Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations
Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations
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DOI：
10.1016/j.jcp.2018.10.045
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发表时间：
2019-02-01
影响因子：
4.1
通讯作者：
Karniadakis, G. E.
中科院分区：
文献类型：
--
作者：
Raissi, M.;Perdikaris, P.;Karniadakis, G. E.
我们介绍了物理信息神经网络-神经网络经过训练，可以解决监督学习任务，同时尊重由一般非线性偏微分方程描述的任何给定的物理定律。在这项工作中，我们提出了解决两类主要问题的背景下，我们的发展：数据驱动的解决方案和数据驱动的偏微分方程的发现。根据可用数据的性质和安排，我们设计了两种不同类型的算法，即连续时间和离散时间模型。第一种类型的模型形成了一个新的家庭的数据高效的时空函数逼近器，而后一种类型允许使用任意精确的隐式龙格-库塔时间步进计划与无限数量的阶段。所提出的框架的有效性证明，通过收集经典问题的流体，量子力学，反应扩散系统，和非线性浅水波的传播。(C)2018爱思唯尔公司All rights reserved.
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. (C) 2018 Elsevier Inc. All rights reserved.