Causally enhanced initial conditions: A novel soft constraints strategy for physics informed neural networks  

作　　者：Wenshu Zha Dongsheng Chen Daolun Li Luhang Shen Enyuan Chen 查文舒;陈东升;李道伦;沈路航;陈恩源

机构地区：[1]School of Mathematic,Hefei University of Technology,Hefei 230009,China

出　　处：《Chinese Physics B》2025年第4期365-375,共11页中国物理B(英文版)

基　　金：supported by the National Natural Science Foundation of China(Grant Nos.1217211 and 12372244).

摘　　要：Physics informed neural networks(PINNs)are a deep learning approach designed to solve partial differential equations(PDEs).Accurately learning the initial conditions is crucial when employing PINNs to solve PDEs.However,simply adjusting weights and imposing hard constraints may not always lead to better learning of the initial conditions;sometimes it even makes it difficult for the neural networks to converge.To enhance the accuracy of PINNs in learning the initial conditions,this paper proposes a novel strategy named causally enhanced initial conditions(CEICs).This strategy works by embedding a new loss in the loss function:the loss is constructed by the derivative of the initial condition and the derivative of the neural network at the initial condition.Furthermore,to respect the causality in learning the derivative,a novel causality coefficient is introduced for the training when selecting multiple derivatives.Additionally,because CEICs can provide more accurate pseudo-labels in the first subdomain,they are compatible with the temporal-marching strategy.Experimental results demonstrate that CEICs outperform hard constraints and improve the overall accuracy of pre-training PINNs.For the 1D-Korteweg–de Vries,reaction and convection equations,the CEIC method proposed in this paper reduces the relative error by at least 60%compared to the previous methods.

关 键 词：initial condition physics informed neural networks temporal march causality coefficient 

分 类 号：O241.82[理学—计算数学]