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

2025-05-01

AI Summary

To address the high computational cost of the Cellular Potts Model (CPM), which hinders large-scale multicellular simulations, this paper proposes a U-Net–based neural surrogate model that reformulates CPM spatiotemporal evolution as an image segmentation task with periodic boundary conditions—a novel formulation. The architecture explicitly encodes periodic boundaries and enables single-forward-pass prediction of 100 Monte Carlo steps (MCS), supporting long-term simulation via recursive rollout. Experiments demonstrate a 590× speedup over conventional CPM simulation while accurately reproducing key emergent phenomena—including vascular sprouting, anastomosis, and lumen contraction. This substantial acceleration significantly enhances the feasibility of large-scale parameter sweeps and mechanistic investigations in developmental and systems biology.

Technology Category

• Cognitive Modeling & Cognitive Systems: Neural Spike Coding
• Computer Vision: Diffusion Models for Vision
• Machine Learning: Large Multimodal Models (LMMs)

Application Category

• User Modeling, Personalization and Recommendation: User modeling and simulation for interactive and conversational systems
• Web Mining and Content Analysis: Models for Web evolution
• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs

Abstract

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 extit{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.

Problem

• Developing a U-Net CNN surrogate model for Cellular-Potts simulations
• Accelerating computationally expensive multicellular biological system modeling
• Capturing emergent behaviors like vasculogenesis in deep learning surrogates

Innovation

• U-Net CNN for Cellular-Potts surrogate modeling
• Predicts 100 steps ahead, 590x faster
• Captures emergent behaviors like vessel sprouting