现代应用物理2025，Vol.16Issue(1)：73-85,13.DOI:10.12061/j.issn.2095-6223.202412038
求解含时偏微分方程的物理信息神经网络研究进展
Recent Advances of Physics-Informed Neural Networks in Solving Time-Dependent Partial Differential Equations
摘要
Abstract
Physics-informed neural networks(PINN)are a class of neural networks frameworks that integrate physics models and deep learning technologies,gradually becoming a new methodology for the intersection and integration of machine learning and computational science.This method can not only fit the initial conditions,boundary conditions,and observed data,but also be constrained by partial differential equations(PDEs).Recently,PINN has made a series of achievements.However,when it deals with complex time-dependent PDEs,it often encounters training difficulties and results in low accuracy performances.In this paper,the basic principles and main procedures of PINN are systematically introduced for solving time-dependent PDEs.Then,four underlying problems behind the failure from four vital procedures are identified and the recent advances of PINN in four corresponding improvement approaches,i.e.,sampling methods,improved design of loss functions,domain knowledge embedding,and theoretical error analysis are carefully summarised.Finally,the advances of PINN in solving time-dependent PDEs are concluded in the aspects of method,application and theory,and the future directions are discussed.关键词
深度学习/科学计算/物理信息神经网络/含时偏微分方程/研究进展Key words
deep learning/scientific computing/physics-informed neural networks/time-dependent partial differential equations/recent advances分类
计算机与自动化引用本文复制引用
郭嘉,刘子源,侯臣平..求解含时偏微分方程的物理信息神经网络研究进展[J].现代应用物理,2025,16(1):73-85,13.基金项目
国家杰出青年科学基金资助项目(62425607) （62425607）
国家自然科学基金资助项目(62136005) （62136005）
