Data-driven and agent-based modelling for biological pattern formation with Bayesian inference and topological data analysis

Pattern formation is a ubiquitous phenomenon in biology that has served as an inspiration for innovative mathematics. Agent-based models provide a flexible framework for systems driven by interactions between large numbers of autonomous agents, such as interacting cells underlying biological pattern formation. However, such models are typically very high-dimensional and stochastic, making parameter inference and identifiability analysis a computationally challenging inverse problem. In this talk, I present a computationally efficient inference pipeline that combines Bayesian inference with Topological Data Analysis (TDA) to address these challenges. Focusing on a complex, stochastic agent-based model of zebrafish skin pattern formation, I demonstrate how this pipeline enables a multi-objective approach to inference, which was able to accurately infer parameter values while using remaining computationally efficient. Finally, I discuss the connections between parameter inference, uncertainty quantification, and inverse problems, and explore potential future applications in biological and biomedical modeling.