标题： PINNs的综合分析：变体、应用与挑战 显示英文标题

标题： A comprehensive analysis of PINNs: Variants, Applications, and Challenges

摘要： 物理信息神经网络（PINNs）作为一种求解微分方程的强大计算工具正在兴起。然而，这些模型的适用性仍处于初级阶段，需要更多的标准化才能获得更广泛的普及。通过本综述，我们全面概述了PINNs方法，探讨了与其架构、变体、应用领域、实际使用案例、挑战等相关各个方面。尽管已经存在一些综述，但它们未能提供全面的视角，因为它们主要集中在不同的应用场景或者局限于表面层次的研究。本综述试图通过结合PINNs的详细分析以及最新的进展和前沿研究来填补现有文献中的空白。此外，我们还讨论了PINNs实施过程中存在的常见挑战，并提出了未来的研究方向。本综述的整体贡献可以概括为三个部分：PINNs架构及其变体的详细概述，不同方程和应用领域的PINNs性能分析以突出其特性。最后，我们对当前问题和未来研究方向进行了详细讨论。 显示英文摘要

摘要： 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.