BPS2026 – Bayesian inference on reaction-diffusion models

From tissue-level patterning to population dynamics in bacterial microfilm, reaction-diffusion mechanisms provide a universal framework for understanding how local interactions drive emergent spatiotemporal organization. Though these mechanistic models provide physical interpretations to observed data, the inverse task of inferring these models from the data remains challenging due to computationally intractable likelihood functions, i.e., functions that give the probability of observing the data given an assumed model. Here, we discuss a simulation-based approach which alleviates the computational burden by leveraging artificial intelligence as approximate, but efficiently computable, likelihoods. We apply this framework to infer reaction-diffusion parameters of a model system: exciton transport in singlet fission materials. This system captures many of the dynamical processes found in biological systems (e.g., diffusion-driven transport, birth, and death processes), where the population density of the diffusing component, i.e., singlet excitons, could be mapped through transient absorption microscopy (TAM). The ability to observe spatiotemporally resolved population dynamics while only requiring minutes-long acquisition periods makes it an ideal testbed for evaluating simulation-based inference (SBI) methods. The developed methods could then be applied to biological systems exhibiting analogous reaction-diffusion mechanisms, opening the door to the quantitative study of previously out-of-reach systems such as reaction-diffusion in spatial transcriptomics and biofilm growth.