Physics-informed neural networks (PINNs) have been popularized as a deep learning framework that can seamlessly synthesize observational data and partial differential equation (PDE) constraints. Their practical effectiveness however can be hampered by training pathologies, but also oftentimes by poor choices made by users who lack deep learning expertise. In this paper we present a series of best practices that can significantly improve the training efficiency and overall accuracy of PINNs. We also put forth a series of challenging benchmark problems that highlight some of the most prominent difficulties in training PINNs, and present comprehensive and fully reproducible ablation studies that demonstrate how different architecture choices and training strategies affect the test accuracy of the resulting models. We show that the methods and guiding principles put forth in this study lead to state-of-the-art results and provide strong baselines that future studies should use for comparison purposes. To this end, we also release a highly optimized library in JAX that can be used to reproduce all results reported in this paper, enable future research studies, as well as facilitate easy adaptation to new use-case scenarios.

翻译：物理信息神经网络（PINNs）作为一种深度学习框架，可实现观测数据与偏微分方程（PDE）约束的无缝融合，近年来受到广泛关注。然而，其实际应用效果常受训练病态问题影响，更往往因用户缺乏深度学习专业知识而做出不当选择。本文提出了一系列能显著提升PINNs训练效率与整体精度的最佳实践方法。我们同时构建了一系列具有挑战性的基准问题，凸显PINNs训练中最突出的困难，并开展全面且完全可复现的消融研究，揭示不同架构选择与训练策略对模型测试精度的影响。研究表明，本研究提出的方法与指导原则可达到顶尖性能，并为后续研究提供应作为对比基准的强基线。为此，我们还基于JAX框架发布了一个高度优化的代码库，可复现本文所有实验结果，支持未来学术研究，并可便捷适配至新型应用场景。