Publications (5)
The Oracle of DLphi
Dominik Alfke, Weston Baines, Jan Blechschmidt +24
We present a novel technique based on deep learning and set theory which yields exceptional classification and prediction results. Having access to a sufficiently large amount of l…
A comparison of PINN approaches for drift-diffusion equations on metric graphs
Jan Blechschmidt, Jan-Frederik Pietschman, Tom-Christian Riemer +2
In this paper we focus on comparing machine learning approaches for quantum graphs, which are metric graphs, i.e., graphs with dedicated edge lengths, and an associated differentia…
Three Ways to Solve Partial Differential Equations with Neural Networks -- A Review
Jan Blechschmidt, Oliver G. Ernst
Neural networks are increasingly used to construct numerical solution methods for partial differential equations. In this expository review, we introduce and contrast three importa…
Error estimation for second-order PDEs in non-variational form
Jan Blechschmidt, Roland Herzog, Max Winkler
Second-order partial differential equations in non-divergence form are considered. Equations of this kind typically arise as subproblems for the solution of Hamilton-Jacobi-Bellman…
Physics-Informed DeepONets for drift-diffusion on metric graphs: simulation and parameter identification
Jan Blechschmidt, Tom-Christian Riemer, Max Winkler +2
We develop a novel physics informed deep learning approach for solving nonlinear drift-diffusion equations on metric graphs. These models represent an important model class with a…