A comparison of PINN approaches for drift-diffusion equations on metric graphs

no code implementations • 15 May 2022 • Jan Blechschmidt, Jan-Frederik Pietschman, Tom-Christian Riemer, Martin Stoll, Max Winkler

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 differential operator.

Three Ways to Solve Partial Differential Equations with Neural Networks -- A Review

3 code implementations • 23 Feb 2021 • Jan Blechschmidt, Oliver G. Ernst

Neural networks are increasingly used to construct numerical solution methods for partial differential equations.

Numerical Analysis Numerical Analysis

The Oracle of DLphi

no code implementations • 17 Jan 2019 • Dominik Alfke, Weston Baines, Jan Blechschmidt, Mauricio J. del Razo Sarmina, Amnon Drory, Dennis Elbrächter, Nando Farchmin, Matteo Gambara, Silke Glas, Philipp Grohs, Peter Hinz, Danijel Kivaranovic, Christian Kümmerle, Gitta Kutyniok, Sebastian Lunz, Jan Macdonald, Ryan Malthaner, Gregory Naisat, Ariel Neufeld, Philipp Christian Petersen, Rafael Reisenhofer, Jun-Da Sheng, Laura Thesing, Philipp Trunschke, Johannes von Lindheim, David Weber, Melanie Weber

We present a novel technique based on deep learning and set theory which yields exceptional classification and prediction results.

General Classification