Deep embedding probabilistic agent modeling method for heterogeneous parameter simulation experiment

Abstract

This application relates to a deep embedding probabilistic proxy modeling method for simulation experiments with heterogeneous parameters. The method includes: acquiring heterogeneous inputs and corresponding high-fidelity experimental results as labels; normalizing, encoding, and reducing the dimensionality of continuous, discrete, and functional parameters respectively; mapping the concatenated vectors to the probability distribution of latent variables using a deep embedding network with a variational autoencoder architecture; pre-training the embedding network using unlabeled data through a multi-objective contrastive learning framework; constructing a Gaussian process regression model in the latent space, training it with high-fidelity results as output labels and latent variables as input features; jointly fine-tuning the kernel function hyperparameters and embedding network parameters using evaluation data; and finally outputting the predicted mean and variance. This method can effectively accelerate the simulation experiment process in combustion chamber design.

Description

Technical Field

[0001] This application relates to the field of structural simulation experiment technology, and in particular to a deep embedded probabilistic proxy modeling method for heterogeneous parameter simulation experiments. Background Technology

[0002] With the continuous development of aero-engine technology, the requirements for high efficiency, low emissions, and high stability in combustor design are becoming increasingly stringent. Optimizing combustor performance relies on the coordinated matching of multiple design parameters. These parameters include continuous variables such as fuel injection pressure, injection angle, main combustion orifice diameter, and intake air temperature, as well as discrete categorical variables such as combustor configuration type, cooling structure type, and fuel nozzle type. Some inputs may also be functional data (such as inlet velocity profile curves). However, the internal physical processes of the combustor (such as fuel atomization, air mixing, chemical reactions, and wall cooling) are extremely complex. A high-fidelity combustor simulation experiment using tools such as computational fluid dynamics (CFD) typically takes several days or even weeks and requires significant high-performance computing resources. This prevents designers from exploring a broad design scope through large-scale, rapid simulation experiments during the initial combustor design phase, severely limiting design efficiency. To obtain reliable performance predictions with limited simulation or experimental costs, probabilistic surrogate modeling methods based on Gaussian processes are commonly used. These methods construct statistical surrogate models between input parameters and combustion performance (combustion efficiency, temperature distribution uniformity, etc.) to replace expensive simulation experiments and support subsequent parameter optimization and decision-making.

[0003] However, existing methods have the following problems when applied to accelerate combustion chamber simulation experiments: First, the kernel function of traditional Gaussian processes is difficult to define directly on a mixed space that simultaneously contains continuous and discrete categorical variables. Simply encoding categorical variables and using Euclidean distance will destroy the semantic consistency between variables, leading to a significant decrease in the model's prediction accuracy for combustion chamber performance. Second, the combustion chamber parameter space has a high dimension while high-fidelity simulation samples are extremely limited. Under high-dimensional sparse conditions, the distance between sample points tends to be uniform, and traditional distance metrics lose their discriminative power, making it difficult for the model to capture the true pattern of combustion performance changes with parameters. Third, limited simulation samples cannot support direct modeling of high-dimensional heterogeneous spaces. Traditional surrogate models are prone to overfitting, and the prediction error is amplified sharply in unsampled parameter regions. Fourth, existing surrogate modeling methods usually only fit the simulation results as static data points, failing to effectively utilize the physical laws governing the simulation experiment itself (such as mass conservation, energy conservation, component transport equations, etc.). When experimental samples are extremely scarce, purely data-driven surrogate models are prone to producing predictions that violate physical common sense in design regions where no experiments have been conducted, resulting in poor extrapolation ability and an inability to reliably guide the selection of the next round of simulation experiments. Summary of the Invention

[0004] Based on this, it is necessary to provide a deep embedded probabilistic proxy modeling method for simulation experiments with heterogeneous parameters, which can effectively handle heterogeneous combustion chamber parameters, incorporate physical constraints, solve the problem of distance metric failure under high-dimensional sparsity conditions, improve prediction accuracy and reduce the risk of overfitting.

[0005] A deep embedding probabilistic surrogate modeling method for heterogeneous parameter simulation experiments, the method comprising: Step 1: Obtain heterogeneous input data for the combustion chamber and the corresponding high-fidelity simulation results; the heterogeneous input data includes continuous design parameters, discrete category parameters, and functional performance curves of the combustion chamber; the high-fidelity simulation results include combustion efficiency, outlet temperature distribution coefficient, and pollutant emission index; Step 2: Normalize the continuous design parameters, encode the discrete category parameters, and extract the dimensionality reduction features from the functional performance curves to obtain the corresponding numerical vectors. Step 3: Concatenate all numerical vectors and map them into latent variables in a low-dimensional continuous latent space through a deep embedding network. The deep embedding network adopts a variational autoencoder architecture and outputs the probability distribution of the latent variables. Step 4: Pre-train the deep embedding network using unlabeled heterogeneous input data from the combustion chamber and the probability distribution of the latent variables through a multi-objective contrastive learning framework; Step 5: Construct a Gaussian process regression model in the latent space as a surrogate model to characterize the mapping relationship between heterogeneous inputs in the combustion chamber and combustion performance outputs; the training of the Gaussian process regression model uses the high-fidelity simulation experimental results as output labels and latent variables as input features. Step 6: Optimize the kernel function hyperparameters of the Gaussian process regression model using combustion chamber evaluation data containing input-output pairs and jointly fine-tune the parameters of the pre-trained deep embedding network; Step 7: After processing the heterogeneous combustion chamber input data to be predicted through Step 2 and Step 3, input it into the Gaussian process regression model after fine-tuning in Step 6, and output the simulation results; the simulation results include the predicted mean and predicted variance of combustion chamber performance.

[0006] The aforementioned deep embedding probabilistic surrogate modeling method for heterogeneous parameter simulation experiments acquires heterogeneous input data from the combustion chamber and corresponding high-fidelity simulation results, with the high-fidelity simulation results serving as the true output labels for subsequent surrogate model training. It performs normalization, encoding, and functional principal component analysis to reduce the dimensionality of various parameters. All numerical vectors are concatenated and mapped to latent variables in a low-dimensional continuous latent space using a deep embedding network with a variational autoencoder architecture, and their probability distributions are output. This unifies the heterogeneous inputs into a continuous metric space, solving the problem that traditional Gaussian process kernel functions cannot be directly defined in a mixed space. This paper addresses the problem of homogenizing sample point distances in high-dimensional sparse environments by utilizing low-dimensional embeddings. Furthermore, the output, in the form of a probability distribution, characterizes the embedding uncertainty, providing a structured input for subsequent modeling based on finite simulation samples. Unlabeled heterogeneous input data from combustion chambers is used to pre-train the deep embedding network using a multi-objective contrastive learning framework, incorporating contrastive loss, variational autoencoder loss, and knowledge-enhancing regularization terms. This enables the latent space to possess semantic preservation capabilities and a good geometric structure even under unsupervised conditions, reducing the dependence on finite high-fidelity simulation samples. A Gaussian process regression model is then constructed on the latent space. Using a surrogate model, the training of this model uses high-fidelity simulation experimental results as output labels and latent variables as input features, transferring surrogate modeling from the original heterogeneous space to a low-dimensional continuous latent space, further avoiding high-dimensional distance failure and kernel function design difficulties. Utilizing the acquired heterogeneous input data of the combustion chamber and the corresponding high-fidelity simulation experimental results as evaluation data containing input-output pairs, the hyperparameters of the Gaussian process kernel function and the parameters of the pre-trained embedded network are jointly fine-tuned. Furthermore, physical consistency loss and parameter change penalty terms are introduced, enabling the surrogate model to satisfy combustion requirements while fitting finite simulation data. This paper addresses the issue of pure data-driven models producing predictions that violate physical principles in unsampled regions by applying the physical laws of combustion chambers. Furthermore, the fine-tuning process does not disrupt the semantic structure obtained through pre-training, resolving inconsistencies between dimensionality reduction and prediction targets, as well as overfitting under limited sample conditions. The heterogeneous input data of the combustion chamber to be predicted is sequentially fed into the fine-tuned Gaussian process model, outputting simulation results—the predicted mean and variance of combustion chamber performance—to replace high-fidelity simulation experiments. The prediction variance can be decomposed into cognitive uncertainty and random uncertainty, providing a mathematical basis for information gain and confidence intervals for subsequent sequential sampling. This application achieves a unified representation and efficient probabilistic surrogate modeling of heterogeneous combustion chamber parameters, significantly improving prediction accuracy and reducing overfitting risk under limited high-fidelity simulation sample conditions, while ensuring the model's extrapolation ability and physical interpretability, thereby effectively accelerating the simulation experiment process in combustion chamber design. Attached Figure Description

[0007] Figure 1 This is a flowchart illustrating a deep embedding probabilistic proxy modeling method for heterogeneous parameter simulation experiments in one embodiment. Detailed Implementation

[0008] To make the objectives, technical solutions, and advantages of this application clearer, the following detailed description is provided in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the scope of this application.

[0009] In one embodiment, such as Figure 1 As shown, a deep embedded probabilistic surrogate modeling method for heterogeneous parameter simulation experiments is provided, including the following steps: Step 1: Obtain heterogeneous input data of the combustion chamber and the corresponding high-fidelity simulation results; the heterogeneous input data includes the continuous design parameters, discrete category parameters and functional performance curves of the combustion chamber; the high-fidelity simulation results include combustion efficiency, outlet temperature distribution coefficient and pollutant emission index.

[0010] The physical processes inside the combustion chamber are extremely complex. A high-fidelity combustion chamber simulation using tools such as computational fluid dynamics (CFD) typically takes several days or even weeks and requires significant high-performance computing resources, resulting in a very limited number of high-fidelity simulation samples. The obtained high-fidelity simulation results will serve as the true output labels for the surrogate model training in subsequent steps 5 and 6. For ease of description, let the heterogeneous input vector be... ,in, For continuous design parameters; For discrete category parameters, The performance curve is a function, defined in the continuous domain. functions on Let the corresponding actual output label be , indicating the results of high-fidelity simulation experiments.

[0011] Continuous design parameters include one or more of the following: fuel injection pressure, injection angle, main combustion orifice diameter, intake air temperature, intake air velocity, and combustion chamber volume; discrete category parameters include one or more of the following: combustion chamber configuration type, cooling structure form, fuel nozzle type, and flame tube material grade; functional performance curves include one or more of the following: fuel spray droplet size distribution curve, inlet velocity profile curve, and flame temperature distribution curve along the axial direction.

[0012] Step 2: Normalize the continuous design parameters, encode the discrete category parameters, and extract the dimensionality reduction features from the functional performance curves to obtain the corresponding numerical vectors.

[0013] Continuous design parameters are normalized to eliminate the influence of dimensions: ; in, and They represent the first The maximum and minimum values ​​of each continuous design parameter are used. Discrete categorical parameters are assigned a unique vector representation for each discrete combination using one-hot encoding or random fixed embedding. The functional performance curves are dimensionality-reduced using functional principal component analysis, and their dimensionality is reduced to that of the basis functions. Expand above: ; Take the expansion coefficient vector As a feature representation. If the functional data is given in a discrete form with a high sampling rate, time series feature extraction methods can also be used.

[0014] Step 3: Concatenate all numerical vectors and map them into latent variables in a low-dimensional continuous latent space through a deep embedding network. The deep embedding network adopts a variational autoencoder architecture and outputs the probability distribution of the latent variables.

[0015] The block encoding results are concatenated to construct a deep embedding network. heterogeneous input space Mapping to a low-dimensional continuous latent space : ; To characterize the uncertainty of embeddings, a variational autoencoder architecture is introduced, extending deterministic embeddings to probability distributions, and defining the encoder output as a variational posterior: ; in, and By embedded network After the wiring is mapped, the parameters are uniformly categorized. For the sparse combustion chamber design region of the high-fidelity simulation sample, the corresponding variance A larger value indicates that the model is "uncertain" about the embedding of the design, and this uncertainty can be passed on to subsequent proxy models.

[0016] Step 4: Pre-train the deep embedding network using unlabeled heterogeneous input data from the combustion chamber and the probability distribution of the latent variables through a multi-objective contrastive learning framework.

[0017] The goal of the pre-training phase is to learn a structurally sound and semantically preserving latent space without high-fidelity simulation evaluation. That is, optimizing parameters Unlabeled heterogeneous combustion chamber input data and the probability distribution of the latent variables are used as pre-training input data. During pre-training, the unlabeled heterogeneous combustion chamber input data provides the core training material: it constructs positive and negative sample pairs through data augmentation, serving as the self-reconstruction target of the VAE, forcing the latent variables to retain original key information; it also provides sample pairs for the knowledge augmentation regularization term, injecting expert priors. The probability distribution of the latent variables provides sampleable latent variables for the contrastive loss, enhancing noise robustness; it provides optimizable mean and variance for the VAE loss, ensuring the integrity and geometric regularity of the latent space information; the output variance serves as an uncertainty measure, passed to the subsequent Gaussian process. Together, these two aspects enable the model to learn a high-quality latent space with semantic alignment, structural continuity, and uncertainty using only unlabeled data.

[0018] Construct a multi-objective contrastive learning framework, jointly optimize three loss terms, and first pre-train a VAE with reconstruction as the main focus. , Then gradually introduce contrast loss () Gradually increase to the target value) and prior constraints ( Fine-tuning is performed by gradually reducing the value to the target value. To control the complexity of deeply embedded networks, an additional factor can be introduced into the loss function. It employs multiple regularization techniques, including regularization, Dropout, and spectral normalization.

[0019] Step 5: Construct a Gaussian process regression model in the latent space as a surrogate model to characterize the mapping relationship between heterogeneous inputs in the combustion chamber and combustion performance outputs; the training of the Gaussian process regression model uses high-fidelity simulation experimental results as output labels and latent variables as input features.

[0020] In the subspace A Gaussian process regression model is constructed as the main thread for surrogate modeling. The training data pairs for this model are... ,in These are latent variables (obtained by sampling or taking the mean from a probability distribution). To obtain the corresponding high-fidelity simulation experimental results: ; Among them, the mean function It can be a constant or a linear function. Kernel function Take the RBF core: ; Alternatively, other kernel functions such as the Matern kernel can be used.

[0021] By shifting the proxy modeling from the original high-dimensional heterogeneous space to a low-dimensional continuous latent space, the problem of distance metric failure under high-dimensional sparse conditions of traditional Gaussian processes is effectively avoided.

[0022] Step 6: Optimize the kernel function hyperparameters of the Gaussian process regression model using combustion chamber evaluation data containing input-output pairs and jointly fine-tune the parameters of the pre-trained deep embedding network.

[0023] The goal of the fine-tuning phase is to utilize combustion chamber evaluation data that includes input-output pairs. (i.e., a limited number of high-fidelity simulation experiment samples, in which) For heterogeneous input, Adapting the embedded network parameters to downstream tasks based on the corresponding high-fidelity simulation results. Only optimize the hyperparameters of the Gaussian process and : ; in, , ; For the kernel matrix; The combustion chamber physical consistency loss is used to quantify the combustion performance values ​​predicted by the model. Deviation from the physical equations governing the combustion chamber system: ; in, This represents the differential equation or conservation law operator governing the system. The purpose of this loss is to force the surrogate model to still satisfy the physical mechanisms in sparse data regions, improving extrapolation ability and interpretability.

[0024] When the sample size is sufficient, the same objective function can be used to further fine-tune the embedded network parameters. To avoid fine-tuning To disrupt the semantics obtained from pre-training, an early stopping mechanism is introduced, and a penalty term for changes in pre-training parameters is added to the loss function. ; in It is a hyperparameter. These are the pre-trained parameters.

[0025] Step 7: After processing the heterogeneous combustion chamber input data to be predicted through Step 2 and Step 3, input the data into the Gaussian process regression model after fine-tuning in Step 6, and output the predicted mean and predicted variance of the combustion chamber performance.

[0026] The predicted mean, as the optimal estimate of combustion chamber performance, can be directly used for design evaluation and performance prediction, replacing expensive high-fidelity CFD simulation experiments and thus significantly reducing the number of simulation experiments. The predicted variance provides the confidence interval of the prediction, helping engineers judge the reliability of the prediction results. The predicted variance can be decomposed into cognitive uncertainty (caused by the sparsity of high-fidelity simulation data, which can be reduced by increasing simulation experimental data) and random uncertainty (inherent noise in the data itself, which cannot be eliminated). This provides the mathematical basis of information gain and confidence interval for subsequent sequential sampling (Bayesian optimization guides the selection of the next round of expensive CFD simulation experiments), thereby achieving the most efficient design space exploration under a limited simulation budget.

[0027] The aforementioned deep embedding probabilistic surrogate modeling method for heterogeneous parameter simulation experiments acquires heterogeneous input data from the combustion chamber and corresponding high-fidelity simulation results, with the high-fidelity simulation results serving as the true output labels for subsequent surrogate model training. It performs normalization, encoding, and functional principal component analysis to reduce the dimensionality of various parameters. All numerical vectors are concatenated and mapped to latent variables in a low-dimensional continuous latent space using a deep embedding network with a variational autoencoder architecture, and their probability distributions are output. This unifies the heterogeneous inputs into a continuous metric space, solving the problem that traditional Gaussian process kernel functions cannot be directly defined in a mixed space. This paper addresses the problem of homogenizing sample point distances in high-dimensional sparse environments by utilizing low-dimensional embeddings. Furthermore, the output, in the form of a probability distribution, characterizes the embedding uncertainty, providing a structured input for subsequent modeling based on finite simulation samples. Unlabeled heterogeneous input data from combustion chambers is used to pre-train the deep embedding network using a multi-objective contrastive learning framework, incorporating contrastive loss, variational autoencoder loss, and knowledge-enhancing regularization terms. This enables the latent space to possess semantic preservation capabilities and a good geometric structure even under unsupervised conditions, reducing the dependence on finite high-fidelity simulation samples. A Gaussian process regression model is then constructed on the latent space. Using a surrogate model, the training of this model uses high-fidelity simulation experimental results as output labels and latent variables as input features, transferring surrogate modeling from the original heterogeneous space to a low-dimensional continuous latent space, further avoiding high-dimensional distance failure and kernel function design difficulties. Utilizing the acquired heterogeneous input data of the combustion chamber and the corresponding high-fidelity simulation experimental results as evaluation data containing input-output pairs, the hyperparameters of the Gaussian process kernel function and the parameters of the pre-trained embedded network are jointly fine-tuned. Furthermore, physical consistency loss and parameter change penalty terms are introduced, enabling the surrogate model to satisfy combustion requirements while fitting finite simulation data. This paper addresses the issue of pure data-driven models producing predictions that violate physical principles in unsampled regions by applying the physical laws of combustion chambers. Furthermore, the fine-tuning process does not disrupt the semantic structure obtained through pre-training, resolving inconsistencies between dimensionality reduction and prediction targets, as well as overfitting under limited sample conditions. The heterogeneous input data of the combustion chamber to be predicted is sequentially fed into the fine-tuned Gaussian process model, outputting simulation results—the predicted mean and variance of combustion chamber performance—to replace high-fidelity simulation experiments. The prediction variance can be decomposed into cognitive uncertainty and random uncertainty, providing a mathematical basis for information gain and confidence intervals for subsequent sequential sampling. This application achieves a unified representation and efficient probabilistic surrogate modeling of heterogeneous combustion chamber parameters, significantly improving prediction accuracy and reducing overfitting risk under limited high-fidelity simulation sample conditions, while ensuring the model's extrapolation ability and physical interpretability, thereby effectively accelerating the simulation experiment process in combustion chamber design.

[0028] In one embodiment, the continuous design parameters include one or more of the following: fuel injection pressure, injection angle, main combustion orifice diameter, intake air temperature, intake air velocity, and combustion chamber volume; the discrete category parameters include one or more of the following: combustion chamber configuration type, cooling structure form, fuel nozzle type, and flame tube material grade; and the functional performance curves include one or more of the following: fuel spray droplet size distribution curve, inlet velocity profile curve, and flame temperature distribution curve along the axial direction.

[0029] Specifically, the aforementioned parameters cover key variables in combustion chamber design. Continuous design parameters such as fuel injection pressure, injection angle, main combustion orifice diameter, intake air temperature, intake air velocity, and combustion chamber volume directly affect combustion efficiency and temperature distribution uniformity. Discrete categorical parameters such as combustion chamber configuration type (single-annular, double-annular, etc.), cooling structure type (film cooling, impingement cooling, etc.), fuel nozzle type, and flame tube material grade determine the basic configuration and thermal protection capability of the combustion chamber. Functional performance curves such as droplet size distribution curves, inlet velocity profile curves, and flame temperature distribution curves along the axial direction provide richer input information. By uniformly encoding and deeply embedding these heterogeneous parameters, the combustion chamber design space can be more comprehensively characterized, improving the prediction accuracy of the surrogate model.

[0030] In one embodiment, the deeply embedded network integrates the heterogeneous input space of the combustion chamber. Mapping to a low-dimensional continuous latent space The mapping relationship is as follows: ; in, As a latent variable, To embed in the network, To embed all learnable parameters of the network, It is a multilayer perceptron. This is the normalized continuous design parameter vector. For the encoding vector of discrete category parameters, This is the vector of characteristic coefficients of the functional performance curve.

[0031] Specifically, a multilayer perceptron is used to map the block-encoded heterogeneous input to a low-dimensional latent space, achieving a unified representation of heterogeneous data. The dimension of the latent space is much smaller than that of the original input space, effectively alleviating the curse of dimensionality. Furthermore, this mapping is learnable and can adaptively adjust according to subsequent tasks, avoiding the inconsistency between the dimensionality reduction objective and the prediction objective in independent dimensionality reduction methods.

[0032] In one embodiment, the variational autoencoder architecture defines the variational posterior of the encoder output as: ; in, and Obtained by wiring mapping after embedding the network. The symbol for Gaussian distribution. This indicates the calculation of the diagonal covariance matrix.

[0033] Specifically, extending deterministic embedding to a probability distribution can characterize the uncertainty in the embedding process. For sparse or fuzzy combustion chamber design regions in the training data, the corresponding variance... A larger value indicates that the model is "uncertain" about its embedding in the design. This uncertainty can be passed to subsequent Gaussian process surrogate models, forming an end-to-end uncertainty quantification capability.

[0034] In one embodiment, the pre-training loss function of the multi-objective contrastive learning framework is: ; in, To compare the losses, To enhance knowledge with regularization terms, For variational autoencoder loss, and To balance the weighting coefficients of each loss term; The comparative loss is: ; in, For the first i Latent variables for each anchor point combustion chamber sample. For latent variables in positive samples, For latent variables of negative samples, For summation index variables, For similarity measurement function, For temperature parameters; The variational autoencoder loss is: ; Among them, prior , The symbol for Gaussian distribution. For the identity matrix, the reconstruction terms Based on the type of combustion chamber input data, Gaussian distribution, categorical distribution, or function value reconstruction are used respectively. For variational posterior distribution, For the parameters of the encoder network, Let KL divergence be denoted as KL divergence.

[0035] Specifically, the multi-objective contrastive learning framework jointly optimizes three losses: contrastive loss brings similar samples closer together and dissimilar samples further apart in the latent space; variational autoencoder loss ensures that latent variables retain key information from the original input and gives the latent space a good geometric structure (approaching a standard normal distribution); and a knowledge-enhancing regularization term injects expert knowledge into the model, aligning the embedding space with human cognition. A progressive training strategy (primarily reconstruction, then gradually introducing contrastive loss and prior constraints) avoids the challenge of manually tuning weights in multi-objective optimization. This pre-training process utilizes only unlabeled data, fully leveraging the rich pool of unlabeled combustion chamber design samples, thereby reducing reliance on limited high-fidelity simulation samples.

[0036] In one embodiment, the knowledge enhancement regularization term is: ; in, For the first i Latent variables for each anchor point combustion chamber sample. For sample similarity weights, For the first j Latent variables of each anchor point combustion chamber sample.

[0037] Specifically, the knowledge-enhancing regularization term is based on the sample similarity provided by combustion chamber design experts. Construct a similarity matrix. The larger the sample size, the higher the expert's opinion. i and samples j The more similar the combustion chamber designs are in a design sense, the more likely they are to be aligned. This regularization term forces expert-labeled combustion chamber designs to be close to each other in the latent space, aligning the embedding space with engineering semantics. When simulation data is limited, expert knowledge can guide the model to learn a more reasonable latent space structure, reducing the risk of overfitting and enhancing the model's interpretability.

[0038] In one embodiment, the kernel function hyperparameter of the Gaussian process regression model is optimized by maximizing the marginal log-likelihood, and the objective function is: ; in, For kernel function hyperparameters, To observe the noise variance, For the marginal log-likelihood, For the loss of physical consistency of the combustion chamber, For balance coefficient, These are the parameters of a multilayer perceptron. The output vector is the combustion performance (i.e., the high-fidelity simulation results obtained in step 1). For a latent variable matrix, This is the input matrix for the heterogeneous combustion chamber.

[0039] Specifically, the fine-tuning phase employs two strategies: fixing the embedded network parameters when the sample size is limited. Only optimize the hyperparameters of the Gaussian process and Joint optimization when sample size is sufficient , and The objective function subtracts the physical consistency loss from the marginal log-likelihood, ensuring the model fits the data while respecting physical laws. Balance coefficient. Adjusting the trade-off between data fitting and physical constraints.

[0040] In one embodiment, the combustion chamber physical consistency loss is used to quantify the combustion performance values ​​predicted by the model. The deviation from the physical equations governing the combustion chamber system is, in specific form: ; in, The differential equations or conservation operators that govern the combustion process in the combustion chamber. The number of training samples. For the first i Heterogeneous combustion chamber inputs for each sample For the first i The model predicts combustion performance values ​​for each sample.

[0041] Specifically, the purpose of this loss is to force the surrogate model to still satisfy the physical mechanism in the sparse data region, solve the problem that the pure data-driven model produces prediction results that violate physical common sense in the design region where no simulation experiment has been conducted, and improve extrapolation ability and interpretability.

[0042] In one embodiment, when jointly fine-tuning the parameters of the deep embedding network, a penalty term for changes in the pre-trained parameters is added to the loss function. The penalty term is as follows: ; in, The penalty coefficient is... For the current fine-tuning parameters, These are the parameters obtained from pre-training.

[0043] Specifically, this penalty term is used to prevent the fine-tuning process from corrupting the semantic structure obtained from pre-training. When the amount of fine-tuning data is small, a larger penalty term is more effective. It can keep the pre-trained parameters unchanged; when there is enough fine-tuning data, smaller... It allows for significant parameter adjustments. Combined with an early stopping mechanism, it effectively prevents overfitting while maintaining the good latent space structure learned during the pre-training phase.

[0044] In one embodiment, the predicted mean and predicted variance of the combustion chamber performance are as follows: ; in, It is a mean function. The covariance vector between test points and training points ， The kernel matrix of the training set. To observe the noise variance, It is the identity matrix. The output vector for combustion performance of the training set. For the mean vector of the training set, To predict the mean, To predict variance, the superscript T indicates the transpose operation. This is the kernel function value of the test point itself.

[0045] It should be understood that, although Figure 1 The steps in the flowchart are shown sequentially as indicated by the arrows, but these steps are not necessarily executed in the order indicated by the arrows. Unless otherwise specified herein, there is no strict order in which these steps are executed, and they can be performed in other orders. Figure 1 At least some of the steps in the process may include multiple sub-steps or multiple stages. These sub-steps or stages are not necessarily completed at the same time, but can be executed at different times. The execution order of these sub-steps or stages is not necessarily sequential, but can be executed in turn or alternately with other steps or at least some of the sub-steps or stages of other steps.

[0046] The technical features of the above embodiments can be combined in any way. For the sake of brevity, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0047] The embodiments described above are merely illustrative of several implementation methods of this application, and while the descriptions are specific and detailed, they should not be construed as limiting the scope of this application. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of this application, and these modifications and improvements all fall within the protection scope of this application. Therefore, the protection scope of this application should be determined by the appended claims.

Claims

1. A deep embedding probabilistic surrogate modeling method for heterogeneous parameter simulation experiments, characterized in that, The method includes: Step 1: Obtain heterogeneous input data of the combustion chamber and the corresponding high-fidelity simulation results; the heterogeneous input data includes continuous design parameters, discrete category parameters and functional performance curves of the combustion chamber; the high-fidelity simulation results include combustion efficiency, outlet temperature distribution coefficient and pollutant emission index; Step 2: Normalize the continuous design parameters, encode the discrete category parameters, and extract dimensionality reduction features from the functional performance curve to obtain the corresponding numerical vectors. Step 3: Concatenate all numerical vectors and map them into latent variables in a low-dimensional continuous latent space through a deep embedding network. The deep embedding network adopts a variational autoencoder architecture and outputs the probability distribution of the latent variables. Step 4: Pre-train the deep embedding network using unlabeled heterogeneous input data from the combustion chamber and the probability distribution of the latent variables through a multi-objective contrastive learning framework; Step 5: Construct a Gaussian process regression model in the latent space as a surrogate model to characterize the mapping relationship between heterogeneous inputs in the combustion chamber and combustion performance outputs; the training of the Gaussian process regression model uses the high-fidelity simulation experimental results as output labels and the latent variables as input features; Step 6: Optimize the kernel function hyperparameters of the Gaussian process regression model using combustion chamber evaluation data containing input-output pairs and jointly fine-tune the parameters of the pre-trained deep embedding network; Step 7: The heterogeneous combustion chamber input data to be predicted is processed sequentially through Step 2 and Step 3 and then input into the Gaussian process regression model after fine-tuning in Step 6, and the simulation results are output; the simulation results include the predicted mean and predicted variance of the combustion chamber performance.

2. The method according to claim 1, characterized in that, The continuous design parameters include one or more of the following: fuel injection pressure, injection angle, main combustion orifice diameter, intake air temperature, intake air velocity, and combustion chamber volume; the discrete category parameters include one or more of the following: combustion chamber configuration type, cooling structure type, fuel nozzle type, and flame tube material grade; the functional performance curves include one or more of the following: fuel spray droplet size distribution curve, inlet velocity profile curve, and flame temperature distribution curve along the axial direction.

3. The method according to claim 1, characterized in that, The deeply embedded network integrates the heterogeneous input space of the combustion chamber. Mapping to a low-dimensional continuous latent space The mapping relationship is as follows: ； in, As a latent variable, To embed in the network, To embed all learnable parameters of the network, It is a multilayer perceptron. This is the normalized continuous design parameter vector. For the encoding vector of discrete category parameters, This is the vector of characteristic coefficients of the functional performance curve.

4. The method according to claim 3, characterized in that, The variational autoencoder architecture defines the variational posterior of the encoder output as: ； in, and Obtained from the wiring mapping after deep embedding of the network. The symbol for Gaussian distribution. This indicates the calculation of the diagonal covariance matrix.

5. The method according to claim 1, characterized in that, The pre-training loss function of the multi-objective contrastive learning framework is: ； in, To compare the losses, To enhance knowledge with regularization terms, For variational autoencoder loss, and To balance the weighting coefficients of each loss term; The comparison loss is: ； in, For the first i Latent variables for each anchor point combustion chamber sample. For latent variables in positive samples, For latent variables of negative samples, For summation index variables, For similarity measurement function, For temperature parameters; The variational autoencoder loss is: ； Among them, prior , The symbol for Gaussian distribution. For the identity matrix, the reconstruction terms Based on the type of combustion chamber input data, Gaussian distribution, categorical distribution, or function value reconstruction are used respectively. For variational posterior distribution, For the parameters of the encoder network, Let KL divergence be denoted as KL divergence.

6. The method according to claim 5, characterized in that, The knowledge-enhancing regular expression is: ； in, For the first i Latent variables for each anchor point combustion chamber sample. For sample similarity weights, For the first j Latent variables of each anchor point combustion chamber sample.

7. The method according to claim 1, characterized in that, The hyperparameters of the kernel function of the Gaussian process regression model are optimized, including: The kernel function hyperparameters of the Gaussian process regression model are optimized by maximizing the marginal log-likelihood, and the objective function is: ； in, For kernel function hyperparameters, To observe the noise variance, For the marginal log-likelihood, For the loss of physical consistency of the combustion chamber, For balance coefficient, These are the parameters of a multilayer perceptron. The output vector is the combustion performance. For a latent variable matrix, This is the input matrix for the heterogeneous combustion chamber.

8. The method according to claim 7, characterized in that, The combustion chamber physical consistency loss is used to quantify the combustion performance values ​​predicted by the model. The deviation from the physical equations governing the combustion chamber system is, in specific form: ； in, The differential equations or conservation operators that govern the combustion process in the combustion chamber. The number of training samples. For the first i Heterogeneous combustion chamber inputs for each sample For the first i The model predicts combustion performance values ​​for each sample.

9. The method according to claim 1, characterized in that, When jointly fine-tuning the parameters of the pre-trained deep embedding network, a penalty term for changes in the pre-trained parameters is added to the loss function. The penalty term is as follows: ； in, The penalty coefficient is... For the current fine-tuning parameters, These are the parameters obtained from pre-training.

10. The method according to claim 1, characterized in that, The predicted mean and predicted variance of the combustion chamber performance are as follows: ; in, It is a mean function. The covariance vector between test points and training points ， The kernel matrix of the training set. To observe the noise variance, It is the identity matrix. The output vector for combustion performance of the training set. For the mean vector of the training set, To predict the mean, To predict variance, the superscript T indicates the transpose operation. This is the kernel function value of the test point itself.

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