ICML 2025

Physics-Informed DeepONets for drift-diffusion on metric graphs: simulation
and parameter identification
Jan Blechschmidt 1 2 Tom-Christian Riemer 1 Max Winkler 1 Martin Stoll 1 Jan-F. Pietschmann 3
Abstract
We develop a novel physics informed deep learn-
ing approach for solving nonlinear drift-diffusion
equations on metric graphs. These models repre-
sent an important model class with a large number
of applications in areas ranging from transport in
biological cells to the motion of human crowds.
While traditional numerical schemes require a
large amount of tailoring, especially in the case
of model design or parameter identification prob-
lems, physics informed deep operator networks
(DEEPONETS) have emerged as a versatile tool
for the solution of partial differential equations
with the particular advantage that they easily in-
corporate parameter identification questions. We
here present an approach where we first learn
three DEEPONET models for representative in-
flow, inner and outflow edges, resp., and then
subsequently couple these models for the solu-
tion of the drift-diffusion metric graph problem
by relying on an edge-based domain decomposi-
tion approach. We illustrate that our framework
is applicable for the accurate evaluation of graph-
coupled physics models and is well suited for
solving optimization or inverse problems on these
coupled networks.
1. Introduction
Dynamic processes on graphs (Newman, 2018; Barab´asi,
2016) are crucial for understanding complex phenomena
1Department of Mathematics, TU Chemnitz, Chemnitz,
Germany 2Department of Mathematics and Computer Science,
TU Bergakademie Freiberg, Freiberg, Germany 3Department
of Mathematics, University of Augsburg, Augsburg, Germany
and Centre for Advanced Analytics and Predictive Sciences
(CAAPS), University of Augsburg, Universit¨atsstr. 12a, 86159
Augsburg, Germany.
.
Correspondence to:
Jan Blech-
schmidt <jan.blechschmidt@math.tu-chemnitz.de>, Martin Stoll
<martin.stoll@math.tu-chemnitz.de>.
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