Deep Neural Cellular Potts Models

2025-02-04

AI Summary

Traditional Cellular Potts Models (CPMs) rely on physics-inspired analytical Hamiltonians, limiting their ability to capture complex multicellular dynamics lacking first-principles foundations. To address this, we propose NeuralCPM—a data-driven CPM variant that replaces handcrafted Hamiltonians with neural networks, yielding the first “neural Hamiltonian” rigorously enforcing cellular dynamical symmetries (e.g., translation, rotation, and permutation invariance). Our architecture enables seamless integration of biological priors and end-to-end training on observational data, unifying physics-guided modeling with data-driven learning. Extensive validation on both synthetic benchmarks and real multicellular systems demonstrates that NeuralCPM substantially outperforms conventional CPMs, successfully reproducing emergent spatiotemporal collective behaviors that standard CPMs fail to explain. By bridging interpretability and fidelity, NeuralCPM establishes a new paradigm for principled, high-accuracy modeling of multicellular dynamics.

Technology Category

• Cognitive Modeling & Cognitive Systems: Neural Spike Coding
• Machine Learning: Multimodal Learning
• Reasoning under Uncertainty: Relational Probabilistic Models

Application Category

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

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.

Problem

• Enhances cellular Potts model
• Trains directly on data
• Models complex cellular dynamics

Innovation

• NeuralCPM integrates neural networks
• Neural Hamiltonian respects cellular symmetries
• Hybrid model combines biological mechanisms