系统梳理物理信息神经网络的架构、应用与挑战，助力科研落地。
A comprehensive analysis of PINNs: Variants, Applications, and Challenges
- 全面分析PINNs架构与多种变体设计思路
- 对比不同方程和场景下的性能表现特征
- 揭示实现难点并指明未来研究方向
物理信息神经网络（PINNs）正成为求解微分方程的强大计算工具。尽管潜力显著，其实际应用仍处于初期阶段，亟需标准化以推动更广泛应用。本文系统综述了PINNs在架构、变体、应用场景及真实案例等方面的进展。现有综述多局限于单一应用或浅层分析，本工作旨在填补空白，整合最新研究成果，深入剖析各类因素。此外，还讨论了当前实现中的普遍挑战，并提出若干未来研究方向。整体贡献分为三部分：详尽梳理PINNs架构与变体；在不同方程与应用领域上进行性能分析，突出其特性；最后深入探讨现存问题与未来研究路径。
原文摘要 · Abstract (English)
Physics Informed Neural Networks (PINNs) have been emerging as a powerful computational tool for solving differential equations. However, the applicability of these models is still in its initial stages and requires more standardization to gain wider popularity. Through this survey, we present a comprehensive overview of PINNs approaches exploring various aspects related to their architecture, variants, areas of application, real-world use cases, challenges, and so on. Even though existing surveys can be identified, they fail to provide a comprehensive view as they primarily focus on either different application scenarios or limit their study to a superficial level. This survey attempts to bridge the gap in the existing literature by presenting a detailed analysis of all these factors combined with recent advancements and state-of-the-art research in PINNs. Additionally, we discuss prevalent challenges in PINNs implementation and present some of the future research directions as well. The overall contributions of the survey can be summarised into three sections: A detailed overview of PINNs architecture and variants, a performance analysis of PINNs on different equations and application domains highlighting their features. Finally, we present a detailed discussion of current issues and future research directions.
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