A data prediction evaluation method and system for CAE simulation

Abstract

The application relates to a data prediction evaluation method and system for CAE simulation, and belongs to the technical field of CAE simulation. The method solves the problem of low prediction result precision caused by insufficient model parameter optimization capability. The method comprises the following steps: based on a historical CAE simulation data set, taking CAE simulation parameters as input and corresponding simulation responses as output, a probability generation model based on a Gaussian process is constructed; a multiple start mechanism is adopted, and an adaptive regularization term is introduced in the maximization of the marginal likelihood function to obtain a target function; based on the historical CAE simulation data set and the target function, the hyperparameters of the probability generation model are optimized to obtain an optimal hyperparameter set, and the training of the probability generation model is completed; and new CAE simulation parameters are input into the trained probability generation model to output simulation response prediction values and uncertainty quantification indexes. The precision of the prediction result is improved.

Description

Technical Field

[0001] This invention relates to the field of CAE simulation technology, and in particular to a data prediction and evaluation method and system for CAE simulation. Background Technology

[0002] Computer-aided engineering (CAE) simulation technology is an indispensable tool in modern engineering design and analysis, widely used in numerical simulation of multiple physical fields such as structures, fluids, and thermodynamics. Emerging technologies such as digital twins and real-time simulation place even higher demands on CAE simulation.

[0003] Traditional CAE simulation methods mainly rely on numerical calculation techniques such as finite element analysis and computational fluid dynamics. By mathematically modeling and discretizing the physical system, key performance indicators such as structural stress, temperature distribution, and flow field characteristics are obtained. Although the accuracy is high, it is difficult to meet the requirements of rapid response and efficient optimization.

[0004] Approximate modeling techniques enable rapid prediction of simulation processes by establishing surrogate models between input parameters and output responses. Early approximate modeling methods mainly employed traditional machine learning methods such as polynomial response surfaces and radial basis functions. However, these methods often suffer from insufficient accuracy and poor generalization ability when dealing with high-dimensional nonlinear problems.

[0005] In recent years, with the development of artificial intelligence technology, probabilistic machine learning methods such as Gaussian process regression have shown unique advantages in the field of engineering optimization. However, traditional Gaussian process methods still face some challenges when applied to CAE simulation data: hyperparameter optimization is prone to getting trapped in local optima; model training efficiency needs improvement; and the ability to process small to medium-sized datasets is insufficient. Especially in the field of CAE simulation, due to the high computational cost of each simulation and the usually limited number of training samples, it is impossible to build a high-precision prediction model to obtain accurate prediction results. Summary of the Invention

[0006] Based on the above analysis, the embodiments of the present invention aim to provide a data prediction and evaluation method and system for CAE simulation, in order to solve the problem of low prediction accuracy caused by insufficient optimization capability of existing model parameters.

[0007] On one hand, embodiments of the present invention provide a data prediction and evaluation method for CAE simulation, comprising the following steps:

[0008] Based on historical CAE simulation datasets, a probabilistic generative model based on Gaussian processes is constructed, with CAE simulation parameters as input and the corresponding simulation response as output. A multi-start mechanism is adopted, and an adaptive regularization term is introduced into the marginal likelihood function to obtain the objective function. Based on the historical CAE simulation dataset and the objective function, the hyperparameters of the probabilistic generation model are optimized to obtain the optimal set of hyperparameters, and the training of the probabilistic generation model is completed. The new CAE simulation parameters are fed into the trained probability generation model, which outputs the simulation response prediction value and its uncertainty quantification index.

[0009] Based on the above method, a further improvement is made to the probabilistic generation model based on Gaussian process. The simulation response is set to be generated by the latent function and the noise term, where the latent function follows a Gaussian process and the noise term follows a Gaussian distribution with a mean of zero.

[0010] Based on further improvements to the above method, the hyperparameters of the probabilistic generation model include: kernel function hyperparameters and noise variance. The kernel function hyperparameters include: signal variance and length scale parameter for each simulation parameter.

[0011] Based on the above method, a further improvement is made to adopt a multi-start mechanism. In the hyperparameter value space, multiple different hyperparameter initial points are generated using the Latin hypercube sampling method. Parallel optimization is performed starting from each hyperparameter initial point, and the solution that maximizes the objective function is selected as the optimal hyperparameter.

[0012] Based on the further improvement of the above method, the marginal likelihood function is constructed according to the hyperparameters of the historical CAE simulation dataset and the probabilistic generation model; the adaptive regularization term is the product of the regularization parameter and the square of the norm of the kernel function hyperparameter; wherein, the regularization parameter is adaptively adjusted according to the norm of the gradient of the marginal likelihood function during the hyperparameter optimization process.

[0013] Based on the further improvement of the above method, the regularization parameter is adaptively adjusted using the following formula: , in, This represents the adjusted regularization parameters. Indicates the initial regularization parameters; The L2 norm of the marginal likelihood function gradient is represented. This represents the adaptive coefficient, used to control the sensitivity of the regularization strength to gradient changes.

[0014] Further improvements to the above method output the simulated response prediction value and its uncertainty quantification index. This is calculated based on the posterior prediction distribution of the trained probability generation model. The mean of the posterior prediction distribution is used as the simulated response prediction value, and the variance of the posterior prediction distribution is used as the uncertainty quantification index.

[0015] Based on the further improvement of the above method, the Gaussian process is defined by the mean function and the covariance function, where the mean function adopts zero prior and the covariance function adopts the squared exponential covariance function.

[0016] Based on further improvements to the above methods, CAE simulation parameters include at least one of the following: geometric dimension parameters, material property parameters, load condition parameters, or boundary condition parameters; simulation responses include at least one of the following: structural mass properties, mechanical response, thermal response, fluid dynamics response, or multidisciplinary coupled response.

[0017] On the other hand, embodiments of the present invention provide a data prediction and evaluation system for CAE simulation, comprising: The model building module is used to construct a probabilistic generative model based on Gaussian processes, using historical CAE simulation datasets, CAE simulation parameters as input, and the corresponding simulation response as output. The model training module employs a multiple activating mechanism and introduces an adaptive regularization term in maximizing the marginal likelihood function to obtain the objective function. Based on historical CAE simulation datasets and the objective function, it optimizes the hyperparameters of the probabilistic generation model to obtain the optimal set of hyperparameters, thus completing the training of the probabilistic generation model. The simulation prediction module is used to input new CAE simulation parameters into the trained probability generation model and output the simulation response prediction value and its uncertainty quantification index.

[0018] Compared with the prior art, the present invention can achieve at least one of the following beneficial effects: 1. By constructing a probabilistic generation model based on Gaussian processes and rapidly predicting new CAE simulation parameters, the technical bottleneck of traditional CAE simulation requiring full-process numerical calculations for each design point is overcome, significantly improving the efficiency of CAE simulation analysis. At the same time, it reduces the continuous dependence on high-performance computing resources and greatly reduces the hardware and time costs of simulation verification, making it particularly suitable for engineering scenarios that require a large number of parameter scans and optimization designs.

[0019] 2. During the training phase, the multiple activation mechanism effectively avoids hyperparameter optimization from getting stuck in local optima, enhancing the robustness of finding the global optimum. The adaptive regularization parameter dynamically balances model complexity and fitting accuracy, preventing overfitting on limited and expensive CAE data. The uncertainty quantification index (prediction variance) of the model output is directly derived from the probabilistic generation model, providing an intrinsic reliability measure for each prediction result, ensuring the high accuracy and strong generalization ability of the prediction model, and improving the accuracy of the prediction results.

[0020] 3. By embedding physical laws (covariance function), simulation constraints, and prior knowledge (mean function is zero) into the probabilistic generative model, physical-guided intelligent learning is achieved. This effectively compensates for the scarcity of CAE simulation data, significantly improves the predictive rationality and extrapolation reliability of the model in sparse data regions, and ensures that the results of the data-driven model strictly conform to physical common sense, thereby enhancing the trust foundation for engineering decisions.

[0021] 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

[0022] 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 is a flowchart of a data prediction and evaluation method for CAE simulation in an embodiment of the present invention. Detailed Implementation

[0023] 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.

[0024] Example 1 A specific embodiment of the present invention discloses a data prediction and evaluation method for CAE simulation, applicable to engineering design and simulation optimization in fields such as aerospace, automotive manufacturing, mechanical engineering, and energy equipment. Figure 1 As shown, this embodiment includes steps S1-S3.

[0025] S1. Based on historical CAE simulation datasets, using CAE simulation parameters as input and the corresponding simulation response as output, construct a probabilistic generative model based on Gaussian processes.

[0026] It should be noted that this embodiment transforms historical CAE simulation data into an intelligent probabilistic generation model, which is used to establish a complex nonlinear relationship between the input CAE simulation parameters and the output simulation response, and to quantify the uncertainty.

[0027] First, historical data is collected and organized from historical CAE simulation projects to construct a training sample set containing CAE simulation parameters and their corresponding simulation responses, denoted as... ,in, Indicates the first CAE simulation parameter vectors for each training sample Indicates the dimension of the simulation parameter vector; express The corresponding simulation response output is usually the key performance indicator calculated by CAE software; This indicates the number of training samples.

[0028] It should be noted that CAE simulation parameters include at least one of the following: geometric dimension parameters, material property parameters, load condition parameters, or boundary condition parameters.

[0029] For example, geometric parameters include: thickness, length, diameter, fillet radius, etc. of the component; material property parameters include: elastic modulus, Poisson's ratio, density, thermal conductivity, etc.; and load and boundary condition parameters include: magnitude, direction, pressure value, constraint location, etc.

[0030] The simulation response includes at least one of the following: structural mass properties, mechanical response, thermal response, fluid dynamics response, or multidisciplinary coupled response.

[0031] For example, the mass properties of the structure include: total mass of the vehicle body and total mass of the anti-collision beam; the mechanical response includes: maximum equivalent stress, maximum deformation displacement and natural frequency; the thermal response includes: maximum temperature and average heat flux density; the fluid dynamic response includes: drag coefficient and lift coefficient; and the multidisciplinary coupling response includes: thermal stress under thermal-structural coupling.

[0032] Considering the high cost of CAE simulation, this embodiment is suitable for modeling small to medium-sized samples. To ensure the model has sufficient training data, it is recommended that the number of training samples be [not specified]. At least 30-50, and the input dimensions The number of dimensions should not be too high; it is generally recommended to keep it below 10 to avoid the curse of dimensionality and ensure model efficiency and stability.

[0033] Taking the CAE simulation scenario of optimizing the stiffness and damping of an automotive suspension system as an example, the suspension system was analyzed. These are two different finite element dynamics simulations. For each simulation, two key simulation parameters are input. =2: Spring stiffness and damping coefficient, where spring stiffness is a combination of geometric and material properties, and damping coefficient is a load and boundary condition; the simulation response we focus on after each simulation is the maximum vertical acceleration of the vehicle body under a specific impact road surface, which is a mechanical response. Finally, we obtained a historical sample set containing 50 training samples: .

[0034] Furthermore, to ensure model convergence and stability, the mean and standard deviation of the CAE simulation parameters and simulation response in the historical dataset were calculated. Then, each value was standardized to transform it to a similar range. The calculated mean and standard deviation of each dimension of the CAE simulation parameters, as well as the mean and standard deviation of the simulation response, were saved for subsequent preprocessing of new simulation parameters and inverse transformation of the prediction results.

[0035] For example, the Z-score standardization method is used, and each standardized value follows a distribution with a mean of 0 and a variance of 1.

[0036] Meanwhile, the variance of the measurement error is calculated based on the numerical characteristics of the simulation data or repeated experiments, and used as the initial value of the noise variance; the noise variance represents the quality or uncertainty of the data itself.

[0037] Furthermore, based on the probabilistic generation model of Gaussian Process (GP), the simulation response is set to be jointly generated by the latent function and the noise term. The latent function follows a Gaussian process, representing a smooth latent physical law function that cannot be directly observed, and the noise term follows a Gaussian distribution with a mean of zero.

[0038] The probabilistic generative model is represented by the following mathematical model: , in, The latent function represents the inherent, deterministic mapping relationship between the input CAE simulation parameters and the actual simulation response; The noise term represents random disturbances in the CAE simulation process, such as numerical errors, mesh discretization errors, and convergence errors. It follows a zero-mean and a noise variance of . Gaussian distribution; noise variance This represents the degree of uncertainty in the simulation response.

[0039] It should be noted that a Gaussian process is determined by the mean function. Sum of covariance functions Fully defined, where the mean function Using zero prior, i.e. The covariance function uses the squared exponential covariance function, as shown in the following formula: , in, This represents the signal variance, the overall fluctuation range of the control function; For the first The length scale parameter of each simulation parameter is used to control the rate of decay of the correlation of the input dimension, that is, the importance of its influence on the output. This represents the kernel function hyperparameters in the hyperparameter set. and These represent the input simulation parameter vectors, and They represent and The Parameter values ​​for each dimension; This represents an exponential function.

[0040] The larger the signal variance, the greater the range of possible variations in the simulation response that the model believes there is. The initial value is set to 1.0. The larger the length scale parameter of the simulation parameter, the more likely the output response will still be highly correlated even if the values ​​of the simulation parameter differ greatly. That is, the influence of the parameter on the simulation response is relatively mild and insensitive. Conversely, it means that a small change in the parameter may lead to a drastic change in the simulation response. The initial values ​​of all parameters are set to 1.0.

[0041] It should be noted that the hyperparameters of the probabilistic generative model include: kernel function hyperparameters. and noise variance The kernel function hyperparameters affect the model's fitting ability and complexity, including signal variance. and the length scale parameter of the simulation parameters These hyperparameters automatically learn their optimal values ​​during subsequent hyperparameter optimization.

[0042] This step constructs a probabilistic generative model characterized by the hyperparameters to be learned. By explicitly modeling the noise term, it acknowledges and quantifies the uncertainty of the data itself, laying a probabilistic foundation for providing subsequent prediction reliability indicators. The length scale parameter provides intuitive insights into the sensitivity of each simulation parameter, enhancing the interpretability of the model.

[0043] S2. By sampling multiple initial points and introducing an adaptive regularization term in maximizing the marginal likelihood function, the objective function is obtained. Based on the historical CAE simulation dataset and the objective function, the hyperparameters of the probabilistic generation model are optimized to obtain the optimal set of hyperparameters, thus completing the training of the probabilistic generation model.

[0044] It's important to note that the essence of training a probabilistic generative model is finding a set of optimal hyperparameters that maximizes the "probability" of historical CAE simulation data occurring under these optimal hyperparameter settings. This probability is measured by the marginal likelihood function, which is constructed based on the historical CAE simulation dataset and the hyperparameters of the probabilistic generative model. Its logarithmic form (for numerical stability, typically maximizing the log-likelihood) is defined as: , in, and These represent the matrix and vector composed of all simulation parameter vectors and simulation responses in the historical CAE simulation dataset, respectively. , ; Represents the covariance matrix including noise. ; It is The covariance matrix, whose elements are derived from the covariance function Calculations show that It is The identity matrix is ​​used to ensure the positive definiteness and numerical stability of the matrix.

[0045] In the marginal likelihood function, the first term The first term is the data fit term, which measures how well the model fits the training data; the larger the value, the better the fit. The second term... This is a complexity penalty term to prevent overfitting; the third term These three parts represent the normalization constant; they embody the balance mechanism between model accuracy and complexity.

[0046] To constrain the size of hyperparameters and encourage the model to choose smoother and simpler solutions, a regularization term is added to the marginal likelihood function, forming the final objective function. As shown below: , in, Represents the regularization parameter. This represents the regularization penalty term.

[0047] Regularization penalty term The kernel function hyperparameters only affect the complexity of the model and do not include noise variance; they are obtained by calculating the squared L2 norm of the kernel function hyperparameters, as shown in the following formula: .

[0048] Furthermore, based on historical CAE simulation datasets, the hyperparameters are iteratively adjusted through optimization algorithms to maximize the value of the objective function, thereby optimizing and training the probabilistic generative model.

[0049] To avoid getting stuck in local optima and to find the global optimum, a multi-startup mechanism is adopted to enhance the global search capability. That is, within the hyperparameter value space, the Latin hypercube sampling method is used to generate multiple different hyperparameter initial points, and parallel optimization is performed starting from each hyperparameter initial point. The solution that maximizes the objective function is selected as the optimal hyperparameter.

[0050] It should be noted that the hyperparameter space includes the range of values ​​for each hyperparameter, and is generated in the hyperparameter space using the Latin hypercube sampling method. Different hyperparameter initial points: The number of hyperparameter initial points is set between 50 and 200 depending on the parameter dimension to ensure sufficient coverage of different regions of the parameter space.

[0051] Starting from each of the aforementioned hyperparameter initialization points, an independent local optimization process is initiated. These processes are computed in parallel to improve computational efficiency and significantly shorten the overall training time. The task of each process is to locally maximize the objective function. After all parallel optimization processes have finished, compare the objective function values ​​corresponding to all solutions and select the solution that maximizes the objective function value. As the globally optimal hyperparameter.

[0052] It is important to emphasize that during the hyperparameter optimization process, the regularization parameter in the regularization term is adaptively adjusted based on the norm of the objective function's gradient within each local optimization process, as shown in the following formula: , in, This represents the adjusted regularization parameters. Indicates the initial regularization parameters; The L2 norm of the marginal likelihood function gradient is represented by the square root of the sum of squares of its components. This represents the adaptive coefficient, used to control the sensitivity of the regularization strength to gradient changes.

[0053] It should be noted that the initial regularization parameter Set a small positive value, such as 0.01 or 0.1; for a small number of training samples ( In cases where the size is relatively small, the size can be increased appropriately. To provide stronger overfit suppression. Adaptive coefficients The value is typically set between 0.5 and 2.0, and in practice, it can be determined using cross-validation.

[0054] During the optimization process, when the norm of the gradient of the marginal likelihood function... A larger value indicates that the current region is experiencing a rapid decline; in this case, the regularization strength should be reduced. This allows for larger step sizes in the search; when the norm of the gradient of the marginal likelihood function... When the value is small, it indicates that the region is close to a stable region, and the regularization strength should be increased to avoid overfitting.

[0055] gradient of objective function It is obtained by subtracting the gradient of the regularization term from the gradient vector of the marginal likelihood function with respect to all the hyperparameters to be optimized, as shown in the following formula: , in, Represents all the first ones to be optimized. There are several hyperparameters (including signal variance, parameters for each length scale, and noise variance). The objective function is expressed as follows: The gradient of each hyperparameter Represents the marginal likelihood function gradient vectors for all hyperparameters to be optimized ; Represents the covariance matrix with respect to the first... The partial derivative matrix of each hyperparameter; This indicates the calculation of the inverse matrix. Represents the matrix trace operation; This represents data dependencies, used to reflect the impact of parameter changes on the degree of data fit; This represents the model complexity term, which reflects the contribution of parameter variations to the model complexity.

[0056] Preferably, when calculating the gradient, the gradient is not directly applied to... Instead of finding the inverse, the Cholesky decomposition method is used to avoid computational errors.

[0057] In the optimization process starting from each initial point, each iteration first calculates the gradient vector of the marginal likelihood function based on the current hyperparameter values. Then, the regularization parameters are adaptively adjusted based on the norm of the gradient to obtain the regularization parameters for the current iteration step, and finally the gradient of the complete objective function is calculated. The system employs analytical gradient-based optimization algorithms (such as the conjugate gradient method and the quasi-Newton method) to update hyperparameters for the next iteration. When the convergence condition is met, the optimal hyperparameters in the current optimization process are output. After all parallel optimization processes are completed, the hyperparameters that maximize the objective function are the globally optimal hyperparameters. These optimal hyperparameters are then substituted into the probabilistic generation model constructed in the first step to obtain the trained probabilistic generation model, which is used for rapid prediction of simulation responses. Furthermore, after training, the noisy covariance matrix calculated based on the optimal hyperparameters is used. Stored for direct use during prediction in step S3, improving computational efficiency in the prediction phase.

[0058] For example, in a CAE simulation scenario for optimizing the stiffness and damping of an automotive suspension system, the hyperparameter space is as follows: the signal variance, spring stiffness, and damping coefficient range from [0.1, 10], and the noise variance ranges from [0.001, 0.1]. Latin hypercube sampling is used to generate [the hyperparameters] within this hyperparameter space. There are 100 initial points (each initial point includes 4 hyperparameters). 100 parallel optimization processes are launched, each starting from one initial point, and the objective function is maximized using a quasi-Newton method. In each iteration, the gradient at the current point is calculated. And calculate the adaptive adjustment Then calculate the gradient of the objective function. The algorithm updates all hyperparameters of the probabilistic generative model. After 100 optimization processes, the optimal objective function values ​​of each process are compared. If the 23rd optimization process obtains the largest objective function value, its corresponding hyperparameters are used as the parameters of the final trained model.

[0059] Based on historical CAE simulation data, this step achieves efficient, stable, and global optimization of hyperparameters through the organic combination of multiple initiation, adaptive regularization, and analytical gradient optimization, thereby obtaining a high-precision prediction model with strong generalization ability.

[0060] S3. Input the new CAE simulation parameters into the trained probability generation model and output the simulation response prediction value and its uncertainty quantification index.

[0061] This step utilizes a trained probabilistic generation model to quickly and accurately predict any new set of CAE simulation parameters, while simultaneously providing a quantitative index of the uncertainty of the prediction results, thereby providing intelligent support for engineering decision-making that combines "point estimation" and "risk perception".

[0062] It should be noted that the new CAE simulation parameters are standardized using the mean and standard deviation of each simulation parameter dimension saved in step S1 before being input into the trained probability generation model.

[0063] The output simulation response prediction value and its uncertainty quantification index are calculated based on the posterior prediction distribution of the trained probability generation model. The mean of the posterior prediction distribution is used as the simulation response prediction value, and the variance of the posterior prediction distribution is used as the uncertainty quantification index.

[0064] Specifically, for a new set of simulation parameters The output simulation response prediction value is calculated using the following formula: , in, This represents the predicted value of the simulation response. It is a correlation vector between the new simulation parameters and each CAE simulation parameter in the historical CAE simulation dataset, calculated based on the covariance function.

[0065] The uncertainty quantification index is used to reflect the confidence level of the prediction results. The smaller the value, the higher the confidence level of the prediction. It is calculated using the following formula: , in, The autocovariance of the new simulation parameters, i.e., the value of the covariance function at its own point, is calculated as follows. This represents prior uncertainty; This indicates the uncertainty caused by noise; This represents the reduction in uncertainty resulting from historical training data.

[0066] Using the mean and standard deviation saved during the simulation response standardization process in step S1, the obtained simulation response prediction values ​​and their uncertainty quantification index are inversely standardized to obtain the simulation response prediction values ​​at the original physical scale. Quantitative indicators of uncertainty and standard deviation .

[0067] Furthermore, based on the simulated response predictions and standard deviations, the 95% confidence interval is obtained as follows: .

[0068] During implementation, a low uncertainty quantification index indicates that the model has high confidence in its predictions for that region (near the new simulation parameters), and the predicted values ​​can be directly used to guide the design. Conversely, a high uncertainty quantification index suggests that the region is located in an area with sparse training data or insufficient parameter space exploration. In this case, an automatic warning signal is triggered, alerting engineers to the high uncertainty of the prediction result and guiding them to supplement CAE simulation calculations for that region. The new data is then added to the training sample set, and the model is retrained, thereby achieving an intelligent "active learning" cycle to improve the model's global prediction capabilities in the most efficient way.

[0069] Compared with existing technologies, this embodiment provides a data prediction and evaluation method for CAE simulation. By constructing a probabilistic generative model based on Gaussian processes and rapidly predicting new CAE simulation parameters, it overcomes the technical bottleneck of traditional CAE simulation requiring full-process numerical calculations for each design point, significantly improving the efficiency of CAE simulation analysis. Simultaneously, it reduces the continuous dependence on high-performance computing resources, greatly reducing the hardware and time costs of simulation verification, making it particularly suitable for engineering scenarios requiring extensive parameter scanning and design optimization. During the training phase, a multi-startup mechanism effectively avoids hyperparameter optimization getting trapped in local optima, enhancing the robustness of finding the global optimum. The adaptive regularization parameter dynamically balances model complexity and fitting accuracy, preventing overfitting on limited and expensive CAE data. The uncertainty quantification index (prediction variance) of the model output is directly derived from the probabilistic generative model, providing an intrinsic reliability measure for each prediction result, ensuring high accuracy and strong generalization ability of the prediction model, and improving the accuracy of the prediction results. By embedding physical laws (covariance function), simulation constraints, and prior knowledge (mean function is zero) into the probabilistic generative model, physical-guided intelligent learning is achieved. This effectively compensates for the scarcity of CAE simulation data, significantly improves the predictive rationality and extrapolation reliability of the model in sparse data regions, and ensures that the results of the data-driven model strictly conform to physical common sense, thereby enhancing the trust foundation for engineering decisions.

[0070] Example 2 Another embodiment of the present invention discloses a data prediction and evaluation system for CAE simulation, thereby implementing the data prediction and evaluation method for CAE simulation in Embodiment 1. The specific implementation of each module is described in the corresponding description in Embodiment 1. The system includes: The model building module is used to construct a probabilistic generative model based on Gaussian processes, using historical CAE simulation datasets, CAE simulation parameters as input, and the corresponding simulation response as output. The model training module employs a multiple activating mechanism and introduces an adaptive regularization term in maximizing the marginal likelihood function to obtain the objective function. Based on historical CAE simulation datasets and the objective function, it optimizes the hyperparameters of the probabilistic generation model to obtain the optimal set of hyperparameters, thus completing the training of the probabilistic generation model. The simulation prediction module is used to input new CAE simulation parameters into the trained probability generation model and output the simulation response prediction value and its uncertainty quantification index.

[0071] Since the data prediction and evaluation system for CAE simulation described in this embodiment and the aforementioned data prediction and evaluation method for CAE simulation are related and can be mutually referenced, this description is redundant and will not be repeated here. Because this system embodiment shares the same principle as the aforementioned method embodiment, it also possesses the corresponding technical effects of the aforementioned method embodiment.

[0072] 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.

[0073] 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. A data prediction and evaluation method for CAE simulation, characterized in that, Includes the following steps: Based on historical CAE simulation datasets, a probabilistic generative model based on Gaussian processes is constructed, with CAE simulation parameters as input and the corresponding simulation response as output. A multi-start mechanism is adopted, and an adaptive regularization term is introduced into the marginal likelihood function to obtain the objective function. Based on the historical CAE simulation dataset and the objective function, the hyperparameters of the probabilistic generation model are optimized to obtain the optimal set of hyperparameters, and the training of the probabilistic generation model is completed. The new CAE simulation parameters are fed into the trained probability generation model, which outputs the simulation response prediction value and its uncertainty quantification index.

2. The data prediction and evaluation method for CAE simulation according to claim 1, characterized in that, The probabilistic generation model based on Gaussian processes assumes that the simulation response is generated jointly by a latent function and a noise term, wherein the latent function follows a Gaussian process and the noise term follows a Gaussian distribution with a mean of zero.

3. The data prediction and evaluation method for CAE simulation according to claim 1, characterized in that, The hyperparameters of the probabilistic generation model include: kernel function hyperparameters and noise variance. The kernel function hyperparameters include: signal variance and length scale parameter for each simulation parameter.

4. The data prediction and evaluation method for CAE simulation according to claim 1, characterized in that, The multi-start mechanism involves generating multiple different initial hyperparameter points within the hyperparameter value space using the Latin hypercube sampling method, performing parallel optimization from each initial hyperparameter point, and selecting the solution that maximizes the objective function as the optimal hyperparameter.

5. The data prediction and evaluation method for CAE simulation according to claim 3, characterized in that, The marginal likelihood function is constructed based on the hyperparameters of historical CAE simulation datasets and probabilistic generation models; the adaptive regularization term is the product of the regularization parameter and the square of the norm of the kernel function hyperparameter; wherein, the regularization parameter is adaptively adjusted according to the norm of the gradient of the marginal likelihood function during the hyperparameter optimization process.

6. The data prediction and evaluation method for CAE simulation according to claim 5, characterized in that, The regularization parameter is adaptively adjusted using the following formula: ， in, This represents the adjusted regularization parameters. Indicates the initial regularization parameters; The L2 norm of the marginal likelihood function gradient is represented. This represents the adaptive coefficient, used to control the sensitivity of the regularization strength to gradient changes.

7. The data prediction and evaluation method for CAE simulation according to claim 1, characterized in that, The output simulation response prediction value and its uncertainty quantification index are calculated based on the posterior prediction distribution of the trained probability generation model. The mean of the posterior prediction distribution is used as the simulation response prediction value, and the variance of the posterior prediction distribution is used as the uncertainty quantification index.

8. The data prediction and evaluation method for CAE simulation according to claim 2, characterized in that, The Gaussian process is defined by a mean function and a covariance function, wherein the mean function adopts zero prior and the covariance function adopts the squared exponential covariance function.

9. The data prediction and evaluation method for CAE simulation according to claim 1, characterized in that, The CAE simulation parameters include at least one of the following: geometric dimension parameters, material property parameters, load condition parameters, or boundary condition parameters; the simulation response includes at least one of the following: structural mass properties, mechanical response, thermal response, fluid dynamics response, or multidisciplinary coupled response.

10. A data prediction and evaluation system for CAE simulation, characterized in that, include: The model building module is used to construct a probabilistic generative model based on Gaussian processes, using historical CAE simulation datasets, CAE simulation parameters as input, and the corresponding simulation response as output. The model training module is used to adopt a multiple start-up mechanism and introduce an adaptive regularization term in maximizing the marginal likelihood function to obtain the objective function. Based on the historical CAE simulation dataset and the objective function, the hyperparameters of the probabilistic generation model are optimized to obtain the optimal set of hyperparameters, thus completing the training of the probabilistic generation model. The simulation prediction module is used to input new CAE simulation parameters into the trained probability generation model and output the simulation response prediction value and its uncertainty quantification index.

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