3 citations · 3 across the 4 of their papers we have counts for
5 papers
Preconditioning and Numerical Stability in Neural Network Training for Parametric PDEs
Markus Bachmayr, Wolfgang Dahmen, Chenguang Duan +1
In the context of training neural network-based approximations of solutions of parameter-dependent PDEs, we investigate the effect of preconditioning via well-conditioned frame rep…
Anderson Mixing in Bures Wasserstein Space of Gaussian Measures
Vitalii Aksenov, Martin Eigel, Mathias Oster
Various statistical tasks, including sampling or computing Wasserstein barycenters, can be reformulated as fixed-point problems for operators on probability distributions. Accelera…
Neural network approximation of regularized density functionals
Mihály A. Csirik, Andre Laestadius, Mathias Oster
Density functional theory is one of the most efficient and widely used computational methods of quantum mechanics, especially in fields such as solid state physics and quantum chem…
Variationally Correct Neural Residual Regression for Parametric PDEs: On the Viability of Controlled Accuracy
Markus Bachmayr, Wolfgang Dahmen, Mathias Oster
This paper is about learning the parameter-to-solution map for systems of partial differential equations (PDEs) that depend on a potentially large number of parameters covering all…
A comparison study of supervised learning techniques for the approximation of high dimensional functions and feedback control
Mathias Oster, Luca Saluzzi, Tizian Wenzel
Approximation of high dimensional functions is in the focus of machine learning and data-based scientific computing. In many applications, empirical risk minimisation techniques ov…