Research On Deep Surrogate Model Method Integrated With Prior Knowledge For Fast Prediction Of Physical Fields

Physical fields are important characteristics that reflect the performance and state of complex systems such as aircraft.Achieving fast and accurate prediction of physical fields is beneficial for improving the optimization design capability and the state awareness and control level of complex systems.Building surrogate models with data-driven methods to approximate complex simulation computations and physical experimental processes is an effective way to reduce computational costs,shorten time consumption,and improve the applicability of physical field prediction.The deep learning techniques have brought new opportunities and challenges to surrogate model research with their powerful learning ability and flexibility.Leveraging powerful deep neural networks(DNNs),deep surrogate model methods can deeply replace numerical simulation and physical experiments,providing efficient and accurate prediction results of physical fields such as temperature and flow fields by combining sensor perception data.However,the physical experiment and numerical simulation of complex systems are often time-consuming,data difficult to obtain,and costly,while deep learning usually requires a large amount of labeled data for desired performance.Therefore,how to improve the prediction accuracy and generalization ability under small samples is one of the key problems that need to be solved when constructing surrogate models based on DNNs.This study focuses on building surrogate models for predicting physical fields of complex physical systems such as aircraft using DNNs.It investigates the methods to construct deep surrogate models by incorporating prior knowledge to enhance the prediction performance of surrogate models under small sample scenarios.Considering the sources of prior knowledge and the applicable scenarios,this study adopts a learning paradigm driven by data and knowledge derived from physical laws,inherent data structure,and correlated tasks.The main contributions and novelties of this paper are as follows:(1)For application scenarios where data is scarce but physical knowledge is rich and easy to describe,this paper proposes a method to construct a physics-informed surrogate model for physical field prediction that introduces physical knowledge to guide the surrogate model training,and improves the physical rationality and interpretability of physical field predictions.Taking the thermal field analysis of a heat source system as an example,the study first models the temperature field prediction as an image-to-image regression task.Then,it constructs a loss function that contains governing equation of heat source system based on the finite difference method.The loss function is used to guide the training of the surrogate model.To improve the stability and efficiency of network training,the method also introduces a hard constraint processing method for boundary conditions,which imposes boundary condition constraints by padding.In addition,the network component is carefully designed by analyzing the characteristics of temperature field prediction task,and a pixel-level online hard instance mining method is developed to balance the optimization difficulty in different calculation areas.The experiments demonstrate that the proposed method can effectively use physical knowledge to guide the training of surrogate models,reduce data requirements,and improve the prediction performance of data-driven methods.(2)For application scenarios where the physical knowledge is unclear but the physical field data implies regularity structures,this paper proposes a method to construct a physical field prediction surrogate model that incorporates the prior information of reducedorder models,aiming to improve the prediction accuracy and interpretability of the model with sparse observation data.This method employs the proper orthogonal decomposition to extract regular modes in physical field data as the essential features of physical system.It solves an optimization problem to obtain the optimal combination of data modes for the target physical field.The optimization problem under sparse observation data essentially involves solving an underdetermined linear equations system,which suffers from ill-posedness and low solution accuracy.To alleviate the underdetermined problem,this paper designs a general prediction framework and proposes to use the powerful approximation capability of DNNs to output the reference physical field as additional observations,combined with sensor data to constrain the optimization problem-solving jointly.Experiments demonstrate that the proposed method can improve the solution accuracy and alleviate the neural network performance bottleneck.It can also enhance the applicability of neural networks on complex and large-scale problems.(3)For application scenarios where there are related tasks that can assist the target task surrogate model in learning new knowledge,this paper proposes a cross-domain transfer learning-based method for constructing physical field prediction surrogate models,which can reduce the data requirement and improve the generalization performance of the target task.This paper first proposes a surrogate model construction method that combines data augmentation and deep transfer learning.The data augmentation method learns the differences between different physical field data by subtracting them,and achieves training efficiency improvement and sample size expansion.Then,it introduces deep transfer learning methods to utilize the knowledge learned in related task models to train the target model.The paper discusses the feasibility of transfer learning between sparse and dense grids,uniform and un-uniform grid types,and different boundary condition tasks in detail.Finally,this paper studies the method based on the neural operator theory to learn physical field prediction mapping in infinite-dimensional function spaces,aiming to improve the prediction performance and the transferability between different grid data of surrogate models.It also designs a representation method for sparse sensing data.Heat field and flow field prediction experiments verify the effectiveness of the proposed method.(4)For application scenarios where multiple related tasks can assist the target task learning simultaneously,this paper proposes a multi-source transfer learning method based on evolutionary computation to integrate rich prior knowledge from multiple source tasks and further improve the performance of the target surrogate model.The proposed method divides each model into blocks according to its structure and function.Then,it controls the knowledge transfer process of each module by applying different learning rates,which defines the form and encoding of the multi-source transfer learning strategy.The objective is to improve the efficiency of multi-source knowledge utilization and reduce the conflicts in the transfer of multiple models by controlling the knowledge transfer process of different models.Then,the proposed method uses the differential evolution method to find the optimal multi-source transfer learning strategy,which is expected to improve the efficiency of transfer learning strategy optimization.Experiments on thermal field and flow field show that the proposed method outperforms vanilla multi-source transfer learning methods and can improve the generalization ability of target model under limited samples.Besides,the optimal transfer learning strategy under small samples can be generalized to transfer learning tasks with more samples.