What is a physics-informed neural network (PINN)?

A physics-informed neural network is a model trained with the governing physical equations built directly into its loss function. Because the physics constrains the solution space, the network needs far less data than a purely data-driven surrogate — often on the order of 0.01% of what a comparable classical approach requires. It is most useful where simulation data is expensive and the equations are known.

The loss has two terms: a data term over whatever measurements exist, and a residual term penalising violations of the differential equations at sampled points in the domain. The second term is what does the work when data is scarce.

The trade-off is training difficulty. PINN losses are stiff and sensitive to how the two terms are weighted, so they need more careful optimisation than a standard supervised model.

They fit industrial simulation problems well — flow, heat, structural response — where the physics is settled and running the classical solver is the expensive part.

Written by Binary AI Labs · Reviewed 2026-11-01