Physics-Informed Neural Network
A neural network trained to satisfy governing physical equations, not just fit data.
Definition
A physics-informed neural network (PINN) incorporates the governing differential equations of a system into its training objective. Alongside any data-fitting term, the loss penalizes violation of the equations, evaluated using automatic differentiation of the network.
PINNs shine at inverse problems, inferring unknown parameters or fields from sparse measurements while respecting the governing equations. They struggle with stiff dynamics and sharp gradients, where the equation-residual loss becomes hard to minimize, an active area of research.
The appeal of embedding physics is a model that respects conservation laws and behaves sensibly where data is sparse, which pure data-driven fits do not guarantee. The difficulty is optimization: balancing the data and equation-residual terms in the loss is delicate, and stiff or multi-scale problems can be hard to train. PINNs are therefore best seen as a complement to established solvers, strongest on inverse and data-assimilation problems.
How it works
- The network outputs the solution field as a function of coordinates.
- Derivatives come from automatic differentiation, exactly.
- The loss combines data mismatch with equation residuals and boundary conditions.
Why it matters
PINNs can solve or invert differential equations with sparse or noisy data, and they produce solutions consistent with known physics rather than arbitrary fits. They complement classical solvers, though they can be hard to train on stiff or multi-scale problems.
Fusion connection
Physics-informed models are a research direction for embedding plasma governing equations directly into Kronos surrogates, so predictions respect conservation laws rather than merely interpolating data.