非线性系统
偏微分方程
人工神经网络
背景(考古学)
计算机科学
应用数学
反问题
偏导数
自动微分
物理定律
功能(生物学)
数学
数学分析
物理
算法
人工智能
量子力学
生物
进化生物学
古生物学
计算
作者
Maziar Raissi,Paris Perdikaris,George Em Karniadakis
标识
DOI:10.1016/j.jcp.2018.10.045
摘要
We introduce physics-informed neural networks – neural networks that are trained to solve supervised learning tasks while respecting any given laws of physics described by general nonlinear partial differential equations. In this work, we present our developments in the context of solving two main classes of problems: data-driven solution and data-driven discovery of partial differential equations. Depending on the nature and arrangement of the available data, we devise two distinct types of algorithms, namely continuous time and discrete time models. The first type of models forms a new family of data-efficient spatio-temporal function approximators, while the latter type allows the use of arbitrarily accurate implicit Runge–Kutta time stepping schemes with unlimited number of stages. The effectiveness of the proposed framework is demonstrated through a collection of classical problems in fluids, quantum mechanics, reaction–diffusion systems, and the propagation of nonlinear shallow-water waves.
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