The physics informed neural network (PINN) is a promising method for solving time-evolution partial differential equations (PDEs). However, the standard PINN method may fail to solve the PDEs with strongly nonlinear characteristics or those with high-frequency solutions. The physics informed neural network (PINN) is a promising method for solving time-evolution partial differential equations (PDEs). However, the standard PINN method may fail to solve the PDEs with strongly nonlinear characteristics or those with high-frequency solutions. The PT-PINN method transforms the difficult problem on the entire time domain to relatively simple problems defined on small subdomains. The neural network trained on small subdomains provides the neural network initialization and extra supervised learning data for the problems on larger subdomains or on the entire time-domain. By numerical experiments, we demonstrate that the PT-PINN succeeds in solving the evolution PDEs with strong non-linearity and/or high frequency solutions, including the strongly nonlinear heat equation, the Allen-Cahn equation, the convection equation with high-frequency solutions and so on, and that the convergence and accuracy of the PT-PINN is superior to the standard PINN method. The PT-PINN method is a competitive method for solving the time-evolution PDEs.

翻译：物理学知情神经网络(PINN)是解决时间演变部分差异方程式(PDEs)的一个很有希望的方法。然而,标准的PINN方法可能无法以强烈的非线性特征或高频解决方案解决时间演变部分差异方程式(PDEs ) 。标准的PINN方法可能无法以强烈的非线性特征或高频解决方案解决时间演变部分差异方程式(PDEs )。标准的PINNN方法可能无法解决时间演变部分方程式(PDEs ) 。但是,标准的PINNN方法可能无法以强烈的非线性特征或高频解决方案解决时间变化部分差异方程式(PDN),将整个时间域的难题转化为小子域定义的相对简单的问题。在小型次域内经培训的神经网络为更大的子域或整个时界的问题提供神经网络初始化和额外监管的学习数据。通过数字实验,PNPNNNNPN(PPPP-P) 的精确度和高频度方程式是高分辨率解决方案。