Datum predavanja: četvrtak, 18.6.2026.
Vrijeme predavanja: 11h u B06

Birgit Hillebrecht, Universität Stuttgart
Title: A rigorous framework to certify predictions from physics-informed neural networks

Abstract:
Since physics-informed neural networks (PINNs) were introduced and their feasibility demonstrated, the topic has attracted growing attention and has been investigated, beyond others, with respect to its a priori approximation capabilities. While a priori results quantify the expressive power of PINNs, they do not guarantee the reliability of a concrete trained instance. Hence, for PINNs to serve as viable alternatives to classical numerical schemes, the availability of rigorous a posteriori error bounds that certify the prediction are essential.

We address this need for certification for PINNs as surrogate models to abstract linear boundary- and initial-value problems (BIVP) by deriving two a posteriori error bounds for the PINN prediction. We leverage for one error estimator the concept of input-to-state stability for infinite-dimensional systems and the therein used gain bounds. Since these gain bounds are often not analytically accessible, we further derive approximation results to retrieve the gain bounds from numerical discretization.