MS04 - MFBM-04

Interaction laws to collective behaviour: Inferring population dynamics

Tuesday, July 15 at 3:50pm

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Rebecca Crossley, Stéphanie Abo (University of Oxford), University of Oxford

Description:

This mini-symposium brings together experts from around the globe who are developing cutting-edge techniques for decoding collective behaviour in complex systems, from cellular dynamics to social phenomena. We focus on techniques such as inferring interaction laws from noisy data, designing novel neural network architectures to model emergent behaviour, and applying information-theoretic approaches to understand collective decision-making. The challenge lies not just in quantifying how local interactions aggregate to produce tissue-level or network-level behaviours, but in developing data-driven mathematical frameworks that bridge these scales while preserving essential features. Speakers will present methodological advances in population modelling and statistical learning alongside practical applications in biological systems, ranging from tissue patterning to organised motion. By uniting diverse perspectives, we aim to bridge theory and experiment, foster collaboration, and extract valuable biological insights into how local interaction rules drive coordinated population dynamics.

John Nardini

The College of New Jersey

"Decoding agent-based model behavior: novel methods for prediction and global sensitivity analysis"

Agent-based models (ABMs) are invaluable tools for studying the emergence of collective behavior in biology. Unfortunately, it is challenging to analyze ABM behavior due to their computational and stochastic nature. In this talk, I will present two recent studies aimed at developing new methodologies to enable the prediction, interpretation, and analysis of ABMs. In the first study, we use biologically-informed neural networks (BINNs) to forecast and predict ABM behavior. In particular, we show BINNs can learn interpretable differential equations to predict ABM data at new parameter values, and demonstrate this success using three case study ABMs of collective migration. In the second study, we combine several machine learning algorithms to develop a global sensitivity analysis pipeline for ABMs that is capable of identifying sensitive parameters, revealing common model patterns, and linking input model parameters to these patterns using a spatial ABM of tumor spheroid growth. Taken together, these studies demonstrate how concepts from machine learning are valuable for studying ABMs and will advance data-driven ABM modeling.

Jinchao Feng

Great Bay University

"A Sparse Bayesian Learning Algorithm for Estimation of Interaction Kernels in Motsch-Tadmor Model"

In this talk, we present a data-driven framework for identifying asymmetric interaction kernels in the Motsch–Tadmor model based on observed agent trajectories. Unlike symmetric models, the asymmetric setting introduces a nonlinear inverse problem due to the normalization of interaction weights. We reformulate the problem using the implicit form of the governing equations, reducing kernel learning to a subspace identification task. To solve this, we develop a sparse Bayesian learning approach that incorporates prior structure and quantifies uncertainty, enabling robust model selection under noise. Numerical experiments on several prototype systems demonstrate the method's ability to recover key interaction patterns and predict collective behavior accurately, even with limited or noisy data.

Seungwoong Ha

Santa Fe Institute

"Toward a Data-Centric Understanding of Collective Dynamics"

Understanding how collective behavior emerges from local interactions is a central question in modeling biological systems. While traditional approaches often assume fixed interaction rules, recent advances in data-driven modeling offer ways to infer these laws directly from empirical observations. In this talk, I present a set of machine learning-based methods developed to recover interaction structures and underlying dynamics in complex systems, from physical to population-level collective behavior. Across different scenarios, these approaches infer continuous interaction strengths, capture emergent phenomena not present in training data, and remain applicable to stochastic or temporally evolving systems. I will also highlight how adaptive agents can develop robust coordination strategies through learning in uncertain environments. These results suggest new pathways for linking observed dynamics to latent interaction rules, offering complementary tools to classical models of population dynamics.

Ming Guo

Massachusetts Institute of Technology

"Collective curvature sensing and fluidity in three-dimensional multicellular systems"

Collective cell migration is an essential process throughout the lives of multicellular organisms, for example in embryonic development, wound healing and tumour metastasis. Substrates or interfaces associated with these processes are typically curved, with radii of curvature comparable to many cell lengths. Using both artificial geometries and lung alveolospheres derived from human induced pluripotent stem cells, here we show that cells sense multicellular-scale curvature and that it plays a role in regulating collective cell migration. As the curvature of a monolayer increases, cells reduce their collectivity and the multicellular flow field becomes more dynamic. Furthermore, hexagonally shaped cells tend to aggregate in solid-like clusters surrounded by non-hexagonal cells that act as a background fluid. We propose that cells naturally form hexagonally organized clusters to minimize free energy, and the size of these clusters is limited by a bending energy penalty. We observe that cluster size grows linearly as sphere radius increases, which further stabilizes the multicellular flow field and increases cell collectivity. As a result, increasing curvature tends to promote the fluidity in multicellular monolayer. Together, these findings highlight the potential for a fundamental role of curvature in regulating both spatial and temporal characteristics of three-dimensional multicellular systems.

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Annual Meeting for the Society for Mathematical Biology, 2025.