2 papers
math.NA2025
A posteriori certification of PDE approximations with particular application to neural networks
Lewin Ernst, Nikolaos Rekatsinas, Karsten Urban
We propose rigorous and efficiently computable lower and upper a posteriori error bounds for given approximations to PDEs on a given domain, which might be geometrically complex. T…
math.NA2022
A certified wavelet-based physics-informed neural network for the solution of parameterized partial differential equations
Lewin Ernst, Karsten Urban
Physics Informed Neural Networks (PINNs) have frequently been used for the numerical approximation of Partial Differential Equations (PDEs). The goal of this paper is to construct…