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领域取得了显著成功。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）的研究近期才受到关注。物理信息神经网络（PINNs）是基于稀疏噪声数据求解偏微分方程的有效工具。本文扩展PINNs以求解障碍相关偏微分方程，这类方程因需要数值方法精确逼近位于给定障碍上方的解而构成重大计算挑战。通过线性与非线性偏微分方程在规则与非规则障碍约束下的多场景实验，验证了所提出PINNs方法的性能。