31 citations · 101 across the 13 of their papers we have counts for
16 papers
Deep smoothness WENO scheme for two-dimensional hyperbolic conservation laws: A deep learning approach for learning smoothness indicators
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. The…
PINN Training using Biobjective Optimization: The Trade-off between Data Loss and Residual Loss
Fabian Heldmann, Sarah Berkhahn, Matthias Ehrhardt +1
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…
Mixed-Dimensional Geometric Coupling of Port-Hamiltonian Systems
Jens Jäschke, Nathanael Skrepek, Matthias Ehrhardt
We propose a new interconnection relation for infinite-dimensional port-Hamiltonian systems that enables the coupling of ports with different spatial dimensions by integrating over…
A gradient based calibration method for the Heston model
Anna Clevenhaus, Claudia Totzeck, Matthias Ehrhardt
The Heston model is a well-known two-dimensional financial model. Because the Heston model contains implicit parameters that cannot be determined directly from real market data, ca…
Enhanced fifth order WENO Shock-Capturing Schemes with Deep Learning
Tatiana Kossaczká, Matthias Ehrhardt, Michael Günther
In this paper we enhance the well-known fifth order WENO shock-capturing scheme by using deep learning techniques. This fine-tuning of an existing algorithm is implemented by train…
Higher Strong Order Methods for Itô SDEs on Matrix Lie Groups
Michelle Muniz, Matthias Ehrhardt, Michael Günther +1
In this paper we present a general procedure for designing higher strong order methods for Itô stochastic differential equations on matrix Lie groups and illustrate this strategy w…