Birgit Hillebrecht

Certified machine learning and its applications in computational biochemistry

Physics-informed neural networks (PINNs) are a powerful method to incorporate a priori available information of the system into a neural network (NN) representing the system. Despite its huge success in diverse application areas, a systematic analysis of the prediction error including rigorous error bounds has not been pursued so far. We use PINNs to discover an approximate solution to a partial or ordinary differential equation. This means especially, that we assume to know the structure and parameters of the surrogate model before applying the method instead of using neural networks to derive the structure or the parameters of the differential equation. During the project, we derive rigorous bounds for the prediction error of a PINN. The theoretical results will be demonstrated numerically with complex problems such as challenges in molecular dynamics research.