Physics-informed machine learning is the broad idea of building known scientific laws directly into how a model is trained, rather than hoping the model rediscovers them from data alone. The 2021 Nature Reviews Physics survey “Physics-informed machine learning,” by George Em Karniadakis and colleagues, laid out the field and its three main ways of injecting physics: through the training data, through the design of the network, and through the loss function.
The most influential instance is the physics-informed neural network, or PINN, which adds a penalty term measuring how far the network’s predictions stray from a governing differential equation. Other instances enforce known symmetries or conservation laws in the architecture itself, or constrain the model with carefully chosen examples. The shared goal is the same: combine the flexibility of machine learning with the hard constraints that centuries of physics provide.
The payoff is most visible when data is limited or expensive, a common situation in science and engineering. A purely data-driven model can wander off into physically impossible predictions between its data points; a physics-informed one is anchored by the equations and tends to generalize better and need less data.
For a general reader, this captures a maturing attitude in AI for science: the most useful scientific models are often not the ones that ignore prior knowledge, but the ones that fuse it with learning. That hybrid is now a standard tool across fluid dynamics, climate modeling, biomechanics, and beyond.