An adaptive optimization method and system for computationally intensive simulation solving

Abstract

The application relates to an adaptive optimization method and system for solving a computation-intensive simulation, and belongs to the technical field of simulation, and solves the problems that different simulation optimization methods are independent of each other and simulation efficiency is low in the prior art. The method comprises the following steps: S1, obtaining a CAE simulation requirement, including target simulation software, a plurality of design variables and an optimization target; S2, performing design sampling on each design variable to form a simulation design space, including a plurality of groups of design variable values; S3, determining a simulation optimal design group according to the simulation design space, the target simulation software and the optimization target; S4, updating the simulation design space by using the target simulation software and a plurality of proxy models based on the simulation design space, the simulation optimal design group and the optimization target, returning to S3 for iteration until an iteration stop condition is met; and S5, determining an optimal solution according to all simulation optimal design groups. The application realizes multi-link cooperation of a simulation solving process, adaptive optimization, and acceleration and optimization of simulation solving.

Description

Technical Field

[0001] This invention relates to the field of simulation technology, and in particular to an adaptive optimization method and system for solving computationally intensive simulations. Background Technology

[0002] With the deepening application of computer simulation technology in industrial design, simulation-based optimization (SBO) has become a key means to improve product performance. However, computationally intensive simulations are often time-consuming, with a single simulation taking anywhere from minutes to days or even months. Traditional optimization algorithms require tens of thousands of function evaluations, resulting in a mismatch between simulation efficiency and optimization theory in engineering applications. This makes the computational cost of solving practical engineering problems unacceptable. Different optimization techniques require algorithm selection and parameter configuration based on specific engineering problems, which places high demands on engineering application personnel and seriously hinders the practical application of related technologies.

[0003] Commonly used techniques include experimental design, surrogate models, optimization solutions, and multi-option evaluation. Each utilizes its corresponding theory to simplify problems from different perspectives, thereby reducing computational costs. Specifically, experimental design allows for sampling exploration of the engineering problem domain, enabling correlation analysis between design variables and target variables, and simplifying the selection and value range of design variables. Surrogate models (also known as approximate models) alleviate this contradiction to some extent by establishing computationally efficient surrogate models to replace the original simulation models. Optimization algorithms utilize different algorithms to achieve rapid optimization solutions for problems that match the algorithm. Multi-option evaluation, on the other hand, is used for multi-objective problems to achieve scientific evaluation and selection of solutions.

[0004] Existing technologies and limitations include the following: 1) Single-stage optimization techniques focus on improving a single stage, such as surrogate model construction, experimental design, or optimization algorithm, resulting in low optimization efficiency. 2) Fixed serial process techniques operate independently, with the three core stages of experimental design, surrogate model construction, and optimization algorithm running in a unidirectional serial manner. This leads to isolated stages, lack of global collaborative and adaptive capabilities, and deep integration. There is no bidirectional closed-loop feedback mechanism, and no dynamic collaborative mechanism with experimental design and optimization search. The model update strategy is rigid, failing to achieve overall cost reduction across the entire process. 3) Single surrogate model-dependent techniques, centered on the Kriging model, rely on model uncertainty to guide sampling updates. The optimization effect depends entirely on the fitting accuracy of a single model, and search efficiency and robustness are limited by the performance of this single surrogate model, making efficient convergence impossible within a limited number of simulations. 4) Algorithm selection and parameter configuration are highly dependent on expert experience, requiring manual configuration of all parameters for specific engineering problems. Different algorithms also have limitations in their applicability. The algorithm selection and parameter configuration processes place high demands on users, requiring them to not only model complex engineering problems as corresponding solution problems, but also to accurately classify the abstracted problems. Furthermore, it requires a deep understanding of the types of problems for which various algorithms are applicable and how to optimally configure all algorithm parameters for specific problems. Users need professional capabilities in engineering simulation, numerical optimization, and machine learning, resulting in extremely high barriers to entry and making it difficult for ordinary engineers to use, thus hindering the achievement of good results in engineering applications. 5) Local adaptive techniques: These only achieve local adaptive tuning of surrogate model parameters and optimization algorithm parameters, or rely on a single surrogate model or fixed algorithm combination. They do not cover the entire process of collaborative adaptation, cannot balance global exploration and local mining, are prone to getting trapped in local optima, have poor convergence reliability, and fail to achieve multi-level collaborative adaptation in experimental design, model selection, and optimization strategies. 6) The algorithm combination and parameter configuration are customized for specific engineering problems. The algorithm is strongly bound to the scenario and has no universality. New simulation scenarios require manual debugging again. It cannot achieve cross-domain and cross-scenario adaptive adaptation, and the engineering application cost is extremely high.

[0005] Therefore, there is an urgent need for an adaptive optimization method and system for computationally intensive simulation solutions, which can solve the problems of variable setting, algorithm selection, and algorithm parameter setting in the adaptive optimization process of simulation solutions, reduce the difficulty of technology application and implementation, realize multi-stage collaborative and adaptive optimization of the simulation solution process, and achieve efficient convergence of simulation solutions. Summary of the Invention

[0006] Based on the above analysis, the embodiments of the present invention aim to provide an adaptive optimization method and system for computationally intensive simulation solutions, in order to solve the problems of different simulation optimization methods being independent of each other and low simulation efficiency in the prior art.

[0007] On one hand, embodiments of the present invention provide an adaptive optimization method for computationally intensive simulation solutions, including: Step S1: Obtain CAE simulation requirements; wherein, the CAE simulation requirements include target simulation software, several design variables and corresponding optimization objectives; Step S2: Perform design sampling on each of the design variables to form a simulation design space; wherein, the simulation design space includes multiple sets of design variable values; Step S3: Determine the optimal simulation design group based on the simulation design space, the target simulation software, and the optimization objective; Step S4: Based on the simulation design space, the simulation optimal design group, and the optimization objective, update the simulation design space using the target simulation software, multiple surrogate models, and multiple optimization algorithms, and return to step S3 to repeat the iteration until the iteration stop condition is met; Step S5: Determine the optimal solution based on all the simulation optimal design groups.

[0008] Further, based on the simulation design space, the target simulation software, and the optimization objective, the optimal simulation design group is determined, including: Input the design variable values ​​of each group in the simulation design space into the target simulation software to obtain the corresponding simulation result variable values; Based on the simulation result variable values ​​and the optimization objective for each group, calculate the target evaluation value corresponding to the design variable values ​​for each group; Based on the evaluation values ​​of each target, the optimal simulation design group is determined from the simulation design space.

[0009] Furthermore, the CAE simulation requirements also include constraints; based on each set of simulation result variable values ​​and the optimization objective, the target evaluation value corresponding to each set of design variable values ​​is calculated, including: Based on the design variable values ​​described in each group and / or the simulation result variable values ​​described in each group, determine the constraint variable values ​​corresponding to the constraint conditions; Based on all the constraint variable values ​​and the constraint conditions, select several sets of the design variable values ​​from the simulation design space; Based on the multiple sets of simulation result variable values ​​corresponding to all the selected sets of design variable values, determine the multiple sets of target variable values ​​corresponding to the optimization objective. The target evaluation value is calculated based on the target variable values ​​of all groups and the optimization objective.

[0010] Furthermore, based on the simulation design space, the optimal simulation design group, and the optimization objective, the simulation design space is updated using the target simulation software and multiple surrogate models, including: Based on the simulation design space, a training dataset is constructed using the target simulation software; Using the training dataset, train multiple agent models to determine the optimal agent model; Based on the simulation optimal design group, a proxy design space is constructed using multiple optimization algorithms. Based on the proxy design space and the optimization objective, the optimal proxy model is used to determine the proxy optimal design group. The simulation design space is updated based on the agent's optimal design group.

[0011] Furthermore, using the training dataset, multiple agent models are trained to determine the optimal agent model, including: Using the training dataset, multiple agent models are trained to obtain multiple trained agent models; For each trained proxy model, calculate the corresponding model performance metric; The optimal proxy model is determined based on the model performance metrics of all trained proxy models.

[0012] Furthermore, based on the simulation optimal design group, a surrogate design space is constructed using various optimization algorithms. Based on the surrogate design space and the optimization objective, the optimal surrogate model is used to determine the surrogate optimal design group, including: Obtain the effect value of each design variable; Based on the simulation optimal design group, for each design variable, according to the corresponding effect value of the design variable, multiple optimization algorithms are used to sample and obtain values ​​to form multiple corresponding proxy design spaces; Input all the agent design spaces into the optimal agent model to obtain multiple sets of agent result variable values; Based on the optimization objective, all the agent design spaces, and the agent result variable values ​​of all groups, the optimal agent design group is determined.

[0013] Furthermore, based on the simulation optimal design group, for each design variable, according to the corresponding effect value of the design variable, multiple optimization algorithms are used to sample and obtain values, forming multiple corresponding surrogate design spaces, including: For each design variable, determine the corresponding scaling factor based on the effect value of the design variable. Based on the simulation optimal design group and each of the value scaling ratios, the value range of each design variable is scaled to determine a new value range; Based on the new value range of each design variable, multiple optimization algorithms are used to sample values ​​to obtain multiple proxy design spaces.

[0014] Furthermore, each of the aforementioned proxy models, optimization algorithms, and experimental design algorithms includes at least one of the following: exploration parameters, development parameters, and structure parameters. During repeated iterations, the parameters of each exploration class, each development class, and each structure class are updated through the following steps: Obtain the update count corresponding to the simulation design space; Obtain the performance metrics and performance change gradients corresponding to each of the aforementioned proxy models, optimization algorithms, and experimental design algorithms; Calculate the corresponding dynamic coupling coefficient based on the number of design variables and the performance change gradients of each variable; Update the corresponding exploration class parameters based on the number of updates, the performance change gradients, and the dynamic coupling coefficients. Update the corresponding development class parameters based on the number of updates and each of the performance change gradients; Update the corresponding structural class parameters based on the number of design variables and each of the performance indicators.

[0015] Furthermore, prior to step S4, the following steps are also included: Step S6: Obtain the optimal target variable value corresponding to the simulation optimal design group, and determine whether the optimal target variable value satisfies the optimization objective. If it does not satisfy the objective, proceed to step S4.

[0016] On the other hand, embodiments of the present invention provide an adaptive optimization system for computationally intensive simulation solutions, comprising: The requirement acquisition module is used to acquire CAE simulation requirements; wherein, the CAE simulation requirements include target simulation software, several design variables and corresponding optimization objectives; The experimental design module is used to sample each of the design variables to form a simulation design space; wherein, the simulation design space includes multiple sets of design variable values; The simulation solution module is used to determine the optimal simulation design group based on the simulation design space, the target simulation software, and the optimization objective. The parallel proxy module, based on the simulation design space, the simulation optimal design group, and the optimization objective, uses the target simulation software, multiple proxy models, and multiple optimization algorithms to update the simulation design space, and returns to the simulation solution module to repeat the iteration until the iteration stopping condition is met; The optimal solution determination module is used to determine the optimal solution based on all the simulation optimal design groups.

[0017] Compared with the prior art, the present invention can achieve at least one of the following beneficial effects: 1. Based on CAE simulation requirements, a simulation design space is formed. The optimal simulation design group is determined using the target simulation software. The simulation design space is updated through the target simulation software and multiple surrogate models. It is determined whether the iteration stopping condition has been met. This achieves multi-stage collaboration, adaptive iteration, and update optimization throughout the entire process of sampling (simulation design space) - modeling (training multiple surrogate models) - optimization (iteration stopping condition). This enables deep integration of experimental design, surrogate models, and scheme evaluation, achieving parallel accelerated solution and adaptive matching in the simulation solution process. This accelerates the optimization process, reduces simulation computation costs, and improves optimization efficiency and convergence reliability.

[0018] 2. Based on the simulation design space and target simulation software, multiple surrogate models are trained in parallel to determine the optimal surrogate model. The training dataset is constructed using data generated by the target simulation software to ensure that the training direction of the surrogate model continuously approaches the CAE simulation requirements. As the simulation design space is updated, the training dataset is continuously expanded. After multiple surrogate models are trained, the optimal surrogate model with the highest accuracy is dynamically selected to achieve the integration and collaboration between the surrogate model and the target simulation software. By utilizing the short solution time of the surrogate model, the optimal surrogate design group is determined, thereby accelerating the solution of CAE simulation requirements.

[0019] 3. Multiple proxy models, multiple optimization algorithms, and multiple experimental design algorithms are used. The initial values ​​of exploration, development, and structural parameters are adaptively set based on CAE simulation requirements. By parallelizing various algorithms or models, the problem of mismatch between a single model or algorithm and the scenario is avoided. As the simulation design space and proxy design space are iteratively updated, the parameters are adaptively adjusted based on the performance change gradient and dynamic coupling coefficient. This eliminates the need for manual configuration, reduces the requirements on users, and solves the problem that the parameter configuration of models or algorithms in existing technologies is highly dependent on expert experience. It improves the robustness and optimization efficiency of heterogeneous computing models in different application scenarios and solves the problem that the technical threshold for implementing computationally intensive simulation solutions in existing technologies is high.

[0020] In this invention, the above-described technical solutions can be combined with each other to achieve more preferred combinations. Other features and advantages of this invention will be set forth in the following description, and some advantages may become apparent from the description or be learned by practicing the invention. The objects and other advantages of this invention can be realized and obtained from what is particularly pointed out in the description and drawings. Attached Figure Description

[0021] The accompanying drawings are for illustrative purposes only and are not intended to limit the invention. Throughout the drawings, the same reference numerals denote the same parts. Figure 1 This is a flowchart illustrating an adaptive optimization method for computationally intensive simulation solutions in an embodiment of the present invention. Figure 2 This is a schematic diagram of the main modules of an adaptive optimization system for computationally intensive simulation solving in an embodiment of the present invention. Detailed Implementation

[0022] Preferred embodiments of the present invention will now be described in detail with reference to the accompanying drawings, which form part of this application and are used together with the embodiments of the present invention to illustrate the principles of the present invention, but are not intended to limit the scope of the present invention.

[0023] A specific embodiment of the present invention discloses an adaptive optimization method for solving computationally intensive simulations, such as... Figure 1 As shown, it includes: Step S1: Obtain CAE simulation requirements; wherein, the CAE simulation requirements include target simulation software, several design variables and corresponding optimization objectives.

[0024] In this embodiment, CAE (Computer Aided Engineering) refers to an approximate numerical analysis method that uses computers to help solve complex engineering and product structures, including structural strength, stiffness, buckling stability, dynamic response, thermal conduction, three-dimensional multibody contact, elastoplasticity, and other mechanical properties, as well as structural performance optimization design problems. CAE simulation requirements can be input by the user through a visual interface, referring to the simulation requirements for solving real business problems.

[0025] CAE simulation requirements include target simulation software, several design variables, and corresponding optimization objectives. The target simulation software needs to execute computationally intensive simulation processes. For example, the target simulation software may be one or more of Matlab, ICEM, Fluent, FluidSIM, and ANSYS, involving different simulation fields and software, or other existing simulation software. For instance, in industrial design fields such as aerospace, automotive manufacturing, energy equipment, and precision machinery, aerodynamic simulations (corresponding simulation software includes FluidSIM, Automation Studio, MATLAB / Simulink, etc.), structural mechanics simulations (corresponding simulation software includes ANSYS, ABAQUS, Hyperworks, Comsol, etc.), thermodynamic simulations (corresponding simulation software includes ANSYS, etc.), and multi-disciplinary, multi-simulation coupling are required. The corresponding target simulation software includes multiple simulation software programs. A single high-precision simulation can take 10 minutes, or even several hours or days, and optimization iterations require thousands of function evaluations, resulting in extremely high computational costs. Design variables refer to the objects of the actual business solution, the variables that need to be designed and valued; optimization objectives include the target variables of the actual business solution and the corresponding optimization thresholds or optimization directions.

[0026] Furthermore, CAE simulation requirements also include value restrictions for each design variable. For example, a real-world business requirement is "during the helicopter design process, within permissible limits, adjust design variables such as helicopter weight, fuel weight, and takeoff fuel consumption to maximize the helicopter's range and endurance." The corresponding CAE simulation requirements include the target simulation software Matlab, 11 design variables and their value restrictions, and the optimization objectives (maximum range, maximum endurance). The 11 design variables and their corresponding value restrictions are, in order: aircraft weight (6000kg-8000kg), fuel weight (700kg-1500kg), takeoff fuel consumption (20 kg / h - 40 kg / h), climb fuel consumption (30 kg / h - 50 kg / h). The optimal solution is determined through steps S2-S5 of this embodiment. This solution is the combination of design variable values ​​that best satisfies the optimization objective and the corresponding combination of target variable values. The 11 design variable values ​​are: total aircraft weight (6607 kg), fuel weight (1500 kg), takeoff fuel consumption (20 kg / h), climb fuel consumption (3000 kW - 1500 kW), difference between engine available power and power required for permanent speed (1000 kW - 1500 kW), climb horizontal speed (1 m / s - 18 m / s), horizontal cruise speed (30 m / s - 50 m / s), descent vertical speed (3 m / s - 8 m / s), cruise fuel consumption per kilometer (3 kg / km - 8 kg / km), takeoff time (200 s - 400 s), and landing time (120 s - 220 s). The target variables for the following parameters are: fuel consumption per kilometer (kg / h), difference between engine available power and power required for permanent speed (1500 kW), climb speed (12 m / s), horizontal cruising speed (50 m / s), descent speed (3 m / s), fuel consumption per kilometer (3 kg / km), takeoff time (400 s), and landing time (120 s). The target variable values ​​for the two corresponding target variables are: range 401.6 km and endurance 2.4 h. For example, a real-world business requirement is to "use the CST parametric method to parametrically represent the airfoil section, use ICEM meshing software to mesh the parametrically adjusted airfoil, and use Fluent to perform lift-to-drag ratio analysis to maximize the lift-to-drag ratio." The corresponding CAE simulation requirements include target simulation software (ICEM, Fluent), 18 design variables, and the optimization objective (maximum airfoil lift-to-drag ratio).

[0027] Step S2: Perform design sampling on each of the design variables to form a simulation design space; wherein the simulation design space includes multiple sets of design variable values.

[0028] Design sampling is performed on each design variable to obtain multiple values ​​for each design variable. The values ​​of each design variable are randomly combined to form multiple sets of design variable values, which constitute the simulation design space. Each set of design variable values ​​is a solution.

[0029] In this embodiment, multiple experimental design algorithms are used to sample each design variable. For example, five experimental design algorithms are included: full factorization, Latin hypercube, orthogonal array, and central composite. In other embodiments, one or more of these algorithms can be selected. Other experimental design algorithms from existing technologies can also be added as needed, such as optimal Latin hypercube and Hamersley sampling. In this embodiment, the number of solutions in the simulation design space is set according to the number of design variables. For example, the number of solutions in the simulation design space is 5-10 times the number of design variables.

[0030] Furthermore, the design sampling for each design variable is carried out within the corresponding value limits. For example, for design variable A, the value limits include an upper limit of 100 and a lower limit of 1. Then, the design sampling for design variable A is carried out within the range of 1-100.

[0031] By using different experimental design algorithms, values ​​can be taken within the range corresponding to the design variables, avoiding the limitations of sampling patterns of a single experimental design algorithm and enhancing the richness of the simulation design space.

[0032] Step S3: Determine the optimal simulation design group based on the simulation design space, the target simulation software, and the optimization objective.

[0033] Based on the simulation design space, target simulation software, and optimization objectives, determine the optimal simulation design group, including steps S31-S33.

[0034] Step S31: Input the design variable values ​​of each group in the simulation design space into the target simulation software to obtain the corresponding simulation result variable values.

[0035] The design variable values ​​of each set in the simulation design space are input into the target simulation software to obtain the corresponding simulation result variable values. Each set of design variable values ​​in the simulation space is then input into the target simulation software (e.g., ANSYS, ABAQUS, FLUENT), which performs simulation calculations to complete a high-precision simulation solution for each set of design variable values, obtaining the corresponding simulation results. The simulation results for each set of design variable values ​​include the simulation result variable values ​​of several result variables; that is, one set of design variable values ​​corresponds to one set of simulation result variable values. In this implementation, the result variables include the target variables, and the corresponding simulation results include the target variable values, such as the range of 401.6 km and the endurance of 2.4 h in the previous example.

[0036] Furthermore, to reduce computational load, during the iterative execution of step S31, a simulation repeatability check is performed on the simulation design space. If a set of design variable values ​​in the simulation design space has already been input into the target simulation software during the previous execution of step S31, it does not need to be input again, thereby reducing the computational load of step S31 during repeated iterations. Through the simulation repeatability check, each iteration only performs simulation calculations on unexplored combinations of design variable values, avoiding redundant simulations, reducing unnecessary simulation computation overhead, and shortening the overall optimization cycle.

[0037] Step S32: Calculate the target evaluation value corresponding to each set of design variable values ​​based on the simulation result variable values ​​and the optimization objective for each set.

[0038] First, based on the single set of simulation result variable values ​​corresponding to each set of design variable values, the single set of target variable values ​​corresponding to the optimization target are determined. In this embodiment, the result variables generated by the target simulation software include the target variables corresponding to the optimization target. According to the name of the target variable, the variable values ​​corresponding to the target variable are extracted from each set of simulation result variable values, i.e., the target variable values. If there are multiple target variables, the corresponding target variable values ​​are extracted one by one to form a set of target variable values.

[0039] Secondly, based on the target variable values ​​and optimization objectives corresponding to each set of design variable values, the target evaluation value corresponding to each set of design variable values ​​is calculated. In this embodiment, there are multiple target variables, and the optimization objectives include the optimization thresholds for each target variable. The target evaluation value is calculated using a target evaluation function. For example, In the formula, The target evaluation value, The number of target variables, For the first The coefficient of the nth objective variable, if the optimization objective is the nth objective variable If the optimization direction for each objective variable is to maximize it, then... If the value is positive, then the optimization objective is... If the optimization direction of the objective variable is to be as small as possible, then... A negative value ensures that the optimization direction of each objective variable is unified. For the first The target deviation corresponding to the nth target variable, i.e. the nth target variable The target variable values ​​corresponding to each target variable With optimized threshold The difference, for example It is understandable that if the optimization objective includes the optimization direction of the objective variable, such as "maximum", then the objective deviation corresponding to the objective variable is taken as the value of the objective variable itself.

[0040] Furthermore, CAE simulation requirements also include constraints, and step S32 can also be executed according to steps S321-S324.

[0041] Step S321: Determine the constraint variable values ​​corresponding to the constraint conditions based on the design variable values ​​of each group and / or the simulation result variable values ​​of each group.

[0042] Based on the single set of simulation result variable values ​​corresponding to each set of design variable values, determine the constraint variable values ​​corresponding to the constraint conditions. The constraint conditions include several constraint variables and the constraint threshold or constraint direction for each constraint variable. The constraint variables may be the same as or different from the design variables or target variables. For example, when designing a cuboid, the design variables are length and height, the target variable is area, and the constraint variable is perimeter.

[0043] If the constraint variable is the same as the design variable or the target variable, or if the result variable includes the constraint variable, then according to the name of the constraint variable, extract the variable value corresponding to the constraint variable from each group of design variable values ​​or the corresponding single group of simulation result variable values. If there are multiple constraint variables, extract the corresponding constraint variable values ​​one by one to form a group of constraint variable values.

[0044] Step S322: Based on all the constraint variable values ​​and the constraint conditions, select several sets of design variable values ​​from the simulation design space.

[0045] Based on the constraint variable values ​​and constraint conditions corresponding to each set of design variable values, several sets of constraint variable values ​​that satisfy the constraint conditions are selected, and the corresponding single set of design variable values ​​are selected from the simulation design space to obtain several sets of selected design variable values.

[0046] Furthermore, if no constraint variable values ​​satisfy the constraint conditions, return to step S2 to redetermine the simulation design space. In other embodiments, the method for calculating the target evaluation value can also be referred to to calculate the constraint similarity between each group of constraint variable values ​​and the constraint conditions, and select the top M groups (e.g., 3 groups) of constraint variable values ​​with the highest similarity, and use the corresponding design variable values ​​as the selected M groups of design variable values.

[0047] Step S323: Based on the multiple sets of simulation result variable values ​​corresponding to all the selected sets of design variable values, determine the multiple sets of target variable values ​​corresponding to the optimization target.

[0048] In this embodiment, based on the multiple sets of simulation result variable values ​​corresponding to all the selected sets of design variable values, the target variable values ​​corresponding to the optimization target are determined from each set of simulation result variable values. That is, for each set of design variable values, the single set of target variable values ​​corresponding to the optimization target are determined from the corresponding single set of simulation result variable values.

[0049] Step S324: Calculate the target evaluation value based on the target variable values ​​of all groups and the optimization target.

[0050] In this embodiment, based on all target variable values ​​and optimization objectives determined in step S323, the target evaluation value corresponding to each group of selected design variable values ​​is calculated using the target evaluation function. For example, In the formula, The target evaluation value, The number of target variables, For the first The coefficients of the target variables, For the first The target deviations corresponding to each target variable.

[0051] Step S33: Determine the optimal simulation design group from the simulation design space based on the target evaluation values.

[0052] Based on the target evaluation values ​​corresponding to each group of design variable values, select the single group of design variable values ​​corresponding to the maximum target evaluation value from the simulation design space as the optimal design group for simulation.

[0053] Step S4: Based on the simulation design space, the simulation optimal design group, and the optimization objective, update the simulation design space using the target simulation software and multiple proxy models, and return to step S3 to repeat the iteration until the iteration stop condition is met.

[0054] Specifically, based on the simulation design space, the optimal simulation design group, and the optimization objective, the simulation design space is updated using the target simulation software and multiple surrogate models. The process returns to step S3, and step S3 is executed again based on the new simulation design space to obtain a new optimal simulation solution. It is then determined whether the iteration stopping condition is met. If not, step S4 is executed again based on the updated simulation design space from step S4 and the new optimal simulation solution from step S3. The optimal simulation design group is then re-determined based on step S3, and the iteration is repeated until the iteration stopping condition is met. The iteration stopping condition can be a default condition (e.g., a default of 5 iterations) or it can be included in the CAE simulation requirements and set by the user.

[0055] In this embodiment, the surrogate model refers to a computational model constructed using machine learning or numerical fitting methods that can replace the actual high-precision simulation process (i.e., the target simulation software). It has a short solution time (e.g., 1ms) and continuously reduces the deviation between the surrogate model and the target simulation software through training on a training dataset. For example, surrogate models include multinomial response surface models, Kriging models, radial basis function models, and deep learning neural network models. In other embodiments, the surrogate model can be adjusted as needed, for example, by adding a random forest regression model or a support vector regression model.

[0056] In this embodiment, the iteration stopping condition includes an iteration count threshold and a convergence condition. The iteration stopping condition is satisfied when the number of times step S3 is executed reaches the iteration count threshold, or when the relative rate of change between the simulation optimal design groups determined by step S3 is not greater than a first rate of change threshold (e.g., 1e-3) after N consecutive (e.g., 3) executions, or when the relative rate of change between the groups ... the relative rate of change between the groups is not greater than a first rate of change threshold (e.g., 1e-3). The relative rate of change between the single-group result variable value, target variable value, or constraint variable value corresponding to the simulation optimal design group determined in step S3 is not greater than the second rate of change threshold (e.g., 1e-4) in each (e.g., 4 times). In other embodiments, it is also possible to set the condition that both conditions must be met simultaneously to determine that the iteration stop condition is met.

[0057] Furthermore, based on the simulation design space, the simulation optimal design group, and the optimization objective, the simulation design space is updated using the target simulation software, multiple surrogate models, and various optimization algorithms, including steps S41-S44.

[0058] Step S41: Based on the simulation design space, construct a training dataset using the target simulation software.

[0059] The design variable values ​​of each set in the simulation design space are input into the target simulation software to obtain the corresponding simulation result variable values. A training dataset is constructed based on the design variable values ​​and the simulation result variable values. In this embodiment, the execution result of step S31 can be directly used to construct the training dataset. The training dataset includes multiple samples, and each sample includes a set of design variable values ​​and a corresponding set of simulation result variable values.

[0060] It should be noted that during the iterative execution of step S4, based on the new simulation design space, the design variable values ​​of each group are input into the target simulation software to obtain the corresponding new simulation result variable values. The design variable values ​​of each group in the new simulation design space and the corresponding simulation result variable values ​​are added to the training dataset constructed in the previous execution of step S4. That is, as steps S3 and S4 are iteratively executed, the training dataset is continuously updated and expanded, making the training dataset better reflect the CAE simulation requirements and the data processing process of the target simulation software, so as to improve the degree of conformity between the optimal surrogate model determined in step S42 and the CAE simulation requirements, and obtain a more accurate surrogate model.

[0061] Step S42: Using the training dataset, train multiple agent models to determine the optimal agent model.

[0062] Using a training dataset, multiple surrogate models are trained. From these trained models, the one with the best performance metrics is selected as the optimal surrogate model. A training dataset is constructed based on the simulation design space and the target simulation software. Each trained surrogate model acquires the ability to derive outcome variables from design variables. Furthermore, as training progresses, the surrogate model can output surrogate outcome variable values ​​that more closely approximate the simulation outcome variable values ​​for each set of design variable values; that is, the surrogate model can more accurately express the relationship between design variables and outcome variables.

[0063] Understandably, each time step S4 is executed, the optimal surrogate model determined in step S42 may be different as the training dataset expands. This is to select a surrogate model that better addresses the target simulation software, so that the calculation of the optimal surrogate model can represent the time-consuming target simulation software more quickly and accurately, thereby accelerating the single-round solution (step S43) and speeding up the entire optimization process.

[0064] In this embodiment, multiple agent models are trained using a training dataset to determine the optimal agent model, including steps S421-S423.

[0065] Step S421: Using the training dataset, train multiple agent models to obtain multiple trained agent models.

[0066] Using the training dataset, multiple surrogate models are trained to obtain multiple trained surrogate models. For example, the single-set design variable values ​​of each sample in the training dataset are used as inputs to the surrogate models to obtain the predicted values ​​output by each surrogate model. The single-set simulation result variable values ​​of each sample are used as the true values. The cross-entropy loss is calculated using the predicted and true values ​​of each surrogate model. The cross-entropy loss is then used to iteratively optimize each surrogate model until at least the model iteration optimization stopping condition is met (e.g., 10 iterations). This yields a trained surrogate model. Alternatively, existing techniques for training other models can be used; no restrictions are placed here.

[0067] It should be noted that during the iterative execution of step S4, multiple proxy models are trained based on the updated and expanded training dataset.

[0068] Step S422: For each trained proxy model, calculate the corresponding model performance index.

[0069] In this embodiment, based on the training dataset, the corresponding model performance metric is calculated for each trained proxy model. For example, the training dataset is divided into a training set and a validation set. Each proxy model is trained based on the training set to obtain a trained proxy model. The model performance metric is then calculated based on the validation set. In this embodiment, the coefficient of determination, root mean square error (RMSE), and single-sample inference time are used to calculate the model performance metric. For example, the coefficient of determination for a given proxy model... Root mean square error Single-sample inference time ,in, For the first The true value of a sample, that is, the value of a single set of simulation result variables included in that sample; No. The predicted value corresponding to each sample is the model output value obtained after inputting the single set of design variable values ​​included in the sample into the surrogate model. The number of samples; for The mean of the true values ​​of each sample; For the first The inference time for a sample is the time from when the sample is input into the surrogate model until the corresponding predicted value is obtained.

[0070] Step S423: Determine the optimal proxy model based on the model performance metrics of all trained proxy models.

[0071] The optimal surrogate model is determined based on the performance metrics of all trained surrogate models. In this embodiment, the optimal surrogate model is selected using the coefficient of determination, root mean square error (RMSE), and single-sample inference time. For example, if there are no multiple surrogate models with similar coefficients (e.g., the difference in coefficients is less than the coefficient deviation threshold, such as 0.2), the surrogate model with the coefficient of determination closest to 1 is selected as the optimal surrogate model. If there are multiple surrogate models with similar coefficients, the RMSE of these surrogate models is compared. If the RMSEs are not similar, the surrogate model with the smallest RMSE is selected as the optimal surrogate model. If the RMSEs are similar, the surrogate model with the shortest single-sample inference time is selected as the optimal surrogate model. In other embodiments, a weighted sum of the coefficient of determination, RMSE, and single-sample inference time can be used to determine the overall model performance metric, and the surrogate model with the highest overall performance can be selected as the optimal surrogate model.

[0072] Multiple approximate models are trained in parallel using a training dataset. The optimal surrogate model is selected based on model performance metrics. During the iteration process, the training dataset is continuously expanded and updated, ensuring that the selected optimal surrogate model continuously approximates the real business problem (i.e., the target simulation software). This simplifies and replaces the time-consuming simulation solution process, accelerating the optimization speed of step S43. Simultaneously, the parallel training of multiple surrogate models and the use of a unified evaluation accuracy criterion to select the current optimal surrogate model effectively avoids biases caused by the limitations of a single surrogate model's underlying principles. This ensures that subsequent optimization processes are always based on the most reliable approximate model, improving convergence stability and the quality of the final simulation optimal design group. This, combined with the optimization algorithm and simulation design space updates, achieves a balance between global and local exploration, reducing the risk of premature convergence.

[0073] Step S43: Based on the simulation optimal design group, construct a proxy design space using multiple optimization algorithms. Based on the proxy design space and the optimization objective, determine the proxy optimal design group using the optimal proxy model.

[0074] Based on the simulation optimal design group, multiple surrogate design spaces are constructed using various optimization algorithms. Based on the multiple surrogate design spaces and optimization objectives, the optimal surrogate design group is determined using the optimal surrogate model, including steps S431-S434.

[0075] Step S431: Obtain the effect value of the design variable corresponding to each design variable.

[0076] In this embodiment, the effect value of the design variable is calculated using the following formula: ,in, For the first The effect value of the design variable for each design variable. For the first The fluctuation of the variable corresponding to each design variable For all design variables, the error variability is determined. For example, an analysis of variance is performed based on the training dataset to determine the error variability and the variability of each design variable, according to the formula... Calculate the effect value of the design variable for each design variable. The higher the effect value of the design variable, the stronger the sensitivity of the target variable to that design variable.

[0077] For example, total fluctuation In the formula, For the first Group simulation result variable values, This is the global mean, which is the average of the variable values ​​in the simulation results of all groups. The number of variable values ​​in a single set of simulation results; the variable fluctuation corresponding to each design variable. In the formula, For the first The number of single-group design variable values ​​that each value of a design variable participates in. For the first The total number of values ​​that a design variable can take. For the first The first design variable The mean of all simulation result variable values ​​corresponding to each value; error fluctuation , This represents the total number of design variables. For example, the training dataset includes 6 samples, with 6 sets of design variable values ​​as (A1-B1), (A1-B2), (A1-B3), (A2-B1), (A2-B2), and (A2-B3), corresponding to 6 sets of simulation result variable values ​​as follows: , , , , , For example, if design variable A is the first design variable and design variable B is the second design variable, then... , Since there are only two design variables and a full factorial design is used, the number of single-group design variable values ​​that each value of design variable A participates in is equal to the total number of values ​​for design variable B. , Similarly, for design variable B, we have , .

[0078] In other embodiments, variance analysis and Pearson correlation coefficient calculations can be performed based on the training dataset to determine the effect value of each design variable.

[0079] Furthermore, in step S32, when calculating the target evaluation value based on the target deviation, the effect value of the design variable can be used to evaluate the first... The target deviation of each target variable Make corrections using the formula. Calculate the corrected target deviation, where, For the first The effect value of the design variable for each design variable. The normalized version The design variable values ​​corresponding to each design variable. The number of design variables.

[0080] Step S432: Based on the simulation optimal design group, for each design variable, according to the corresponding design variable effect value, various optimization algorithms are used to sample and obtain values ​​to form multiple corresponding surrogate design spaces.

[0081] Based on the simulation optimal design group, for each design variable, according to the corresponding design variable effect value, multiple optimization algorithms are used to sample and obtain values ​​to form multiple corresponding surrogate design spaces, including steps S4321-S4323.

[0082] Step S4321: For each design variable, determine the corresponding scaling ratio based on the corresponding effect value of the design variable.

[0083] In this embodiment, a mapping relationship between the effect value of the design variable and the scaling ratio is established based on the historical simulation data of the target simulation software. For each design variable, the corresponding scaling ratio is determined based on the effect value of the design variable and the established mapping relationship. This allows for different degrees of narrowing of the value range for design variables with different result sensitivities. For example, the scaling ratio corresponding to a design variable with high sensitivity (e.g., an effect value of not less than 0.6) is small (e.g., 0.1-0.3), which facilitates step S4322 in narrowing the value range of the design variable around the optimal design group of the simulation, and realizing local fine-grained exploration and solution. The scaling ratio corresponding to a design variable with low sensitivity (e.g., an effect value of less than 0.6) is large (e.g., 0.5-1.0), which retains a relatively large value range, taking into account both local and global exploration.

[0084] For example, establishing a mapping relationship between design variable effect values ​​and scaling ratios based on historical simulation data from the target simulation software includes: 1) Based on historical simulation data, extracting the last simulation design space corresponding to each CAE simulation requirement, the value constraints of each design variable, and the design variable effect value of each design variable; 2) For each design variable, based on the maximum and minimum values ​​of the last simulation design space, using the difference between the maximum and minimum values ​​as the historical value range of the design variable, calculating the historical scaling ratio corresponding to the historical value range and value constraints; 3) Performing cluster analysis on multiple design variable effect values ​​and multiple historical scaling ratios for all design variables in the historical simulation data, determining the scaling ratio range corresponding to different design variable effect values, standardizing and unifying them, and forming a mapping relationship between design variable effect values ​​and scaling ratios. Step S4322: Based on the simulation optimal design group and each of the value scaling ratios, scaling the value range of each design variable to determine a new value range.

[0085] For each design variable, based on the corresponding simulation optimal design variable value in the simulation optimal design group, the value range of each design variable is continuously focused to the vicinity of the simulation optimal design variable value according to the corresponding value scaling ratio, and a new value range is determined. This realizes the dynamic scaling of the value range of design variables based on the simulation optimal design group within the value constraints, and allows for a detailed exploration of the periphery of the simulation optimal design group.

[0086] For example, design variable A currently ranges from 1 to 100, and design variable B currently ranges from 6 to 45. Based on the effect values ​​of the two design variables, the corresponding scaling ratios are determined to be 0.4 and 0.5, respectively. In the simulation optimal design group, the design variable values ​​of the two design variables are 30 and 15, respectively. Then, with 30 and 10 as the center, the new value ranges are determined according to the corresponding scaling ratios, which are 11-50 and 6-25, respectively.

[0087] Step S4323: Based on the new value range of each design variable, sample values ​​using various optimization algorithms to obtain multiple proxy design spaces.

[0088] For each design variable, within the corresponding new value range, multiple optimization algorithms are used to sample and obtain several sets of design variable values ​​corresponding to each optimization algorithm. These sets of design variable values ​​for each optimization algorithm form the corresponding surrogate design space.

[0089] In this embodiment, the optimization algorithms include intelligent optimization algorithms (such as adaptive particle swarm optimization and adaptive simulated annealing) and numerical optimization algorithms (such as sequential quadratic programming, downhill simplex algorithm, and Hawke-Gevis algorithm). Intelligent optimization algorithms, also known as metaheuristic algorithms, refer to a general optimization framework that does not rely on the specific mathematical properties of the objective function (such as differentiability or continuity). It finds approximate globally optimal design sets in complex design spaces by simulating natural phenomena, biological behaviors, or the laws of social systems. Its core characteristics are random search and group collaboration, effectively escaping local optima, and it is suitable for complex optimization problems that are high-dimensional, nonlinear, multimodal, or discrete. Numerical optimization algorithms are based on mathematical analysis (such as calculus and linear algebra) and iteratively approximate the optimal combination of design values ​​of the objective function. Their core reliance is on the differentiability or continuity of the objective function. They are suitable for problems with well-defined and quantifiable structures, pursuing high accuracy and fast convergence. In other embodiments, optimization algorithms can be selected from the prior art as needed, such as adding genetic algorithms or differential evolution algorithms.

[0090] Furthermore, based on CAE simulation requirements, the algorithm parameters of each optimization algorithm are determined to achieve automated configuration of the optimization algorithm parameters. In other embodiments, the algorithm parameters of each optimization algorithm are determined according to the number of design variables and the model performance index of the surrogate model. If the algorithm parameters of the optimization algorithm include the number of iterations, then based on the number of iterations, the iteration step S4323 is repeated to determine multiple surrogate design spaces for the optimization algorithm.

[0091] Taking the adaptive particle swarm optimization (PSO) algorithm as an example, the algorithm parameters are determined based on the number of design variables and the determination coefficient of the optimal surrogate model in the CAE simulation requirements, thus achieving automated configuration of the algorithm parameters. In this embodiment, the algorithm parameters of the adaptive PSO algorithm include the population size and the number of iterations. The number of single design variable values ​​in the surrogate design space obtained by executing step S4323 in a single execution is determined based on the population size. For example, if the population size is 55, then the corresponding surrogate design space includes at least 55 sets of design variable values. The number of times step S4323 is executed is determined based on the number of iterations. For example, if the number of iterations is 10, then step S4323 is executed at least 10 times for the optimization algorithm. For instance, the population size and the number of iterations are determined based on the number of variables, and the population size and the number of iterations are corrected based on the determination coefficient of the optimal surrogate model. Number of iterations In the formula, For population size, For the number of iterations, The coefficient of determination represents the optimal surrogate model. A higher coefficient indicates a more accurate optimal surrogate model and a lower degree of population expansion. Use the base scaling factor (e.g., 5-10). To determine the number of design variables, The fewer the number of design variables, the better, as the inverse dimension adjustment coefficient (e.g., 5-10) is used. The larger the value, the greater the population size, allowing for fewer design variables to be added and sampling increased, thus ensuring the richness of the corresponding surrogate design space. The iteration coefficient (e.g., 5-20) increases with the number of design variables to avoid insufficient search for problems with multiple design variables. Accordingly, for this optimization algorithm, the optimal surrogate model needs to be calculated... Next, get Group proxy result variable values ​​to ensure sufficient search strength.

[0092] Furthermore, for optimization algorithms that require repeated iterations of step S4323, a number of surrogate design spaces equal to the number of iterations can be obtained. Multiple surrogate design spaces of the optimization algorithm can be processed simultaneously using step S433. Alternatively, based on the iteration mechanism of the optimization algorithm, the last surrogate design space can be used as the surrogate design space of the optimization algorithm. For example, the adaptive particle swarm optimization algorithm iterates 10 times. The first execution of step S4323 yields surrogate design space 1. Surrogate design space 1 is input into the optimal surrogate model to obtain multiple sets of surrogate result variable values. Using the optimal design group selection method inherent in the optimization algorithm itself, or referring to steps S32-S33 to calculate the corresponding target evaluation value, the optimal design group 1 corresponding to the optimization algorithm is determined. The adaptive particle swarm optimization algorithm adjusts its sampling strategy based on the optimal design group 1 (e.g., sampling more concentrated around the optimal design group 1), and samples again to obtain surrogate design space 2. This process is repeated iteratively, and the last obtained surrogate design space 10 is used as the surrogate design space of the adaptive particle swarm optimization algorithm to execute subsequent steps S433. In other embodiments, an early termination strategy can also be set. For example, starting from the optimal design group 2 corresponding to surrogate design space 2, convergence judgment is performed. If convergence is determined (e.g., the difference between two consecutive optimal design groups is less than 0.1%), a new surrogate design space is obtained based on the converged optimal design group, which serves as the last surrogate design space of the optimization algorithm, i.e., the surrogate design space of the optimization algorithm, and is used to execute step S433. In addition, during the iteration process, the simulation repeatability judgment method can be used to perform surrogate repeatability judgment. For single-group design variable values ​​that have already been input into the optimal surrogate model, there is no need to input them again.

[0093] By using the effect value of each design variable, the range of values ​​for each design variable is dynamically adjusted and scaled. A local range of values ​​is determined around the optimal design group in the simulation, and the optimal solution is explored. This ensures that all explorations revolve around the optimal design group in the simulation, while also ensuring that the scope of exploration is continuously narrowed, so as to determine the optimal solution more efficiently and complete the simulation solution.

[0094] Furthermore, if the optimization algorithm includes intelligent optimization algorithms and numerical optimization algorithms, and the algorithm parameters of the intelligent optimization algorithm include the number of iterations, step S4323 further includes: determining whether the optimal design group corresponding to the intelligent optimization algorithm has converged; if it has converged, then based on the converged optimal design group, for each design variable, a new range of values ​​is determined according to the corresponding effect value of the design variable, and the numerical optimization algorithm is used to sample and obtain values ​​to form a new surrogate design space; step S433 is executed based on all surrogate design spaces of the numerical optimization algorithm or the new surrogate design space.

[0095] By implementing multiple optimization algorithms in parallel, the range of design variable values ​​is fully explored. By dynamically combining intelligent optimization algorithms and numerical optimization algorithms, the characteristics of different optimization algorithms are fully utilized, overcoming the limitations of premature convergence of intelligent optimization algorithms and local optima of numerical optimization algorithms. This achieves a dynamic combination of global optimization exploration by intelligent algorithms and local tuning by numerical algorithms, thus accelerating the overall optimization process.

[0096] Step S433: Input all the agent design spaces into the optimal agent model to obtain multiple sets of agent result variable values.

[0097] Input the design variable values ​​of each group in the entire surrogate design space into the optimal surrogate model, and output the single predicted value corresponding to each group of design variable values. This yields multiple sets of surrogate result variable values, representing the variable values ​​of each result variable obtained based on the optimal surrogate model.

[0098] Furthermore, data sharing is implemented across all surrogate design spaces to avoid redundant calculations and reduce the computational load of the optimal surrogate model. For example, for a set of design variable values ​​that exist in both surrogate design space (A) and surrogate design space (B), only the optimal surrogate model needs to be input once, and the corresponding single set of surrogate result variable values ​​are fed back to the two surrogate design spaces (or the corresponding optimization algorithm) for subsequent determination of the optimal design group and / or the optimal surrogate design group.

[0099] Step S434: Determine the optimal agent design group based on the optimization objective, all agent design spaces, and the agent result variable values ​​of all groups.

[0100] Based on the optimization objective, all agent design spaces, and all group agent result variable values, the optimal agent design group is determined. In this embodiment, steps S4341-S4342 are included.

[0101] Step S4341: Based on the optimization objective, all surrogate design spaces corresponding to each optimization algorithm, and the corresponding surrogate result variable values, determine the corresponding optimal design group.

[0102] Based on the optimization objective, all surrogate design spaces corresponding to each optimization algorithm, and the corresponding surrogate result variable values ​​for each group, the optimal design group corresponding to that optimization algorithm is determined. For example, the optimal design group selection method inherent in the optimization algorithm itself can be used to determine the optimal design group corresponding to that optimization algorithm. Alternatively, referring to steps S32-S33, for each optimization algorithm, based on the optimization objective, the design variable values ​​for each group, and the corresponding surrogate result variable values ​​for each group, the corresponding target evaluation value is calculated, and the optimal design group corresponding to each optimization algorithm is determined based on the target evaluation value.

[0103] Step S4342: Determine the surrogate optimal design group based on the optimal design group corresponding to each optimization algorithm.

[0104] Based on the single-group surrogate result variable values ​​corresponding to the optimal design group of each optimization algorithm, calculate the target evaluation value corresponding to the optimal design group of each optimization algorithm, and determine the surrogate optimal design group from the optimal designers corresponding to various optimization algorithms.

[0105] In other embodiments, step S434 may also determine the optimal agent design group for all agent design spaces and all group agent result variable values, referring to steps S32-S33.

[0106] By combining optimization algorithms with optimal surrogate models, the time-consuming simulation process of the target simulation software is replaced, accelerating the parallel optimization solution process of multiple optimization algorithms. The sampling range of each design variable for the optimization algorithms is updated based on the simulation optimal design group, and the algorithm parameters of each optimization algorithm are determined according to CAE simulation requirements. The optimal surrogate model is used for rapid optimization search, and the surrogate optimal design group is fed back to step S44.

[0107] Step S44: Based on the agent optimal design group, update the simulation design space using a variety of experimental design algorithms.

[0108] Based on the surrogate optimal design group, multiple experimental design algorithms are used to sample each design variable to obtain multiple design variable values ​​for each design variable. The design variable values ​​of different design variables are randomly combined, and the design variable values ​​of each group are included in the simulation design space to complete the update of the simulation design space.

[0109] First, based on the surrogate optimal design group, for each design variable, a new value range is determined according to the corresponding value scaling ratio, which can be performed as per step S4233. It is understood that the surrogate optimal design group may differ from the simulation optimal design group, and the value range determined in step S44 will also differ from the value range determined in step S4322. For example, the value range of design variable A determined in step S4322 is 11-50, while the value range determined in step S44 is 21-60. In other embodiments, during iterative execution of step S44, the value scaling ratio can be adjusted or different experimental design algorithms can be selected based on the distance between several consecutive surrogate optimal design groups (e.g., Euclidean distance). For example, if the distance between five consecutive surrogate optimal design groups continuously decreases, the value scaling ratio is reduced to further narrow the value range of the design variable and accelerate the solution process.

[0110] Secondly, for each design variable, multiple sets of design variable values ​​are obtained using various experimental design algorithms to update the simulation design space. For example, design variable A currently ranges from 1 to 100, and design variable B currently ranges from 6 to 45. Based on the effect values ​​of the two design variables, the corresponding scaling ratios are determined to be 0.4 and 0.5, respectively. In the surrogate optimal design group, the design variable values ​​corresponding to the two design variables are 40 and 20, respectively. Then, using 40 and 20 as centers, new value ranges are determined according to the corresponding scaling ratios: 21-60 and 11-30, respectively. The Latin hypercube and central loading methods are used to generate multiple values ​​for the two design variables within the intervals of 21-60 and 11-30, respectively. These multiple values ​​are then randomly combined to form multiple sets of design variable values, which are added to the simulation design space.

[0111] Furthermore, before updating the simulation design space based on the surrogate optimal design group, the process includes: determining whether the surrogate optimal design group is the simulation optimal design group; if so, correcting the scaling ratio; and updating the simulation design space based on the surrogate optimal design group and the corrected scaling ratio. By comparing the surrogate optimal design group with the simulation optimal design group from step S3, it is determined whether to adjust the scaling ratio. If both are the same, increasing the scaling ratio yields a larger value range, ensuring that the updated simulation design space includes a sufficient number of new variable design values ​​and avoiding getting trapped in local optima.

[0112] By using a surrogate optimal design group and effect values ​​of design variables, the range of values ​​for each design variable is dynamically adjusted and scaled. The exploration of the optimal solution revolves around the surrogate optimal design group, ensuring that all explorations are conducted within this group while continuously narrowing the design space and reducing the scope of exploration. This achieves automatic optimization of the simulation design space, improves the efficiency of design space exploration, and determines the optimal solution more efficiently, thus completing the simulation solution. Furthermore, the combination of multiple experimental design algorithms enables a combination of coarse-grained and fine-grained sampling, avoiding the limitations of sampling data under a single experimental design algorithm.

[0113] Furthermore, each surrogate model, optimization algorithm, and experimental design algorithm includes at least one of the following: exploration parameters, development parameters, and structure parameters. For example, the population size mentioned in step S4323 is a structure parameter of the optimization algorithm, and the number of iterations is a development parameter. During the repeated iteration of step S4, after each execution of step S44, each exploration parameter, development parameter, and structure parameter is updated through steps a-f. When step S4 needs to be executed again, steps S41-S44 are executed with the updated exploration parameters, development parameters, and structure parameters.

[0114] Step a: Obtain the number of updates corresponding to the simulation design space.

[0115] Obtain the number of updates corresponding to the simulation design space, i.e., the number of times step S44 is executed.

[0116] Step b: Obtain the performance indicators and performance change gradients corresponding to each of the aforementioned proxy models, optimization algorithms, and experimental design algorithms.

[0117] The performance metrics and performance change gradients for each surrogate model, each optimization algorithm, and each experimental design algorithm are obtained. In this embodiment, the loss function value corresponding to each trained surrogate model is used as the performance metric for that surrogate model, and the change in the loss function value is used as the corresponding performance change gradient. The Chebyshev minimum distance in the surrogate design space of each optimization algorithm after two consecutive executions of step S4 is used as the performance metric for that optimization algorithm, and the change in the Chebyshev minimum distance is used as the performance change gradient. The Chebyshev minimum distance in the simulation design space after two consecutive executions of step S4 is used as the performance metric for each experimental design algorithm, and the change in the Chebyshev minimum distance is used as the performance change gradient.

[0118] Taking the simulated design space as an example, this section explains the calculation process of the corresponding Chebyshev minimum distance and the change of the Chebyshev minimum distance. First, the Chebyshev minimum distance is calculated; for example, the... The next execution step, S44, updates the simulation design space. , No. The next execution step, S44, updates the simulation design space. Simulation design space , The corresponding Chebyshev minimum distances are respectively , ,in , Represents the simulation design space or The Middle Group design variable values The One design variable value, Represents the simulation design space or The Middle Group design variable values The One design variable value, Indicates the first Group design variable values With the Group design variables The Chebyshev distance is the maximum value of the difference between individual design variable values ​​corresponding to two sets of design variable values. Represents the simulation design space The minimum value among all Chebyshev distances, Represents the simulation design space The minimum Chebyshev distance is calculated by traversing all sets of design variable values ​​in the simulation design space, calculating the Chebyshev distance for each pair, and taking the minimum value as the minimum Chebyshev distance for that simulation design space. A larger minimum Chebyshev distance indicates a greater spacing between sets of design variable values ​​along the most crowded design variable dimension, and a more uniform overall distribution. Next, the experimental design fitting error is calculated, including calculating the change in the minimum Chebyshev distance between two adjacent simulation design spaces and normalizing the change, which is then used to calculate the experimental design fitting error. In the formula, This is the standard deviation of the Chebyshev minimum distance for all simulation design spaces within the sliding window (e.g., the standard deviation of the Chebyshev minimum distance for each of the last 10 executions of step S44). To prevent small constants from being divided by zero.

[0119] Step c: Calculate the corresponding dynamic coupling coefficient based on the number of design variables and the performance change gradient of each performance index.

[0120] Calculate the corresponding dynamic coupling coefficient based on the number of design variables and the performance change gradient of each performance index. Used to characterize the ruggedness of the simulation design space, for example, In the formula, Represents the norm function, It is a constant. This is the sensitivity factor.

[0121] Step d: Update the corresponding exploration class parameters according to the number of updates, the performance change gradients, and the dynamic coupling coefficients.

[0122] Exploratory parameters are used to control global search capabilities and escape mechanisms. Examples include the model initialization step size and hyperparameter search range for surrogate models, the step size and mutation probability for optimization algorithms, and the sampling radius for experimental design algorithms. The update of the exploration class parameters employs a responsive perturbation strategy, adjusted using the performance change gradient and dynamic coupling coefficients. For example, when the performance change gradient approaches 0 (e.g., less than 0.001), it utilizes... The parameters for each exploration class are amplified exponentially and strong perturbations are injected.

[0123] For the exploratory parameters corresponding to the surrogate model, the initial values ​​are set based on experience. For example, the initial step size is set to 0.001-0.01, and the hyperparameter search range is set according to the type of surrogate model. For example, the learning rate search range for neural networks is 0.0001-0.1. During the iteration process, the corresponding decay values ​​are calculated for the exploratory parameters corresponding to the surrogate model. In the formula, These are the initial values ​​for the exploratory parameters corresponding to the surrogate model. To simulate the number of times the design space is updated, As the threshold for the number of iterations, asymmetric adjustment and update are performed based on the dynamic coupling coefficient. Characterized by flat terrain ( If this is the case, then an exponentially amplified perturbation is applied to the exploratory parameters corresponding to the surrogate model for updating. In the formula, This represents the updated value of the exploratory parameters corresponding to the optimization algorithm; if Characterizing topographic oscillations ( Then, logarithmic contraction inhibition is applied to the exploratory parameters corresponding to the surrogate model for updating. By achieving asymmetric adjustment through dynamic coupling coefficients, the optimization algorithm balances global and local optimization. For any exploratory parameter corresponding to the surrogate model, it realizes global search and local refinement of model hyperparameters. For the exploratory parameters corresponding to the optimization algorithm, the initial values ​​are set based on experience. For example, the initial step size is usually taken as 0.01-0.1, and the initial mutation probability is usually taken as 0.05-0.1. During the iteration process, for any exploratory parameter corresponding to the optimization algorithm, the corresponding decay value is calculated. In the formula, To optimize the initial values ​​of the exploratory parameters corresponding to the algorithm, the exploratory parameters corresponding to the surrogate model are updated by referring to the asymmetric adjustment and update method of the exploratory parameters, thus adapting the optimization algorithm to balance global and local optimization.

[0124] For the exploratory parameters corresponding to the experimental design algorithm, taking the sampling radius as an example, the initial value is set based on experience. For instance, the initial value of the sampling radius for each design variable is 1 / 10 of the value limit of that design variable. During the iteration process, referring to the update method of the exploratory parameters corresponding to the surrogate model and optimization algorithm, the exploratory parameters corresponding to the experimental design algorithm are updated asymmetrically. For example, if Characterized by flat terrain ( If ), then increase the sampling radius; if Characterizing topographic oscillations ( If the sampling radius is reduced, the responsive perturbation update of the exploratory parameters corresponding to the experimental design algorithm can be achieved through the dynamic coupling coefficient.

[0125] Step e: Update the corresponding development class parameters according to the number of updates and the performance change gradients.

[0126] Developing parameters are used to control local convergence accuracy. Examples include the kernel function length scale and smoothing factor for surrogate models, the elite ratio and local search radius for optimization algorithms, and the sampling accuracy and sample selection threshold for experimental design algorithms. Updates to these parameters employ a gradual decay + reset strategy, adjusted based on the number of updates and performance change gradients. For instance, when the number of updates is less than... Times (e.g., 8 times), when the performance change gradient is continuous If the performance gradient is less than the improvement threshold (e.g., 0.001) three times (e.g., 3 times), a periodic reset is triggered, restoring the parameter values ​​of each development class to the corresponding baseline values ​​to prevent premature entry into local extrema. When the performance gradient approaches 0 (e.g., less than 0.001), it utilizes... The parameters for each exploration class are amplified exponentially and strong perturbations are injected.

[0127] For the development class parameters corresponding to the proxy model, the initial values ​​are set based on the number of design variables or experience. For example, the kernel function length scale is set to 1 / 5 to 1 / 3 of the number of design variables, and the initial value of the smoothing factor is set to 0.1 to 0.2 based on experience. During the iteration process, taking the kernel function length scale as an example, through... Achieving gradual decay improves the fitting accuracy of each surrogate model, among which... These are the initial values ​​for the parameters of the development class corresponding to the proxy model. This represents the corresponding attenuation value.

[0128] For the development class parameters corresponding to the optimization algorithm, the initial values ​​are set based on experience. For example, the initial value of the elite ratio is usually 0.1-0.2, and the initial value of the local search radius is usually 1-2 times the step size. During the iteration process, for any development class parameter corresponding to the optimization algorithm, through... Achieving asymptotic decay means that the gradient remains continuous as the performance of the optimization algorithm changes. If the value is less than the improvement threshold (e.g., 0.001) three times (e.g., 3 times), a periodic reset is triggered, and all development class parameters are reset to their initial values. This ensures that the parameters decay with the number of updates, and the reset is triggered when convergence is smooth, preventing premature convergence of the algorithm. To optimize the initial values ​​of the parameters in the development class corresponding to the algorithm, This represents the corresponding attenuation value.

[0129] For the development class parameters corresponding to the experimental design algorithm, the initial values ​​are set based on experience or automatically configured according to CAE simulation requirements. For example, the initial value of sampling accuracy is set to 0.001-0.01, and the initial value of the sample selection threshold is configured based on convergence conditions. For example, the initial value of the sample selection threshold is equal to the first rate of change threshold or the second rate of change threshold. During the iteration process, the sampling accuracy gradually decreases with the number of updates, and the sample selection threshold is dynamically adjusted according to the performance change gradient. The smaller the performance change gradient, the smaller the sample selection threshold becomes. Achieving asymptotic decay means that the gradient remains continuous as the performance of the optimization algorithm changes. If the value is less than the improvement threshold (e.g., 0.001) three times (e.g., 3 times), a periodic reset is triggered. The initial values ​​for the parameters of the development class corresponding to the experimental algorithm are used. This corresponds to the decay value. The parameters of each development class corresponding to the experimental design algorithm decay with the increase of the number of updates, thereby improving the sample validity of the updated simulation design space (the sample is a single set of design variable values).

[0130] Step f: Update the corresponding structural class parameters according to the number of design variables and each of the performance indicators.

[0131] Structural parameters determine computational load and are used to manage periodic mutations. Examples include the number of network layers and basis function orders for the surrogate model, the population size for the optimization algorithm, and the number of samples and sampling dimensions for the experimental design algorithm. Updating structural parameters employs an event-driven mutation strategy, adjusting them through the number of design variables and performance metrics. For instance, when the loss function value of the detection surrogate model becomes overfitted (e.g., the loss function value on the training set continuously decreases while the loss function value on the validation set begins to rise at a certain point), the structural parameters are adjusted based on the number of design variables whose effect values ​​reach the effect value threshold. When the performance change gradient approaches 0 (e.g., less than 0.001), the system utilizes... The parameters for each exploration class are amplified exponentially and strong perturbations are injected.

[0132] For the structural parameters corresponding to the surrogate model, the initial values ​​are set based on the number of design variables or experience. For example, if the number of design variables is no more than 10, the initial number of network layers is set to 3-5; if the number of design variables is more than 10, the initial number of network layers is set to 5-8. The initial value of the basis function order is set to 2-3 based on experience. During the iteration process, taking the number of network layers as an example, if overfitting of the surrogate model occurs, the number of network layers is adjusted according to the number of design variables whose effect values ​​reach the effect value threshold. For example, for every 10 increase in the number of design variables whose effect values ​​reach the effect value threshold, the number of network layers increases by 1-2, balancing fitting accuracy and generalization ability.

[0133] For the structure parameters corresponding to the optimization algorithm, the initial values ​​are set based on the number of design variables. Referring to step S4323, during the iteration process, the structure parameters are adjusted according to the number of design variables whose effect values ​​reach the effect value threshold. For example... In the formula, To optimize the attenuation value corresponding to the structure class parameter of the algorithm, The number of design variables whose effect values ​​reach the effect value threshold is used to trigger event-driven mutations based on changes in the number of design variables whose effect values ​​reach the effect value threshold and performance indicators, thus balancing computational power consumption and optimization efficiency.

[0134] For the structure parameters corresponding to the experimental design algorithm, the initial values ​​are configured based on the number of design variables. For example, the sampling dimension division is the same as the number of design variables. During the iteration process, the sampling dimension division is adjusted based on the number of design variables whose effect values ​​reach the effect value threshold. The sample size is also adjusted accordingly. , The decay value corresponding to the structure class parameter of the experimental design algorithm, and Proportional to the performance change gradient, if the performance change gradient approaches 0 (e.g., less than 0.001), then... The parameters of each exploration class are exponentially amplified and strong perturbations are injected to avoid redundancy or insufficient sampling in the simulation design space.

[0135] Through steps a-f, adaptive adjustments are made to the exploration parameters, development parameters, and structural parameters of each proxy model, optimization algorithm, and experimental design algorithm, eliminating the need for manual configuration and improving the robustness and optimization efficiency of heterogeneous computing models in different application scenarios.

[0136] Step S5: Determine the optimal solution based on all the simulation optimal design groups.

[0137] The optimal solution is determined based on all simulation optimal design groups. In this embodiment, the last one or more simulation optimal design groups before the iteration stopping condition is met, and the single simulation result variable value corresponding to each simulation optimal design group is determined as the optimal solution. In other embodiments, for all simulation optimal design groups, the target evaluation value corresponding to each simulation optimal design group can be calculated according to step S32, and the top K (e.g., 3) simulation optimal design groups with the top target evaluation value and the corresponding single simulation result variable value can be selected as the optimal solution. Alternatively, the simulation optimal design group at the convergence center point and the corresponding single simulation result variable value can be selected as the optimal solution according to the acquisition order and convergence direction of each simulation optimal design group.

[0138] Through iterative iteration, the design sampling, proxy model, and optimization algorithm work together to accelerate the overall simulation solution process for real business scenarios, and solve the problems of selecting different optimization algorithms and setting algorithm parameters.

[0139] Furthermore, for the iterative process in steps S3-S4, taking the optimization algorithms including adaptive particle swarm optimization (with 10 iterations) and sequential quadratic programming as examples, an execution order example is given, including steps A-L.

[0140] Step A: Based on the CAE simulation requirements obtained in step S1 and the simulation design space determined in step S2, execute step S31 to obtain the corresponding simulation result variable values ​​for each group, and execute steps S32 and S33 to determine the optimal simulation design group from the simulation design space determined in step S2.

[0141] Step B: Execute step S41 to construct a training dataset based on the simulation design space and the variable values ​​of each group of simulation results, and execute step S42 to train multiple surrogate models in parallel to determine the optimal surrogate model.

[0142] Step C: Execute step S431 to obtain the effect values ​​of the design variables, and execute step S432 (steps S4321-S4323) to form the surrogate design space for the adaptive particle swarm optimization algorithm and the surrogate design space for the sequential quadratic programming algorithm based on the simulation optimal design group determined in step S33 (step A or step K), including steps C1-C3: Step C1: Based on the simulation optimal design group, for each design variable, determine a new value range according to the corresponding value scaling ratio, and use the adaptive particle swarm optimization algorithm to sample values ​​to obtain the corresponding surrogate design space. The quadratic programming algorithm is used to sample values ​​and form the corresponding proxy design space. ); Step C2: Agent design space based on adaptive particle swarm optimization algorithm ( The optimal surrogate model is input, and multiple sets of surrogate result variable values ​​are obtained. The optimal design group 1 is determined, and sampling is performed again to obtain a new surrogate design space. If the adaptive particle swarm optimization algorithm samples less than 10 times, a new optimal design group corresponding to the new surrogate design space is determined. It is then determined whether the optimal design group of the adaptive particle swarm optimization algorithm has converged. If it has not converged, sampling is performed again based on the current optimal design group to obtain a new surrogate design space. If it has converged, sampling is performed again based on the converged optimal design group to obtain a new surrogate design space, which serves as the surrogate design space for this algorithm. ), proceed to step D; if the adaptive particle swarm optimization algorithm has sampled 10 times, then the surrogate design space obtained on the 10th sampling is used as the surrogate design space for this algorithm ( Proceed to step E; Step C3: Based on the convergence of the adaptive particle swarm optimization algorithm, optimize the optimal design group. For each design variable, determine a new value range according to the corresponding value scaling ratio, and use the sequential quadratic programming algorithm to sample values ​​again, forming a new surrogate design space for the sequential quadratic programming algorithm. ); Step D: Execute step S433 based on the surrogate design space of the adaptive particle swarm algorithm ( ), surrogate design space of sequential quadratic programming algorithm ( , This yields multiple sets of corresponding proxy result variable values.

[0143] Step E: Execute step S434, first based on the surrogate design space of the adaptive particle swarm algorithm ( ), determine the optimal design set for the adaptive particle swarm optimization algorithm ( According to the sequential quadratic programming algorithm ( , ), determine the optimal design set of the sequential quadratic programming algorithm ( Then, from the two optimal design groups , The optimal design group of agents is determined in the middle.

[0144] Step F: Execute step S44 to update the simulation design space based on the surrogate optimal design group, which is used to execute step S31 to obtain the corresponding new simulation result variable values ​​for each group. Then execute steps S32 and S33 to determine the new simulation optimal design group from the new simulation design space determined in step S44. Step G: Based on the simulation optimal design group in Step A and the simulation optimal design group in Step F, determine whether the iteration stopping condition is met. If it is met, proceed to Step S5; if not, return to Step B. Based on the new simulation design space and the new simulation result variable values ​​of each group, expand the training dataset and determine the optimal surrogate model.

[0145] Furthermore, for optimization objectives including optimization thresholds for objective variables, especially those with single-valued thresholds, to reduce computational load, the following steps are included before step S4: Step S6: Obtain the optimal target variable value corresponding to the simulation optimal design group, and determine whether the optimal target variable value satisfies the optimization objective. If it does not satisfy the objective, proceed to step S4.

[0146] Obtain the single-group objective variable value (i.e. optimal objective variable value) corresponding to the optimal design group in the simulation, and determine whether the optimal objective variable value meets the optimization objective. If it does not meet the objective, proceed to step S4 for the next iterative optimization.

[0147] Furthermore, if the optimal objective variable value satisfies the optimization objective, then the corresponding simulation optimal design group and the corresponding single-group design variable result value are determined as the optimal solution, and step S4 is no longer executed, thus reducing the amount of computation.

[0148] The method in this embodiment reduces the number of calls to the target simulation software by 1-2 orders of magnitude, significantly reducing reliance on high-cost and time-consuming software. The overall simulation solution cycle is shortened by 5-10 times, addressing the industry pain point of excessively high optimization costs in computationally intensive simulations. Through parallel training and optimization of multiple surrogate models, the fitting bias of a single model is avoided, resulting in an average improvement of over 20% in the fitting accuracy of the surrogate models. Multiple optimization algorithms work together dynamically, balancing global exploration and local discovery, reducing the risk of premature convergence by over 80%, significantly improving convergence reliability, and enabling the stable finding of the global optimum within a limited number of simulations. Through end-to-end collaboration and dynamic adaptive adjustment, the overall simulation solution is significantly improved. It enables automatic selection and adaptive parameter configuration of experimental design algorithms, surrogate models, and optimization algorithms without human intervention, reducing manual operations by over 90% and eliminating reliance on cross-domain expert experience, significantly lowering the difficulty of technology implementation. In practical applications, the experimental design, surrogate models, and optimization algorithms can be extended to quickly adapt to various computationally intensive simulation and optimization scenarios in aerospace, automotive, energy, and machinery fields, demonstrating strong engineering versatility. The data sharing mechanism avoids redundant calculations, improving hardware resource utilization by over 60%. At the same time, the automated process frees engineers from tedious parameter tuning and algorithm matching work, reducing human resource costs by over 70%.

[0149] This invention provides another adaptive optimization method for computationally intensive simulation solutions. Taking the aerodynamic simulation optimization of aero-engine blades as an example, the execution process of the adaptive optimization method is illustrated. Aero-engine blade aerodynamic simulation optimization is a typical computationally intensive simulation process, with a single high-precision aerodynamic simulation taking approximately 4 hours. Traditional optimization methods require thousands of simulation calls, with an optimization cycle exceeding 6 months. Specifically, it includes: Step 1: Obtain CAE simulation requirements.

[0150] Design variables: 8 blade profile control parameters, all of which are continuous variables, with upper and lower boundaries being the reference value ±10% (i.e., value limits). Target simulation software: CFD simulation software; Constraints: Blade mass ≤ 105% of reference mass, maximum stress ≤ allowable material stress; Optimization objective: Minimize the blade aerodynamic drag coefficient and improve aerodynamic efficiency; Iteration stopping condition: The relative error of the optimal resistance coefficient after 5 consecutive iterations is ≤0.5%.

[0151] Step 2: Initial Iterative Sampling. The Latin hypercube sampling algorithm is used to perform global sampling within the upper and lower boundaries of the 8 design variables, generating a simulation design space including 40 sets of design variable values.

[0152] Step 3: Initial Simulation and Training Dataset Construction. Use CFD simulation software to complete the aerodynamic simulation solution for 40 sets of design variable values, obtaining 40 sets of simulation result variable values ​​(including drag coefficient, mass, and stress). Determine the optimal design set for the current simulation. If the iteration stopping condition is not met, store the 40 sets of design variable values ​​and the 40 sets of simulation result variable values ​​into the training dataset.

[0153] Step 4: Initial surrogate model training and optimal surrogate model determination. Based on 40 sets of design variable values ​​and 40 sets of simulation result variable values ​​in the training dataset, four surrogate models—multinomial response surface model, Kriging model, radial basis function model, and BP neural network—were trained in parallel. Among them, the Kriging model showed the best performance indicators, specifically R²=0.942, RMSE=0.0021, and inference time of 0.2ms, making it the current optimal surrogate model.

[0154] Step 5: Calculate the effect sizes of the design variables. Calculate the effect sizes of the eight design variables based on the training dataset, where two design variable effect sizes are ≥0.6 (high sensitivity) and six design variable effect sizes are <0.6 (low sensitivity).

[0155] Step 6: Parallel optimization to determine the surrogate optimal design group. Based on the simulation optimal design group (including the variable values ​​of each design variable, i.e., the optimal values) and the effect values ​​of each design variable determined in Step 3, the sampling range of the two highly sensitive design variables is narrowed to ±3% of the optimal value, and the range of the six low-sensitivity variables is retained within ±8%. The algorithm parameters are automatically configured: population size 80, iteration count 40. Three optimization algorithms—adaptive particle swarm optimization, simulated annealing, and sequential quadratic programming—are run in parallel, sharing the solution data. Finally, the optimal drag coefficient under the approximate model is obtained as 0.0287, which is better than the drag coefficient corresponding to the current simulation optimal design group. The corresponding single-group design variable value is the surrogate optimal design group.

[0156] Step 7: Closed-loop iterative optimization. Around the surrogate optimal design group, a central composite design is used for highly sensitive variables, and a Latin hypercube design is used for low-sensitivity variables, generating 15 new sets of design variable values. Groups that have already undergone simulation are excluded, completing a new round of simulation and updating the training dataset.

[0157] Repeat steps 3-6, adding 10-20 new samples to the training dataset in each iteration, continuously updating the optimal surrogate model and optimizing it.

[0158] Following steps 1-7, 12 iterations were performed, resulting in 186 high-precision simulations (i.e., 186 CFD simulation calculations). This reached the iteration termination condition, and the drag coefficient corresponding to the optimal design group in the final simulation was 12.8% lower than that of the optimal design group in the first simulation, satisfying all constraints. This method demonstrates a significant efficiency improvement over traditional optimization methods. Traditional optimization methods require at least 1500 simulation calls to achieve the same level of precision, with an optimization cycle exceeding 6 months. In contrast, the method in this embodiment reduces the number of simulation calls by 87.6% (more than an order of magnitude), and the overall optimization cycle is only 28 days, shortening it by more than 85%. Furthermore, the method in this embodiment can achieve automated verification. Throughout the optimization process, no manual algorithm selection or parameter configuration is required; only the CAE simulation requirements need to be determined, achieving fully automated, setup-free optimization.

[0159] This invention provides an adaptive optimization system for computationally intensive simulation solutions, such as... Figure 2 As shown, it includes: The requirement acquisition module is used to acquire CAE simulation requirements; wherein, the CAE simulation requirements include target simulation software, several design variables and corresponding optimization objectives; The experimental design module is used to sample each of the design variables to form a simulation design space; wherein, the simulation design space includes multiple sets of design variable values; The simulation solution module is used to determine the optimal simulation design group based on the simulation design space, the target simulation software, and the optimization objective. The parallel proxy module, based on the simulation design space, the simulation optimal design group, and the optimization objective, uses the target simulation software and multiple proxy models to update the simulation design space, and returns to the simulation solution module to repeat the iteration until the iteration stopping condition is met; The optimal solution determination module is used to determine the optimal solution based on all the simulation optimal design groups.

[0160] Furthermore, it also includes an early stopping judgment module, which is used to obtain the optimal target variable value corresponding to the optimal design group in the simulation, and judge whether the optimal target variable value meets the optimization objective. If it does not meet the objective, it enters the parallel agent module.

[0161] The above-described method and system embodiments are based on the same principles, and their related aspects can be referenced from each other to achieve the same technical effects. For specific implementation processes, please refer to the foregoing embodiments, which will not be repeated here.

[0162] In summary, the adaptive optimization method and system for computationally intensive simulation solving according to embodiments of the present invention have at least one of the following beneficial effects: 1. Based on CAE simulation requirements, a simulation design space is formed. The optimal simulation design group is determined using the target simulation software. The simulation design space is updated through the target simulation software and multiple surrogate models. It is determined whether the iteration stopping condition has been met. This achieves multi-stage collaboration, adaptive iteration, and update optimization throughout the entire process of sampling (simulation design space) - modeling (training multiple surrogate models) - optimization (iteration stopping condition). This enables deep integration of experimental design, surrogate models, and scheme evaluation, achieving parallel accelerated solution and adaptive matching in the simulation solution process. This accelerates the optimization process, reduces simulation computation costs, and improves optimization efficiency and convergence reliability.

[0163] 2. Based on the simulation design space and target simulation software, multiple surrogate models are trained in parallel to determine the optimal surrogate model. The training dataset is constructed using data generated by the target simulation software to ensure that the training direction of the surrogate model continuously approaches the CAE simulation requirements. As the simulation design space is updated, the training dataset is continuously expanded. After multiple surrogate models are trained, the optimal surrogate model with the highest accuracy is dynamically selected to achieve the integration and collaboration between the surrogate model and the target simulation software. By utilizing the short solution time of the surrogate model, the optimal surrogate design group is determined, thereby accelerating the solution of CAE simulation requirements.

[0164] 3. Multiple proxy models, multiple optimization algorithms, and multiple experimental design algorithms are used. The initial values ​​of exploration, development, and structural parameters are adaptively set based on CAE simulation requirements. By parallelizing various algorithms or models, the problem of mismatch between a single model or algorithm and the scenario is avoided. As the simulation design space and proxy design space are iteratively updated, the parameters are adaptively adjusted based on the performance change gradient and dynamic coupling coefficient. This eliminates the need for manual configuration, reduces the requirements on users, and solves the problem that the parameter configuration of models or algorithms in existing technologies is highly dependent on expert experience. It improves the robustness and optimization efficiency of heterogeneous computing models in different application scenarios and solves the problem that the technical threshold for implementing computationally intensive simulation solutions in existing technologies is high.

[0165] Those skilled in the art will understand that all or part of the processes of the methods described in the above embodiments can be implemented by a computer program instructing related hardware, and the program can be stored in a computer-readable storage medium. The computer-readable storage medium may be a disk, optical disk, read-only memory, or random access memory, etc.

[0166] The above description is only a preferred embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any changes or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in the present invention should be included within the scope of protection of the present invention.

Claims

1. An adaptive optimization method for computationally intensive simulation solutions, characterized in that, include: Step S1: Obtain CAE simulation requirements; wherein, the CAE simulation requirements include target simulation software, several design variables and corresponding optimization objectives; Step S2: Perform design sampling on each of the design variables to form a simulation design space; wherein, the simulation design space includes multiple sets of design variable values; Step S3: Determine the optimal simulation design group based on the simulation design space, the target simulation software, and the optimization objective; Step S4: Based on the simulation design space, the simulation optimal design group, and the optimization objective, update the simulation design space using the target simulation software and multiple proxy models, and return to step S3 to repeat the iteration until the iteration stop condition is met; Step S5: Determine the optimal solution based on all the simulation optimal design groups.

2. The method according to claim 1, characterized in that, Based on the simulation design space, the target simulation software, and the optimization objective, the optimal simulation design group is determined, including: Input the design variable values ​​of each group in the simulation design space into the target simulation software to obtain the corresponding simulation result variable values; Based on the simulation result variable values ​​and the optimization objective for each group, calculate the target evaluation value corresponding to the design variable values ​​for each group; Based on the evaluation values ​​of each target, the optimal simulation design group is determined from the simulation design space.

3. The method according to claim 2, characterized in that, The CAE simulation requirements also include constraints. Based on the simulation result variable values ​​and optimization objectives of each group, calculate the target evaluation value corresponding to the design variable values ​​of each group, including: Based on the design variable values ​​described in each group and / or the simulation result variable values ​​described in each group, determine the constraint variable values ​​corresponding to the constraint conditions; Based on all the constraint variable values ​​and the constraint conditions, select several sets of the design variable values ​​from the simulation design space; Based on the multiple sets of simulation result variable values ​​corresponding to all the selected sets of design variable values, determine the multiple sets of target variable values ​​corresponding to the optimization objective. The target evaluation value is calculated based on the target variable values ​​of all groups and the optimization objective.

4. The method according to claim 1, characterized in that, Based on the simulation design space, the optimal simulation design group, and the optimization objective, the simulation design space is updated using the target simulation software and multiple surrogate models, including: Based on the simulation design space, a training dataset is constructed using the target simulation software; Using the training dataset, train multiple agent models to determine the optimal agent model; Based on the simulation optimal design group, a proxy design space is constructed using multiple optimization algorithms. Based on the proxy design space and the optimization objective, the optimal proxy model is used to determine the proxy optimal design group. Based on the aforementioned agent optimal design group, the simulation design space is updated using a variety of experimental design algorithms.

5. The method according to claim 4, characterized in that, Using the training dataset, multiple agent models are trained to determine the optimal agent model, including: Using the training dataset, multiple agent models are trained to obtain multiple trained agent models; For each trained proxy model, calculate the corresponding model performance metric; The optimal proxy model is determined based on the model performance metrics of all trained proxy models.

6. The method according to claim 4, characterized in that, Based on the simulation optimal design group, a surrogate design space is constructed using various optimization algorithms. Based on the surrogate design space and the optimization objective, the optimal surrogate model is used to determine the surrogate optimal design group, including: Obtain the effect value of each design variable; Based on the simulation optimal design group, for each design variable, according to the corresponding effect value of the design variable, multiple optimization algorithms are used to sample and obtain values ​​to form multiple corresponding proxy design spaces; Input all the agent design spaces into the optimal agent model to obtain multiple sets of agent result variable values; Based on the optimization objective, all the agent design spaces, and the agent result variable values ​​of all groups, the optimal agent design group is determined.

7. The method according to claim 6, characterized in that, Based on the simulation optimal design group, for each design variable, according to the corresponding effect value of the design variable, multiple optimization algorithms are used to sample and obtain values, forming multiple corresponding surrogate design spaces, including: For each design variable, determine the corresponding scaling factor based on the effect value of the design variable. Based on the simulation optimal design group and each of the value scaling ratios, the value range of each design variable is scaled to determine a new value range; Based on the new value range of each design variable, multiple optimization algorithms are used to sample values ​​to obtain multiple proxy design spaces.

8. The method according to claim 4, characterized in that, Each of the aforementioned proxy models, optimization algorithms, and experimental design algorithms includes at least one of the following: exploration parameters, development parameters, and structural parameters. During repeated iterations, the parameters of each exploration class, each development class, and each structure class are updated through the following steps: Obtain the update count corresponding to the simulation design space; Obtain the performance metrics and performance change gradients corresponding to each of the aforementioned proxy models, optimization algorithms, and experimental design algorithms; Calculate the corresponding dynamic coupling coefficient based on the number of design variables and the performance change gradients of each variable; Update the corresponding exploration class parameters based on the number of updates, the performance change gradients, and the dynamic coupling coefficients. Update the corresponding development class parameters based on the number of updates and each of the performance change gradients; Update the corresponding structural class parameters based on the number of design variables and each of the performance indicators.

9. The method according to claim 1, characterized in that, Before step S4, the following are also included: Step S6: Obtain the optimal target variable value corresponding to the simulation optimal design group, and determine whether the optimal target variable value satisfies the optimization objective. If it does not satisfy the objective, proceed to step S4.

10. An adaptive optimization system for computationally intensive simulation solutions, characterized in that, include: The requirement acquisition module is used to acquire CAE simulation requirements; wherein, the CAE simulation requirements include target simulation software, several design variables and corresponding optimization objectives; The experimental design module is used to sample each of the design variables to form a simulation design space; wherein, the simulation design space includes multiple sets of design variable values; The simulation solution module is used to determine the optimal simulation design group based on the simulation design space, the target simulation software, and the optimization objective. The parallel proxy module, based on the simulation design space, the simulation optimal design group, and the optimization objective, uses the target simulation software, multiple proxy models, and multiple optimization algorithms to update the simulation design space, and returns to the simulation solution module to repeat the iteration until the iteration stopping condition is met; The optimal solution determination module is used to determine the optimal solution based on all the simulation optimal design groups.

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