engineering field.

[0348] In one example, it is necessary to implement an electromagnetic performance optimization simulation of an electromagnetic valve, and the electromagnetic performance optimization simulation of the electromagnetic valve belongs to a two-dimensional low-frequency electromagnetic nonlinear simulation.

[0349] Among them, the solenoid valve is an axisymmetric model, and a two-dimensional axisymmetric computer model can be used for solution and calculation. After the solution, the core electromagnetic performance parameters such as magnetic flux density, current density, loss, current, voltage, inductance, back electromotive force, response time, response acceleration, valve core (plunger) electromagnetic force, etc. can be obtained, so as to carry out a comprehensive electromagnetic performance evaluation, analysis and design optimization of the solenoid valve.

[0350] Fig. 9 is an exemplary schematic diagram of a two-dimensional axisymmetric computer model of a solenoid valve.

[0351] Based on the computer model, the electromagnetic performance optimization simulation of the electromagnetic valve electromagnetic simulation can be performed. In this scenario, a nonlinear equation group can be obtained based on the physical problem to be solved, and the Newton iteration method can be used to construct an iterative equation group of the nonlinear equation group for iterative solution, and the iterative equation group includes the Jacobian matrix and the right-hand side term.

[0352] At this point, the neural network model can be used to obtain the first convergence strategy in each nonlinear iteration process.

[0353] The neural network model can be pre-trained based on a pre-collected data set. The data set includes training data in the electromagnetic performance optimization simulation scenario of the solenoid valve and labels corresponding to the training data. The labels include the optimal convergence strategy corresponding to the training data. The optimal convergence strategy can be determined by the user from multiple candidate convergence strategies corresponding to the training data according to preset performance evaluation indicators and weights corresponding to the preset performance evaluation indicators. In addition, the training data in the electromagnetic performance optimization simulation scenario of the solenoid valve includes description information of the nonlinear equation group in the electromagnetic performance optimization simulation scenario of the solenoid valve, for example, including physical problem information corresponding to the nonlinear equation group, the nonlinear equation group, the Jacobian matrix and right-hand side terms of the iterative equation group corresponding to the nonlinear equation group, and the initial solution of the nonlinear equation group.

[0354] Therefore, the neural network model trained by the data set has the ability to provide a suitable first convergence strategy for the iterative process of the nonlinear equation group in the electromagnetic performance optimization simulation scenario of the solenoid valve.

[0355] In this way, during the reasoning process, in each iteration of the nonlinear equation group to be solved, the convergence strategy recommendation service can obtain descriptive information of this iteration process, which may include the physical problem information corresponding to the nonlinear equation group, the nonlinear equation group, the Jacobian matrix and right-hand side information of the iterative equation group corresponding to the nonlinear equation group, and the solution obtained in the previous iteration.

[0356] After obtaining the description information, the description information is input into the neural network model to obtain the first convergence strategy of this iteration.

[0357] Then, through the convergence strategy optimization service, the best convergence strategy can be determined as the target convergence strategy from multiple strategies including the first convergence strategy according to one or more performance evaluation indicators (such as nonlinear evaluation and / or linear evaluation, etc.) determined by the user.

[0358] Next, the convergence strategy recommendation service may transmit the target convergence strategy to the nonlinear iterative solution service, so that the nonlinear iterative solution service performs an i-th iterative solution on the corresponding nonlinear equation group according to the target convergence strategy.

[0359] Based on the above method, the nonlinear iterative solution service performs multiple iterations to solve the nonlinear equation group until the iteration termination condition is met, and obtains the final solution result, and the final solution result can be returned to the CAE simulation service.

[0360] In the actual test of this example, two meshes with different degrees of refinement can be generated for the two-dimensional axisymmetric computer model of the solenoid valve, namely:

[0361] Grid 1: 19917 second-order triangular elements, 39558 unknowns;

[0362] Grid 2: 5692 second-order triangular elements, 5404 unknowns.

[0363] The nonlinear equations are solved for these two grid conditions respectively. During the solution process, a comparative test is conducted on whether to use the above convergence strategy recommendation.

[0364] The test results are shown in Table 1 and Table 2.

[0365] Table 1: Grid 1 solution results

[0366] Whether to use convergence strategy to recommend services Iterations Solving time (s) no - time out yes 27 146.86

[0367] Table 2: Grid 2 solution results

[0368] Whether to use convergence strategy to recommend services Iterations Solving time (s) no - time out yes 4 11

[0369] It can be seen that for the two grid division situations of Grid 1 and Grid 2, the nonlinear iterative solution service can converge to the final solution when the convergence strategy recommendation service is used; without the convergence strategy recommendation service, the nonlinear iterative solution service times out. Therefore, in this example, when iteratively solving a nonlinear system of equations, determining the convergence strategy in the iterative process through any of the above embodiments to perform iterative solution can significantly improve the convergence efficiency and reduce the time consumption of solution.

[0370] The above describes the method for solving a nonlinear system of equations provided in the embodiment of the present application from multiple aspects. The following describes the device for solving a nonlinear system of equations provided in the embodiment of the present application in conjunction with the accompanying drawings.

[0371] like Fig.10 As shown, the embodiment of the present application provides a nonlinear equation solving device 100, and the nonlinear equation solving device 100 includes:

[0372] Interface module 1001, used to obtain a first nonlinear equation group;

[0373] The processing module 1002 is used to:

[0374] Based on the first nonlinear equation group, obtaining description information of the i-th iteration of the first nonlinear equation group, wherein the description information of the i-th iteration is used to describe characteristic information of the first nonlinear equation group at the i-th iteration, and i is a positive integer;

[0375] Reasoning descriptive information of the i-th iteration of the first nonlinear equation system through a neural network model to obtain at least one first convergence strategy of the i-th iteration;

[0376] A target convergence strategy is determined according to at least one first convergence strategy, and the first nonlinear equation group is iteratively solved for an i-th time using the target convergence strategy to obtain a target solution to the first nonlinear equation group.

[0377] Optionally, the description information of the i-th iteration includes at least one of the first nonlinear equation group, the Jacobian matrix of the i-th iteration, the right-hand side term of the i-th iteration, and the current solution of the i-th iteration.

[0378] Optionally, the target convergence strategy includes one or more of the following strategies:

[0379] Convergence algorithm, step size strategy, direction strategy.

[0380] Optionally, the description information further includes information about a physical problem to be solved, and the first nonlinear equation set is obtained by numerically simulating the information about the physical problem to be solved, and the information about the physical problem to be solved includes at least one of the following:

[0381] Boundary conditions, mesh information, physical equations.

[0382] Optionally, the interface module 1001 is used to: obtain first configuration information, where the first configuration information is used to indicate the use of a recommended convergence strategy set, and / or at least one of a historical convergence strategy set, a user-defined convergence strategy set, and a default convergence strategy set as a convergence strategy set, where the recommended convergence strategy set includes at least one first convergence strategy, and at least one of the historical convergence strategy set, the user-defined convergence strategy set, and the default convergence strategy set includes at least one second convergence strategy;

[0383] The processing module 1002 is used for:

[0384] Determine, according to the first configuration information, a plurality of convergence strategies for the i-th iteration, the plurality of convergence strategies including at least one first convergence strategy and / or at least one second convergence strategy;

[0385] Select a target convergence strategy from multiple convergence strategies;

[0386] The target convergence strategy is used to iterate and solve the first nonlinear equation group for the i-th time to obtain the target solution of the first nonlinear equation group.

[0387] Optionally, the interface module 1001 is used to: obtain second configuration information, where the second configuration information includes performance evaluation indicators, or includes performance evaluation indicators and a weight corresponding to each performance evaluation indicator;

[0388] The processing module 1002 is used to select a target convergence strategy from the multiple convergence strategies according to the second configuration information and the performance parameter information of each convergence strategy in the multiple convergence strategies.

[0389] Optionally, the performance evaluation indicators include one or more of the following:

[0390] Non-linear evaluation, and / or, linear evaluation;

[0391] Wherein, the nonlinear evaluation is evaluated based on the first nonlinear equation group and the performance parameter information of each convergence strategy in the multiple convergence strategies, and the linear evaluation is evaluated based on the iterative equation group corresponding to the first nonlinear equation group and the performance parameter information of each convergence strategy in the multiple convergence strategies;

[0392] Among them, nonlinear evaluation includes one or more of the following: convergence evaluation, solution speed evaluation, and accuracy evaluation;

[0393] Linear evaluation includes one or more of the following: convergence evaluation, solution speed evaluation, and accuracy evaluation.

[0394] Optionally, the neural network model is obtained by training based on a data set, the data set includes first training data and a label of the first training data, the first training data includes description information of the second nonlinear equation group, the description information of the second nonlinear equation group is used to describe characteristic information of the second nonlinear equation group during a historical iteration process, and the label of the first training data includes a third convergence strategy corresponding to the second nonlinear equation group.

[0395] Optionally, the first training data corresponds to a plurality of groups of candidate convergence strategies and performance parameter information corresponding to each group of candidate convergence strategies;

[0396] The interface module 1001 is used to: receive third configuration information input by a user, where the third configuration information includes performance evaluation indicators, or includes performance evaluation indicators and a weight corresponding to each performance evaluation indicator;

[0397] The processing module 1002 is used to determine the third convergence strategy in the label of the first training data from multiple groups of candidate convergence strategies corresponding to the first training data according to the third configuration information and the performance parameter information of each group of candidate convergence strategies corresponding to the first training data.

[0398] Optionally, the interface module 1001 is used to: receive fourth configuration information input by a user, where the fourth configuration information is used to indicate a strategy range to which the candidate convergence strategy belongs, where the strategy range includes one or more of the following: one or more convergence algorithms, one or more step strategies, and one or more direction strategies;

[0399] The processing module 1002 is used to obtain multiple groups of candidate convergence strategies corresponding to each first training data according to the fourth configuration information.

[0400] Optionally, the processing module 1002 is used to:

[0401] Generate second training data and a label of the second training data, the second training data including description information of the i-th iteration, and the label of the second training data including a target convergence strategy;

[0402] The neural network model is trained according to the second training data to obtain an optimized neural network model.

[0403] In an embodiment of the present application, a module is used as an example of a software functional unit, and a nonlinear equation solving device may include code running on a computing instance. Among them, the computing instance may be at least one of a physical host (computing device), a virtual machine, a container and other computing devices. Furthermore, the above-mentioned computing device may be one or more. For example, the nonlinear equation solving device may include code running on multiple hosts / virtual machines / containers. It should be noted that the multiple hosts / virtual machines / containers used to run the application may be distributed in the same region or in different regions. The multiple hosts / virtual machines / containers used to run the code may be distributed in the same available zone (availablezone, AZ) or in different AZs, each AZ including a data center or multiple data centers with close geographical locations. Among them, usually a region may include multiple AZs.

[0404] Similarly, multiple hosts / virtual machines / containers used to run the code can be distributed in the same virtual private cloud (VPC) or in multiple VPCs. Usually, a VPC is set up in a region. For cross-region communication between two VPCs in the same region and between VPCs in different regions, a communication gateway must be set up in each VPC to achieve interconnection between VPCs through the communication gateway.

[0405] As an example of a hardware functional unit, the nonlinear equation solving device may include at least one computing device, such as a server, etc. Alternatively, the nonlinear equation solving device may also be a device implemented by an application specific integrated circuit (ASIC) or a programmable logic device (PLD). The PLD may be a complex PLD (CPLD), a field programmable gate array (FPGA), a generic array logic (GAL) or any combination thereof.

[0406] The multiple computing devices included in the apparatus for solving a nonlinear system of equations can be distributed in the same region or in different regions. The multiple computing devices included in the apparatus for solving a nonlinear system of equations can be distributed in the same AZ or in different AZs. Similarly, the multiple computing devices included in the apparatus for solving a nonlinear system of equations can be distributed in the same VPC or in multiple VPCs. The multiple computing devices can be any combination of computing devices such as servers, ASICs, PLDs, CPLDs, FPGAs, and GALs.

[0407] It should be noted that, in other embodiments, the interface module can be used to execute any step in the method for solving a nonlinear system of equations, and the processing module can be used to execute any step in the method for solving a nonlinear system of equations. The steps that the interface module and the processing module are responsible for implementing can be specified as needed. The full functions of the nonlinear system of equations solving device can be realized by respectively implementing different steps in the method for solving a nonlinear system of equations through the interface module and the processing module.

[0408] The present application embodiment also provides a computing device 110. Fig.11 As shown, the computing device 110 includes: a bus 112, a processor 114, a memory 116, and a communication interface 118. The processor 114, the memory 116, and the communication interface 118 communicate with each other through the bus 112. The computing device 110 can be a server or a terminal device. It should be understood that the present application does not limit the number of processors and memories in the computing device 110.

[0409] The bus 112 may be a peripheral component interconnect (PCI) bus or an extended industry standard architecture (EISA) bus. The bus may be divided into an address bus, a data bus, a control bus, etc. For ease of representation, Fig.11 The bus 114 may include a path for transmitting information between various components of the computing device 110 (eg, the memory 116, the processor 114, and the communication interface 118).

[0410] The processor 114 may include any one or more of a central processing unit (CPU), a graphics processing unit (GPU), a microprocessor (MP), or a digital signal processor (DSP).

[0411] The memory 116 may include a volatile memory, such as a random access memory (RAM). The memory 116 may also include a non-volatile memory, such as a read-only memory (ROM), a flash memory, a hard disk drive (HDD), or a solid state drive (SSD).

[0412] The memory 116 stores executable program codes, and the processor 114 executes the executable program codes to respectively implement the functions of the aforementioned interface module and the processing module, thereby realizing the method for solving a group of nonlinear equations applied to a computing device cluster in the above-mentioned embodiment. That is, the memory 116 stores instructions for executing the method for solving a group of nonlinear equations applied to a computing device cluster in the above-mentioned embodiment.

[0413] The communication interface 118 uses a transceiver module such as, but not limited to, a network interface card or a transceiver to implement communication between the computing device 110 and other devices or a communication network.

[0414] The embodiment of the present application also provides a computing device cluster. The computing device cluster includes at least one computing device. The computing device can be a server, such as a central server, an edge server, or a local server in a local data center. In some embodiments, the computing device can also be a terminal device such as a desktop computer, a laptop computer, or a smart phone.

[0415] like Fig.12 In the example shown, the computing device cluster includes at least one computing device 110. The memory 116 in one or more computing devices 110 in the computing device cluster may store the same instructions for executing the method for solving a nonlinear system of equations.

[0416] In some possible implementations, the memory 116 of one or more computing devices 110 in the computing device cluster may also store partial instructions for executing the method for solving the nonlinear system of equations. In other words, the combination of one or more computing devices 110 may jointly execute instructions for executing the method for solving the nonlinear system of equations.

[0417] It should be noted that the memory 116 in different computing devices 110 in the computing device cluster can store different instructions, which are respectively used to execute part of the functions of the method for solving the nonlinear system of equations. That is, the instructions stored in the memory 116 in different computing devices 110 can implement the functions of one or more modules in the interface module and the processing module.

[0418] In some possible implementations, one or more computing devices in the computing device cluster may be connected via a network, which may be a wide area network or a local area network. Fig.13 A possible implementation is shown. Fig.13 As shown, two computing devices 110A and 110B are connected via a network. Specifically, the connection to the network is made through the communication interface in each computing device. In this type of possible implementation, the memory 116 in the computing device 110A may store instructions for executing the functions of the interface module. At the same time, the memory 116 in the computing device 110B may store instructions for executing the functions of the processing module. Alternatively, the memory 116 in the computing device 110A may store instructions for executing part of the functions of the processing module. At the same time, the memory 116 in the computing device 110B may store instructions for executing another part of the functions of the processing module.

[0419] It should be understood that Fig.13 The functionality of the computing device 110A shown in FIG. 1 may also be implemented by multiple computing devices 110 . Similarly, the functionality of the computing device 110B may also be implemented by multiple computing devices 110 .

[0420] The present application embodiment also provides another computing device cluster. The connection relationship between the computing devices in the computing device cluster can be similar to that of Fig.12 and Fig.13 Connection mode of computing device cluster. The difference is that the memory 116 in one or more computing devices 110 in the computing device cluster may store the same instructions for executing the method for solving the nonlinear system of equations.

[0421] In some possible implementations, the memory 116 of one or more computing devices 110 in the computing device cluster may also store partial instructions for executing the method for solving the nonlinear system of equations. In other words, the combination of one or more computing devices 110 may jointly execute instructions for executing the method for solving the nonlinear system of equations.

[0422] It should be noted that the memory 116 in different computing devices 110 in the computing device cluster may store different instructions for executing part of the functions of the method for solving a nonlinear system of equations. That is, the instructions stored in the memory 116 in different computing devices 110 may implement the functions of one or more modules in the interface module and the processing module.

[0423] The present application also provides a computer program product including instructions. The computer program product may be software or a program product including instructions that can be run on a computing device or stored in any available medium. When the computer program product is run on at least one computing device, the at least one computing device executes a method for solving a nonlinear system of equations.

[0424] The embodiment of the present application also provides a computer-readable storage medium. The computer-readable storage medium can be any available medium that can be stored by the computing device or a data storage device such as a data center containing one or more available media. The available medium can be a magnetic medium (e.g., a floppy disk, a hard disk, a tape), an optical medium (e.g., a DVD), or a semiconductor medium (e.g., a solid-state hard disk). The computer-readable storage medium includes instructions that instruct the computing device to execute a method for solving a nonlinear system of equations.

[0425] The embodiment of the present application also provides a chip system, which includes a processor, and the processor is used to implement the steps performed by the above-mentioned computing device cluster. In a possible design, the chip system may also include a memory, and the memory is used to store necessary program instructions and data. The chip system can be composed of a chip, or it can include a chip and other discrete devices.

[0426] Those skilled in the art can clearly understand that, for the convenience and brevity of description, the specific working processes of the systems, devices and units described above can refer to the corresponding processes in the aforementioned method embodiments and will not be repeated here.

[0427] In the several embodiments provided in the present application, it should be understood that the disclosed systems, devices and methods can be implemented in other ways. For example, the device embodiments described above are only schematic. For example, the division of units is only a logical function division. There may be other division methods in actual implementation. For example, multiple units or components can be combined or integrated into another system, or some features can be ignored or not executed. Another point is that the mutual coupling or direct coupling or communication connection shown or discussed can be an indirect coupling or communication connection through some interfaces, devices or units, which can be electrical, mechanical or other forms.

[0428] The units described as separate components may or may not be physically separated, and the components shown as units may or may not be physical units, that is, they may be located in one place or distributed on multiple network units. Some or all of the units may be selected according to actual needs to achieve the purpose of the solution of this embodiment.

[0429] In addition, each functional unit in each embodiment of the present application may be integrated into one processing unit, or each unit may exist physically separately, or two or more units may be integrated into one unit. The above-mentioned integrated unit may be implemented in the form of hardware or in the form of software functional units.

[0430] If the integrated unit is implemented in the form of a software functional unit and sold or used as an independent product, it can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of the present application, or the part that contributes to the prior art, or all or part of the technical solution can be embodied in the form of a software product, which is stored in a storage medium and includes several instructions for a computer device (which can be a personal computer, server, or network device, etc.) to perform all or part of the steps of the various embodiments of the present application. The aforementioned storage medium includes: U disk, mobile hard disk, read-only memory (ROM, read-only memory), random access memory (RAM, random access memory), disk or optical disk, etc. Various media that can store program codes.

Claims

1. A method for solving a system of nonlinear equations, characterized in that: Applied to a computing device cluster, the method comprises: Obtaining a first nonlinear system of equations; Based on the first nonlinear equation group, obtaining description information of the i-th iteration of the first nonlinear equation group, wherein the description information of the i-th iteration is used to describe equation group characteristic information of the first nonlinear equation group at the i-th iteration, and i is a positive integer; Reasoning the description information of the i-th iteration of the first nonlinear equation system through a neural network model to obtain at least one first convergence strategy of the i-th iteration; A target convergence strategy is determined according to the at least one first convergence strategy, and the first nonlinear equation group is solved for an i-th iteration using the target convergence strategy to obtain a target solution to the first nonlinear equation group.

2. The method according to claim 1, characterized in that: The description information of the i-th iteration includes at least one of the first nonlinear equation group, the Jacobian matrix of the i-th iteration, the right-hand side term of the i-th iteration, and the current solution of the i-th iteration.

3. The method according to claim 1 or 2, characterized in that: The target convergence strategy includes one or more of the following strategies: Convergence algorithm, step size strategy, direction strategy.

4. The method according to any one of claims 1 to 3, characterized in that: The description information of the i-th iteration further includes physical problem information to be solved, the first nonlinear equation set is obtained by numerically simulating the physical problem information to be solved, and the physical problem information to be solved includes at least one of the following: Boundary conditions, mesh information, physical equations.

5. The method according to any one of claims 1 to 4, characterized in that: The step of determining a target convergence strategy according to the at least one first convergence strategy, and using the target convergence strategy to perform an i-th iteration to solve the first nonlinear equation group to obtain a target solution to the first nonlinear equation group includes: Acquire first configuration information, where the first configuration information is used to indicate the use of a recommended convergence strategy set, and / or at least one of a historical convergence strategy set, a user-defined convergence strategy set, and a default convergence strategy set as a convergence strategy set, where the recommended convergence strategy set includes the at least one first convergence strategy, and at least one of the historical convergence strategy set, the user-defined convergence strategy set, and the default convergence strategy set includes at least one second convergence strategy; Determining, according to the first configuration information, a plurality of convergence strategies for the i-th iteration, the plurality of convergence strategies including the at least one first convergence strategy and / or the at least one second convergence strategy; Filtering the target convergence strategy from the multiple convergence strategies; The first nonlinear equation group is solved for an i-th iteration using the target convergence strategy to obtain a target solution to the first nonlinear equation group.

6. The method according to claim 5, characterized in that The step of selecting the target convergence strategy from the multiple convergence strategies includes: Acquire second configuration information, where the second configuration information includes a performance evaluation indicator, or includes a performance evaluation indicator and a weight corresponding to each performance evaluation indicator; A target convergence strategy is selected from the multiple convergence strategies according to the second configuration information and the performance parameter information of each convergence strategy in the multiple convergence strategies.

7. The method according to claim 6, characterized in that The performance evaluation indicators include one or more of the following: Non-linear evaluation, and / or, linear evaluation; The nonlinear evaluation is performed based on the first nonlinear equation group and the performance parameter information of each convergence strategy in the multiple convergence strategies, and the linear evaluation is performed based on the iterative equation group corresponding to the first nonlinear equation group and the performance parameter information of each convergence strategy in the multiple convergence strategies; Wherein, the nonlinear evaluation includes one or more of the following: convergence evaluation, solution speed evaluation, and accuracy evaluation; The linear evaluation includes one or more of the following: convergence evaluation, solution speed evaluation, and accuracy evaluation.

8. The method according to any one of claims 1 to 7, characterized in that: The neural network model is obtained by training based on a data set, and the data set includes first training data and a label of the first training data, the first training data includes description information of a second nonlinear set of equations, the description information of the second nonlinear set of equations is used to describe characteristic information of the second nonlinear set of equations during a historical iteration process, and the label of the first training data includes a third convergence strategy corresponding to the second nonlinear set of equations.

9. The method according to claim 8, characterized in that The first training data corresponds to a plurality of groups of candidate convergence strategies and performance parameter information corresponding to each group of candidate convergence strategies; The method further comprises: Receive third configuration information input by a user, wherein the third configuration information includes the performance evaluation indicator, or includes the performance evaluation indicator and a weight corresponding to each of the performance evaluation indicators; According to the third configuration information and the performance parameter information of each group of candidate convergence strategies corresponding to the first training data, the third convergence strategy in the label of the first training data is determined from multiple groups of candidate convergence strategies corresponding to the first training data.

10. The method according to claim 9, characterized in that The method further comprises: Receive fourth configuration information input by a user, where the fourth configuration information is used to indicate a strategy range to which the candidate convergence strategy belongs, where the strategy range includes one or more of the following: one or more convergence algorithms, one or more step size strategies, and one or more direction strategies; According to the fourth configuration information, multiple groups of candidate convergence strategies corresponding to each first training data are obtained.

11. The method according to any one of claims 1 to 10, characterized in that: The method further comprises: Generate second training data and a label of the second training data, wherein the second training data includes description information of the i-th iteration, and the label of the second training data includes the target convergence strategy; The neural network model is trained according to the second training data to obtain an optimized neural network model.

12. A device for solving a nonlinear system of equations, characterized in that: include: An interface module, used for obtaining a first nonlinear equation system; Processing modules for: Based on the first nonlinear equation group, obtaining description information of the i-th iteration of the first nonlinear equation group, wherein the description information of the i-th iteration is used to describe equation group characteristic information of the first nonlinear equation group at the i-th iteration, and i is a positive integer; Reasoning the description information of the i-th iteration of the first nonlinear equation system through a neural network model to obtain at least one first convergence strategy of the i-th iteration; A target convergence strategy is determined according to the at least one first convergence strategy, and the first nonlinear equation group is solved for an i-th iteration using the target convergence strategy to obtain a target solution to the first nonlinear equation group.

13. The device according to claim 12, characterized in that The description information of the i-th iteration includes at least one of the first nonlinear equation group, the Jacobian matrix of the i-th iteration, the right-hand side term of the i-th iteration, and the current solution of the i-th iteration.

14. The device according to claim 12 or 13, characterized in that The target convergence strategy includes one or more of the following strategies: Convergence algorithm, step size strategy, direction strategy.

15. The device according to any one of claims 12 to 14, characterized in that: The interface module is used to: obtain first configuration information, the first configuration information is used to indicate the use of a recommended convergence strategy set, and / or, at least one of a historical convergence strategy set, a user-defined convergence strategy set, and a default convergence strategy set as a convergence strategy set, the recommended convergence strategy set includes the at least one first convergence strategy, and at least one of the historical convergence strategy set, the user-defined convergence strategy set, and the default convergence strategy set includes at least one second convergence strategy; The processing module is used for: Determining, according to the first configuration information, a plurality of convergence strategies for the i-th iteration, the plurality of convergence strategies including the at least one first convergence strategy and / or the at least one second convergence strategy; Filtering the target convergence strategy from the multiple convergence strategies; The first nonlinear equation group is solved for an i-th iteration using the target convergence strategy to obtain a target solution to the first nonlinear equation group.

16. The device according to claim 15, characterized in that The interface module is used to: obtain second configuration information, where the second configuration information includes performance evaluation indicators, or includes performance evaluation indicators and a weight corresponding to each performance evaluation indicator; The processing module is used to: filter out a target convergence strategy from the multiple convergence strategies according to the second configuration information and performance parameter information of each convergence strategy in the multiple convergence strategies.

17. The device according to claim 16, characterized in that The performance evaluation indicators include one or more of the following: Non-linear evaluation, and / or, linear evaluation; The nonlinear evaluation is performed based on the first nonlinear equation group and the performance parameter information of each convergence strategy in the multiple convergence strategies, and the linear evaluation is performed based on the iterative equation group corresponding to the first nonlinear equation group and the performance parameter information of each convergence strategy in the multiple convergence strategies; Wherein, the nonlinear evaluation includes one or more of the following: convergence evaluation, solution speed evaluation, and accuracy evaluation; The linear evaluation includes one or more of the following: convergence evaluation, solution speed evaluation, and accuracy evaluation.

18. The device according to any one of claims 12 to 17, characterized in that: The neural network model is obtained by training based on a data set, and the data set includes first training data and a label of the first training data, the first training data includes description information of a second nonlinear set of equations, the description information of the second nonlinear set of equations is used to describe characteristic information of the second nonlinear set of equations during a historical iteration process, and the label of the first training data includes a third convergence strategy corresponding to the second nonlinear set of equations.

19. The device according to claim 18, characterized in that The first training data corresponds to a plurality of groups of candidate convergence strategies and performance parameter information corresponding to each group of candidate convergence strategies; The interface module is used to: receive third configuration information input by a user, wherein the third configuration information includes the performance evaluation indicator, or includes the performance evaluation indicator and a weight corresponding to each of the performance evaluation indicators; The processing module is used to determine the third convergence strategy in the label of the first training data from multiple groups of candidate convergence strategies corresponding to the first training data according to the third configuration information and performance parameter information of each group of candidate convergence strategies corresponding to the first training data.

20. The device according to claim 19, characterized in that The interface module is used to: receive fourth configuration information input by a user, the fourth configuration information is used to indicate a strategy range to which the candidate convergence strategy belongs, the strategy range including one or more of the following: one or more convergence algorithms, one or more step size strategies, and one or more direction strategies; The processing module is used to obtain, according to the fourth configuration information, multiple groups of candidate convergence strategies corresponding to each first training data.

21. A computing device cluster, characterized in that: comprising at least one computing device, the at least one computing device comprising a processor and a memory; The processor is used to execute instructions stored in the memory so that the computing device cluster executes the method according to any one of claims 1-11.

22. A computer-readable storage medium, characterized in that: The computer-readable storage medium stores a computer program, and when the computer program runs on a processor, the processor is enabled to execute the method according to any one of claims 1 to 11.

23. A computer program product comprising instructions, characterized in that When the instructions are executed by a processor, the method according to any one of claims 1 to 11 is implemented.

Images