Simultaneous imposition of initial and boundary conditions via decoupled physics-informed neural networks for solving initialboundary value problems  

作　　者：K.A.LUONG M.A.WAHAB J.H.LEE 

机构地区：[1]Deep Learning Architecture Research Center,Sejong University,Seoul,05006,Republic of Korea [2]Soete Laboratory,Department of Electrical Energy,Metals,Mechanical Constructions,and Systems,Faculty of Engineering and Architecture,Ghent University,Gent,9000,Belgium [3]College of Engineering,Yuan Ze University,Taoyuan,32026,Taiwan,China

出　　处：《Applied Mathematics and Mechanics(English Edition)》2025年第4期763-780,共18页应用数学和力学(英文版)

基　　金：Project supported by the Basic Science Research Program through the National Research Foundation(NRF)of Korea funded by the Ministry of Science and ICT(No.RS-2024-00337001)。

摘　　要：Enforcing initial and boundary conditions(I/BCs)poses challenges in physics-informed neural networks(PINNs).Several PINN studies have gained significant achievements in developing techniques for imposing BCs in static problems;however,the simultaneous enforcement of I/BCs in dynamic problems remains challenging.To overcome this limitation,a novel approach called decoupled physics-informed neural network(d PINN)is proposed in this work.The d PINN operates based on the core idea of converting a partial differential equation(PDE)to a system of ordinary differential equations(ODEs)via the space-time decoupled formulation.To this end,the latent solution is expressed in the form of a linear combination of approximation functions and coefficients,where approximation functions are admissible and coefficients are unknowns of time that must be solved.Subsequently,the system of ODEs is obtained by implementing the weighted-residual form of the original PDE over the spatial domain.A multi-network structure is used to parameterize the set of coefficient functions,and the loss function of d PINN is established based on minimizing the residuals of the gained ODEs.In this scheme,the decoupled formulation leads to the independent handling of I/BCs.Accordingly,the BCs are automatically satisfied based on suitable selections of admissible functions.Meanwhile,the original ICs are replaced by the Galerkin form of the ICs concerning unknown coefficients,and the neural network(NN)outputs are modified to satisfy the gained ICs.Several benchmark problems involving different types of PDEs and I/BCs are used to demonstrate the superior performance of d PINN compared with regular PINN in terms of solution accuracy and computational cost.

关 键 词：decoupled physics-informed neural network(dPINN) decoupled formulation Galerkin method initial-boundary value problem(IBVP) machine learning 

分 类 号：O241[理学—计算数学] TP18[理学—数学]