Forecasting and predicting stochastic agent-based models of cell migration with biologically-informed neural networks

Collective migration, or the coordinated movement of many individuals, is an important component of many biological processes, including wound healing, tumorigenesis, and embryo development. Spatial agent-based models (ABMs) are often used to model collective migration, but it is challenging to thoroughly study these models' behavior due to their random and computational nature. Modelers often overcome these obstacles by coarse-graining discrete ABM rules into continuous mean-field partial differential equation (PDE) models. These models are advantageous because they are fast to simulate; unfortunately, these PDE models can poorly predict ABM behavior (or even be ill-posed) at certain parameter values. In this work, we describe how biologically-informed neural networks (BINNs) can be used to learn BINN-guided PDE models that are capable of accurately predicting ABM behavior. In particular, we show that BINN-guided PDE simulations can forecast future ABM data not seen during model training. Additionally, we demonstrate how to predict ABM data at previously-unexplored parameter values by combining BINN-guided PDE simulations with multivariate interpolation. We highlight these results using three separate ABMs that consist of rules on agent pulling and/or adhesion. Surprisingly, BINN-guided PDEs can accurately forecast and predict ABM data with a one-compartment PDE when the mean-field PDE is ill-posed or requires two compartments. While we focus our presentation on the biological applications, this work is broadly applicable to studying many systems that exhibit the collective migration of individuals.