Deep Neural Cellular Potts Models

Koen Minartz, Tim D’Hondt, Leon Hillmann, Jörn Starruß, Lutz Brusch, Vlado Menkovski
Proceedings of the 42nd International Conference on Machine Learning, PMLR 267:44351-44371, 2025.

Abstract

The cellular Potts model (CPM) is a powerful computational method for simulating collective spatiotemporal dynamics of biological cells. To drive the dynamics, CPMs rely on physics-inspired Hamiltonians. However, as first principles remain elusive in biology, these Hamiltonians only approximate the full complexity of real multicellular systems. To address this limitation, we propose NeuralCPM, a more expressive cellular Potts model that can be trained directly on observational data. At the core of NeuralCPM lies the Neural Hamiltonian, a neural network architecture that respects universal symmetries in collective cellular dynamics. Moreover, this approach enables seamless integration of domain knowledge by combining known biological mechanisms and the expressive Neural Hamiltonian into a hybrid model. Our evaluation 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.

Cite this Paper

BibTeX
@InProceedings{pmlr-v267-minartz25a, title = {Deep Neural Cellular Potts Models}, author = {Minartz, Koen and D'Hondt, Tim and Hillmann, Leon and Starru{\ss}, J\"{o}rn and Brusch, Lutz and Menkovski, Vlado}, booktitle = {Proceedings of the 42nd International Conference on Machine Learning}, pages = {44351--44371}, year = {2025}, editor = {Singh, Aarti and Fazel, Maryam and Hsu, Daniel and Lacoste-Julien, Simon and Berkenkamp, Felix and Maharaj, Tegan and Wagstaff, Kiri and Zhu, Jerry}, volume = {267}, series = {Proceedings of Machine Learning Research}, month = {13--19 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v267/main/assets/minartz25a/minartz25a.pdf}, url = {https://proceedings.mlr.press/v267/minartz25a.html}, abstract = {The cellular Potts model (CPM) is a powerful computational method for simulating collective spatiotemporal dynamics of biological cells. To drive the dynamics, CPMs rely on physics-inspired Hamiltonians. However, as first principles remain elusive in biology, these Hamiltonians only approximate the full complexity of real multicellular systems. To address this limitation, we propose NeuralCPM, a more expressive cellular Potts model that can be trained directly on observational data. At the core of NeuralCPM lies the Neural Hamiltonian, a neural network architecture that respects universal symmetries in collective cellular dynamics. Moreover, this approach enables seamless integration of domain knowledge by combining known biological mechanisms and the expressive Neural Hamiltonian into a hybrid model. Our evaluation 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.} }
Endnote
%0 Conference Paper %T Deep Neural Cellular Potts Models %A Koen Minartz %A Tim D’Hondt %A Leon Hillmann %A Jörn Starruß %A Lutz Brusch %A Vlado Menkovski %B Proceedings of the 42nd International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2025 %E Aarti Singh %E Maryam Fazel %E Daniel Hsu %E Simon Lacoste-Julien %E Felix Berkenkamp %E Tegan Maharaj %E Kiri Wagstaff %E Jerry Zhu %F pmlr-v267-minartz25a %I PMLR %P 44351--44371 %U https://proceedings.mlr.press/v267/minartz25a.html %V 267 %X The cellular Potts model (CPM) is a powerful computational method for simulating collective spatiotemporal dynamics of biological cells. To drive the dynamics, CPMs rely on physics-inspired Hamiltonians. However, as first principles remain elusive in biology, these Hamiltonians only approximate the full complexity of real multicellular systems. To address this limitation, we propose NeuralCPM, a more expressive cellular Potts model that can be trained directly on observational data. At the core of NeuralCPM lies the Neural Hamiltonian, a neural network architecture that respects universal symmetries in collective cellular dynamics. Moreover, this approach enables seamless integration of domain knowledge by combining known biological mechanisms and the expressive Neural Hamiltonian into a hybrid model. Our evaluation 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.
APA
Minartz, K., D’Hondt, T., Hillmann, L., Starruß, J., Brusch, L. & Menkovski, V.. (2025). Deep Neural Cellular Potts Models. Proceedings of the 42nd International Conference on Machine Learning, in Proceedings of Machine Learning Research 267:44351-44371 Available from https://proceedings.mlr.press/v267/minartz25a.html.

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