Understanding Physics-Informed Neural Networks: Techniques, Applications, Trends, and Challenges

• Published in: AI (Basel) Vol. 5; no. 3; pp. 1534 - 1557
• Main Authors: Farea, Amer, Yli-Harja, Olli, Emmert-Streib, Frank
• Format: Journal Article
• Language: English
• Published: Basel MDPI AG 01.09.2024
• Subjects: Bibliometrics; Cognitive science; Complexity; Computer vision; data-driven modeling; Deep learning; Engineering; Fluid dynamics; Inverse problems; Knowledge; Machine learning; Mechanics; Methods; Natural language processing; neural network architectures; Neural networks; Ordinary differential equations; Partial differential equations; Physical sciences; Physics; physics-informed neural networks; Trends
• ISSN: 2673-2688; 2673-2688
• DOI: 10.3390/ai5030074

Physics-informed neural networks (PINNs) represent a significant advancement at the intersection of machine learning and physical sciences, offering a powerful framework for solving complex problems governed by physical laws. This survey provides a comprehensive review of the current state of research on PINNs, highlighting their unique methodologies, applications, challenges, and future directions. We begin by introducing the fundamental concepts underlying neural networks and the motivation for integrating physics-based constraints. We then explore various PINN architectures and techniques for incorporating physical laws into neural network training, including approaches to solving partial differential equations (PDEs) and ordinary differential equations (ODEs). Additionally, we discuss the primary challenges faced in developing and applying PINNs, such as computational complexity, data scarcity, and the integration of complex physical laws. Finally, we identify promising future research directions. Overall, this survey seeks to provide a foundational understanding of PINNs within this rapidly evolving field.