ICML 2025

Deep Neural Cellular Potts Models
Koen Minartz 1 Tim d’Hondt 1 Leon Hillmann 2 1 3 J¨orn Starruß 4 Lutz Brusch 4 Vlado Menkovski 1
Abstract
The cellular Potts model (CPM) is a power-
ful computational method for simulating collec-
tive spatiotemporal dynamics of biological cells.
To drive the dynamics, CPMs rely on physics-
inspired Hamiltonians. However, as first prin-
ciples remain elusive in biology, these Hamilto-
nians only approximate the full complexity of
real multicellular systems. To address this limi-
tation, we propose NeuralCPM, a more expres-
sive cellular Potts model that can be trained di-
rectly on observational data. At the core of Neu-
ralCPM lies the Neural Hamiltonian, a neural
network architecture that respects universal sym-
metries in collective cellular dynamics. More-
over, this approach enables seamless integration
of domain knowledge by combining known bi-
ological mechanisms and the expressive Neural
Hamiltonian into a hybrid model. Our evalua-
tion with synthetic and real-world multicellular
systems demonstrates that NeuralCPM is able to
model cellular dynamics that cannot be accounted
for by traditional analytical Hamiltonians.
1. Introduction
Cell migration and multicellular self-organization are cru-
cial biological processes that drive many phenomena of life,
such as embryo growth and the spread of cancer (Friedl
& Gilmour, 2009; Gottheil et al., 2023). Understanding
these cellular dynamics is not only a fundamental goal of
1Department of Mathematics and Computer Science, Eind-
hoven University of Technology, Eindhoven, the Netherlands
2Department of Applied Physics and Science Education, Eind-
hoven University of Technology, Eindhoven, the Netherlands
3Department of Biomedical Engineering, Eindhoven University of
Technology, Eindhoven, the Netherlands 4Center for Information
Services and High Performance Computing, TUD Dresden Univer-
sity of Technology, Dresden, Germany. Correspondence to: Koen
Minartz <k.minartz@tue.nl>, Lutz Bru...