Physics-Informed Neural Networks Explained Simply

A standard neural network learns only from data. A physics-informed neural network also learns from the equations that describe the system, which are added directly to the loss function.

The model is therefore penalised twice: once when its predictions disagree with observations, and once when they disagree with physics.

Scientific datasets are often small, noisy and irregularly sampled. Physics constraints act like extra training data that never runs out.

The result tends to generalise better outside the observed range, which is exactly where forecasting lives.

In my solar flare work, the constraints keep the forecast consistent with how flare energy is expected to build and release, instead of letting the network fit noise.