Physics-Informed ML

Physics-informed machine learning studies how to combine observations with governing equations, conservation laws, symmetries, and other scientific knowledge. Common approaches include physics-informed neural networks (PINNs) that penalize equation residuals, weak or variational formulations, neural operators for families of PDE solutions, and hybrid models that learn corrections to mechanistic simulators. These methods are used for forward simulation, inverse problems, parameter estimation, forecasting, and fast surrogates when measurements or computational resources are limited. A central challenge is that physical constraints can improve data efficiency and consistency but can also hinder training or harm predictions when the equations, discretization, or assumed structure do not match the system.