A Review of Physics-Informed Neural Networks

This article presents Physics-Informed Neural Networks (PINNs), which integrate physical laws into neural network training to model complex systems governed by partial differential equations (PDEs). PINNs enhance data efficiency, allowing for accurate predictions with less training data, and have applications in fields such as biomedical engineering, geophysics, and material science. Despite their advantages, PINNs face challenges like learning high-frequency components and computational overhead. Proposed solutions include causality constraints and improved boundary condition handling. A numerical experiment demonstrates the effectiveness of PINNs in solving the one-dimensional heat conduction equation, showcasing enhanced model stability and accuracy. Overall, PINNs represent a significant advancement in merging machine learning with physics.