Deep smoothness WENO scheme for two-dimensional hyperbolic conservation laws: A deep learning approach for learning smoothness indicators

no code implementations • 18 Sep 2023 • Tatiana Kossaczká, Ameya D. Jagtap, Matthias Ehrhardt

In this paper, we introduce an improved version of the fifth-order weighted essentially non-oscillatory (WENO) shock-capturing scheme by incorporating deep learning techniques.

PINN Training using Biobjective Optimization: The Trade-off between Data Loss and Residual Loss

no code implementations • 3 Feb 2023 • Fabian Heldmann, Sarah Berkhahn, Matthias Ehrhardt, Kathrin Klamroth

Physics informed neural networks (PINNs) have proven to be an efficient tool to represent problems for which measured data are available and for which the dynamics in the data are expected to follow some physical laws.

Stochastic Primal-Dual Three Operator Splitting with Arbitrary Sampling and Preconditioning

no code implementations • 2 Aug 2022 • Junqi Tang, Matthias Ehrhardt, Carola-Bibiane Schönlieb

In this work we propose a stochastic primal-dual preconditioned three-operator splitting algorithm for solving a class of convex three-composite optimization problems.