  Stochastic agent-based models (ABMs) are widely used to describe collective
processes in ecology, epidemiology, and cellular biology. It is challenging to
predict how ABMs behave over many parameter values due to their computational
nature. Modelers often address this limitation by coarse-graining ABM rules
into mean-field differential equation (DE) models. These DE models are
advantageous because they are fast to simulate; unfortunately, DE models can
provide poor ABM predictions (or be ill-posed) in certain regions of parameter
space. In this work, we describe how biologically-informed neural networks
(BINNs) can be trained to learn BINN-guided PDE models to predict ABM behavior.
In particular, we show that BINN-guided PDE simulations can forecast future ABM
data not seen during model training, and we can predict ABM data at
previously-unexplored parameter values by combining BINN-guided PDE simulations
with multivariate interpolation. We demonstrate our approach using three case
study ABMs of collective migration. We find through these case studies that
BINN-guided PDEs accurately forecast and predict ABM data with a
one-compartment PDE when the mean-field PDE is ill-posed or requires two
compartments. This work is broadly applicable to studying biological systems
that exhibit collective behavior. All code and data from our study is available
at https://github.com/johnnardini/Forecasting_predicting_ABMs
