Deep learning has been highly successful in some applications. Nevertheless, its use for solving partial differential equations (PDEs) has only been of recent interest with current state-of-the-art machine learning libraries, e.g., TensorFlow or PyTorch. Physics-informed neural networks (PINNs) are an attractive tool for solving partial differential equations based on sparse and noisy data. Here extend PINNs to solve obstacle-related PDEs which present a great computational challenge because they necessitate numerical methods that can yield an accurate approximation of the solution that lies above a given obstacle. The performance of the proposed PINNs is demonstrated in multiple scenarios for linear and nonlinear PDEs subject to regular and irregular obstacles.

翻译：深度学习在某些应用中取得了巨大成功。然而，利用当前最先进的机器学习库（如TensorFlow或PyTorch）求解偏微分方程（PDEs）仅是近期才受到关注。物理信息神经网络（PINNs）是一种基于稀疏且含噪声数据求解偏微分方程的重要工具。本文扩展PINNs以求解障碍相关偏微分方程，此类方程因要求数值方法能够精确逼近位于给定障碍上方的解而带来重大计算挑战。所提出的PINNs性能在线性和非线性偏微分方程中针对规则与不规则障碍的多种场景得到了验证。