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AsPINN: Adaptive symmetry-recomposition physics-informed neural networks

文献类型：期刊论文

作者Liu ZT(刘子提)2,3; Liu Y(刘洋)3; Yan, Xunshi1; Liu W(刘文)3; Guo SQ(郭帅旗)3; Zhang CA(张陈安)3; Liu Y(刘洋); Zhang CA(张陈安); Liu W(刘文); Liu W(刘文)
刊名COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
出版日期2024-12-01
卷号432页码:34
关键词Network structure Parameter-sharing Feature-enhanced physics-informed neural networks Symmetry decomposition
ISSN号0045-7825
DOI10.1016/j.cma.2024.117405
通讯作者Liu, Yang(liuyang2@imech.ac.cn) ; Yan, Xunshi(yanxs@tsinghua.edu.cn)
英文摘要Physics-informed neural networks (PINNs) have shown promise for solving partial differential equations (PDEs). However, PINNs' loss, the regularization terms, can only guarantee that the prediction results conform to the physical constraints in the average sense, which results in PINNs' inability to strictly adhere to implied physical laws such as conservation laws and symmetries. This limits the optimization speed and accuracy of PINNs. Although some feature- enhanced PINNs attempt to address this issue by adding explicit constraints, their generality is limited due to specific question settings. To overcome this limitation, our study proposes the adaptive symmetry-recomposition PINN (AsPINN). By analyzing the parameter-sharing patterns of fully connected PINNs, specific network structures are developed to provide predictions with strict symmetry constraints. These structures are incorporated into diverse subnetworks to provide constrained intermediate outputs, then a specialized multi-head attention mechanism is attached to evaluate and composite them into final predictions adaptively. Thus, AsPINN maintains precise constraints while addressing the inability of individual structural subnetworks' generality. This method is then applied to address several physically significant PDEs, including both forward and inverse problems. The numerical results demonstrates AsPINN's mathematical consistency and generality, offering advantages in terms of optimization speed and accuracy with a reduced number of trainable parameters. The results also manifest that AsPINN mitigates the impact of ill-conditioned data.
分类号一类
资助项目Strategic Priority Research Program (B) of Chinese Academy of Science, China[XDB0620402] ; Youth Innovation Promotion Association CAS, China[2023023]
WOS研究方向Engineering ; Mathematics ; Mechanics
语种英语
WOS记录号WOS:001327870300001
资助机构Strategic Priority Research Program (B) of Chinese Academy of Science, China ; Youth Innovation Promotion Association CAS, China
其他责任者Liu, Yang ; Yan, Xunshi
源URL[http://dspace.imech.ac.cn/handle/311007/96913]  
专题力学研究所_高温气体动力学国家重点实验室
通讯作者Liu Y(刘洋); Liu Y(刘洋)
作者单位1.Tsinghua Univ, Inst Nucl & New Energy Technol, Beijing 100084, Peoples R China
2.Univ Chinese Acad Sci, Sch Engn Sci, Beijing 100049, Peoples R China;
3.Chinese Acad Sci, Inst Mech, State Key Lab High Temp Gas Dynam, Beijing 100190, Peoples R China;
推荐引用方式
GB/T 7714		 Liu ZT,Liu Y,Yan, Xunshi,et al. AsPINN: Adaptive symmetry-recomposition physics-informed neural networks[J]. COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING,2024,432:34.
APA 刘子提.,刘洋.,Yan, Xunshi.,刘文.,郭帅旗.,...&Liu ZT.(2024).AsPINN: Adaptive symmetry-recomposition physics-informed neural networks.COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING,432,34.
MLA 刘子提,et al."AsPINN: Adaptive symmetry-recomposition physics-informed neural networks".COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING 432(2024):34.

入库方式： OAI收割

来源：力学研究所

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