Maximum entropy inference of reaction-diffusion models

Reaction-diffusion equations are commonly used to model a diverse array of complex systems, including biological, chemical, and physical processes. Typically, these models are phenomenological, requiring the fitting of parameters to experimental data. In this talk, we will present a novel formalism to construct reaction-diffusion models that is grounded on the principle of maximum entropy. This new formalism aims to incorporate various types of data, including ensemble currents, distributions at different points in time, or moments of such. To this end, we expand the framework of both Schrödinger bridges and Maximum Caliber problems to nonlinear interacting systems. We illustrate the usefulness of the proposed approach by modeling the evolution of (i) a bone morphogenetic protein responsive element across the fin of a zebrafish, and (ii) the population of two varieties of toads in southern Poland, so as to match experimental data.