Physics-informed neural networks (PINNs) have emerged as a versatile and widely applicable concept across various science and engineering domains over the past decade. This article offers a comprehensive overview of the fundamentals of PINNs, tracing their evolution, modifications, and various variants. It explores the impact of different parameters on PINNs and the optimization algorithms involved. The review also delves into the theoretical advancements related to the convergence, consistency, and stability of numerical solutions using PINNs, while highlighting the current state of the art. Given their ability to address equations involving complex physics, the article discusses various applications of PINNs, with a particular focus on their utility in computational fluid dynamics problems. Additionally, it identifies current gaps in the research and outlines future directions for the continued development of PINNs.

翻译：物理信息神经网络（PINNs）在过去十年中已成为一个多功能且广泛适用于各科学与工程领域的概念。本文全面概述了PINNs的基础理论，追溯其发展历程、改进方案及各类变体。文章探讨了不同参数对PINNs的影响以及所涉及的优化算法。本综述深入分析了与PINNs数值解的收敛性、一致性和稳定性相关的理论进展，同时突出了当前的技术前沿。鉴于PINNs处理复杂物理方程的能力，本文讨论了其多种应用场景，特别聚焦于计算流体动力学问题中的实用价值。此外，文章指出了当前研究存在的空白，并展望了PINNs持续发展的未来方向。