Physics-Informed Learning

Vanilla neural networks treat physical data like any other data - and then waste their capacity rediscovering, badly, structure we already know to be exactly true. A network approximating a dynamical system has no reason to conserve energy, respect symmetries, or stay stable beyond its training window. It will happily violate all three.

Bake the laws in instead of hoping they emerge. Physics-informed networks put the governing equations into the loss itself: the residual of the PDE becomes a training signal, conservation laws become penalties the optimizer cannot ignore. The model stops being a black-box curve-fitter and becomes a solver constrained to the manifold of physically possible answers.

Research work at TUM at the seam of the two fields I study - and the conviction, carried into everything since, that the best prior you can give a learning system is a law of nature. The same instinct powers this site's lab. I wrote up the full theory and three solvers, with the presented slides, in the deep dive linked below.