# Surrogate modeling of Cellular-Potts Agent-Based Models as a segmentation task using the U-Net neural network architecture

arXiv: https://arxiv.org/abs/2505.00316 · HTML: https://mlsanity.com/paper/2505.00316/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 8 of its 39 references that are in the map.
- First posted on arXiv 1 May 2025.

## Builds on (most cited first, 8 of 8)

- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [Deep Generative Modelling: A Comparative Review of VAEs, GANs, Normalizing Flows, Energy-Based and Autoregressive Models](https://mlsanity.com/paper/2103.04922/) (2021)
- [TorchMD: A deep learning framework for molecular simulations](https://mlsanity.com/paper/2012.12106/) (2020)
- [DeepEMD: Differentiable Earth Mover's Distance for Few-Shot Learning](https://mlsanity.com/paper/2003.06777/) (2020)
- [Deep Learning the Physics of Transport Phenomena](https://mlsanity.com/paper/1709.02432/) (2017)
- [Learning Everywhere: A Taxonomy for the Integration of Machine Learning and Simulations](https://mlsanity.com/paper/1909.13340/) (2019)
- [Deep learning approaches to surrogates for solving the diffusion equation for mechanistic real-world simulations](https://mlsanity.com/paper/2102.05527/) (2021)
- [Analyzing the Performance of Deep Encoder-Decoder Networks as Surrogates for a Diffusion Equation](https://mlsanity.com/paper/2302.03786/) (2023)

## Built on by (most cited first, 1 of 1)

- [Forecasting Without Full Identification: Reliability and Computational Cost in Clot-Growth Simulation](https://mlsanity.com/paper/2608.08165/) (2026)

## Abstract (arXiv)

The Cellular-Potts model is a powerful and ubiquitous framework for developing computational models for simulating complex multicellular biological systems. Cellular-Potts models (CPMs) are often computationally expensive due to the explicit modeling of interactions among large numbers of individual model agents and diffusive fields described by partial differential equations (PDEs). In this work, we develop a convolutional neural network (CNN) surrogate model using a U-Net architecture that accounts for periodic boundary conditions. We use this model to accelerate the evaluation of a mechanistic CPM previously used to investigate in vitro vasculogenesis. The surrogate model was trained to predict 100 computational steps ahead (Monte-Carlo steps, MCS), accelerating simulation evaluations by a factor of 590 times compared to CPM code execution. Over multiple recursive evaluations, our model effectively captures the emergent behaviors demonstrated by the original Cellular-Potts model of such as vessel sprouting, extension and anastomosis, and contraction of vascular lacunae. This approach demonstrates the potential for deep learning to serve as efficient surrogate models for CPM simulations, enabling faster evaluation of computationally expensive CPM of biological processes at greater spatial and temporal scales.