论文标题
高精度分化技术，用于通过物理知识神经网络的非线性PDE的数据驱动解决方案
High Precision Differentiation Techniques for Data-Driven Solution of Nonlinear PDEs by Physics-Informed Neural Networks
论文作者
论文摘要
本文考虑了具有给定初始条件的时间依赖性部分微分方程。提出了关于时间变量的未知解决方案的新分化技术。结果表明，所提出的技术允许在一组空间点同时生成准确的高阶衍生物。然后，计算出的衍生物可以以不同的方式用于数据驱动的解决方案。在Tensorflow背景框架下，Python中著名的DeepXDE软件解决方案的物理知情的神经网络应用程序已针对三个现实生活PDE：Burgers'，Allen-Cahn和Schrodinger方程式。
Time-dependent Partial Differential Equations with given initial conditions are considered in this paper. New differentiation techniques of the unknown solution with respect to time variable are proposed. It is shown that the proposed techniques allow to generate accurate higher order derivatives simultaneously for a set of spatial points. The calculated derivatives can then be used for data-driven solution in different ways. An application for Physics Informed Neural Networks by the well-known DeepXDE software solution in Python under Tensorflow background framework has been presented for three real-life PDEs: Burgers', Allen-Cahn and Schrodinger equations.
