In this paper, we propose a novel framework, Dynamic Domain Decomposition Physics-Informed Neural Networks (D3PINNs), for solving time-dependent partial differential equations (PDEs). In this framework, solutions of time-dependent PDEs are dynamically captured. First, an approximate solution is obtained by the Physics-Informed Neural Networks (PINNs) containing the domain decomposition, then the time derivative terms in the PDE will be retained and the other terms associated with the solution will be replaced with the approximate solution. As a result, the PDE reduces to an ordinary differential equations (ODEs). Finally, the time-varying solution will be solved by the classical numerical methods for ODEs. D3PINNs retain the computational efffciency and ffexibility inherent to PINNs and enhance the ability for capturing solutions of time-dependent PDEs. Numerical experiments validate the effectiveness of the proposed methods.

翻译：本文提出了一种新颖的框架——动态区域分解物理信息神经网络（D3PINNs），用于求解时间依赖的偏微分方程。在该框架中，时间依赖偏微分方程的解被动态捕获。首先，通过包含区域分解的物理信息神经网络获得近似解；随后，保留偏微分方程中的时间导数项，并将与解相关的其他项替换为该近似解。因此，偏微分方程被简化为常微分方程。最后，时变解将通过经典的常微分方程数值方法求解。D3PINNs 保留了物理信息神经网络固有的计算效率和灵活性，并增强了对时间依赖偏微分方程解的捕获能力。数值实验验证了所提方法的有效性。