Physics-Informed Neural Networks
Neural networks trained to respect governing equations, improving data efficiency and extrapolation.
The idea
A physics-informed neural network (PINN) is trained not only to fit data but also to satisfy the differential equations that govern the system. The equations enter as an extra loss term: the network's outputs are differentiated and plugged into the PDE, and the residual is penalized. The network is pushed toward solutions that are both data-consistent and physically consistent.
Why it helps
- Less data needed, because physics constrains the solution
- Better behavior between and beyond data points
- A single framework for forward solving and inferring unknown parameters
Uses in fusion
PINNs and physics-constrained networks are studied for equilibrium reconstruction, where force balance can be imposed; for transport, where conservation laws constrain fluxes; and for inferring hidden parameters from partial measurements. The physics term keeps outputs plausible where data are sparse.
Practical difficulties
PINNs can be hard to train: the data loss and physics loss must be balanced, stiff equations create sharp features the network struggles to represent, and optimization can stall. They are not a universal replacement for classical solvers, which are often faster and more reliable for straightforward forward problems.
Where they shine
The strongest case for physics-informed methods is combining sparse, noisy measurements with known physics, or inferring quantities that are hard to measure directly. Used there, they add value; used as a drop-in for a well-posed forward solve, they often do not. As always, outputs are validated against independent solutions and their valid range is stated.