Identification of underlying partial differential equations(PDEs)for complex systems remains a formidable challenge.In the present study,a robust PDE identification method is proposed,demonstrating the ability to extr...Identification of underlying partial differential equations(PDEs)for complex systems remains a formidable challenge.In the present study,a robust PDE identification method is proposed,demonstrating the ability to extract accurate governing equations under noisy conditions without prior knowledge.Specifically,the proposed method combines gene expression programming,one type of evolutionary algorithm capable of generating unseen terms based solely on basic operators and functional terms,with symbolic regression neural networks.These networks are designed to represent explicit functional expressions and optimize them with data gradients.In particular,the specifically designed neural networks can be easily transformed to physical constraints for the training data,embedding the discovered PDEs to further optimize the metadata used for iterative PDE identification.The proposed method has been tested in four canonical PDE cases,validating its effectiveness without preliminary information and confirming its suitability for practical applications across various noise levels.展开更多
基金supported by the National Natural Science Foundation of China(Grant Nos.92152102 and 92152202)the Advanced Jet Propulsion Innovation Center/AEAC(Grant No.HKCX2022-01-010)。
文摘Identification of underlying partial differential equations(PDEs)for complex systems remains a formidable challenge.In the present study,a robust PDE identification method is proposed,demonstrating the ability to extract accurate governing equations under noisy conditions without prior knowledge.Specifically,the proposed method combines gene expression programming,one type of evolutionary algorithm capable of generating unseen terms based solely on basic operators and functional terms,with symbolic regression neural networks.These networks are designed to represent explicit functional expressions and optimize them with data gradients.In particular,the specifically designed neural networks can be easily transformed to physical constraints for the training data,embedding the discovered PDEs to further optimize the metadata used for iterative PDE identification.The proposed method has been tested in four canonical PDE cases,validating its effectiveness without preliminary information and confirming its suitability for practical applications across various noise levels.
基金supported by the National Natural Science Foundation of China (Grant Nos.92152102,12222203,11972093,and 91852207)the National Key R&D Program of China (Grant No.2020YFE0204200).
