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.

Abstract Correlation analysis is an invaluable tool in many domains, for better understanding the data and extracting salient insights. Most works to date focus on detecting high pairwise correlations. A generalization of this problem with known applications but no known efficient solutions involves the discovery of strong multivariate correlations, i.e., finding vectors (typically in the order of 3–5 vectors) that exhibit a strong dependence when considered altogether. In this work, we propose algorithms for detecting multivariate correlations in static and streaming data. Our algorithms, which rely on novel theoretical results, support four different correlation measures, and allow for additional constraints. Our extensive experimental evaluation examines the properties of our solution and demonstrates that our algorithms outperform the state-of-the-art, typically by an order of magnitude.

Neural networks are emerging as a tool for scalable data-driven simulation of high-dimensional dynamical systems, especially in settings where numerical methods are infeasible or computationally expensive. Notably, it has been shown that incorporating domain symmetries in deterministic neural simulators can substantially improve their accuracy, sample efficiency, and parameter efficiency. However, to incorporate symmetries in probabilistic neural simulators that can simulate stochastic phenomena, we need a model that produces equivariant distributions over trajectories, rather than equivariant function approximations. In this paper, we propose Equivariant Probabilistic Neural Simulation (EPNS), a framework for autoregressive probabilistic modeling of equivariant distributions over system evolutions. We use EPNS to design models for a stochastic n-body system and stochastic cellular dynamics. Our results show that EPNS considerably outperforms existing neural network-based methods for probabilistic simulation. More specifically, we demonstrate that incorporating equivariance in EPNS improves simulation quality, data efficiency, rollout stability, and uncertainty quantification. We conclude that EPNS is a promising method for efficient and effective data-driven probabilistic simulation in a diverse range of domains.

Correlation analysis is an invaluable tool in many domains, for better understanding data and extracting salient insights. Most works to date focus on detecting high pairwise correlations. A generalization of this problem with known applications but no known efficient solutions involves the discovery of strong multivariate correlations, i.e., finding vectors (typically in the order of 3 to 5 vectors) that exhibit a strong dependence when considered altogether. In this work we propose algorithms for detecting multivariate correlations in static and streaming data. Our algorithms, which rely on novel theoretical results, support two different correlation measures, and allow for additional constraints. Our extensive experimental evaluation examines the properties of our solution and demonstrates that our algorithms outperform the state-of-the-art, typically by an order of magnitude.