Fitting Stochastic Lattice Models Using Approximate Gradients

Abstract: Stochastic lattice models (sLMs) are computational tools for simulating spatiotemporal dynamics in physics, computational biology, chemistry, ecology, and other fields. Despite their widespread use, it is challenging to fit sLMs to data, as their likelihood function is commonly intractable and the models non-differentiable. The adjacent field of agent-based modelling (ABM), faced with similar challenges, has recently introduced an approach to approximate gradients in network-controlled ABMs via reparameterization tricks. This approach enables efficient gradient-based optimization with automatic differentiation (AD), which allows for a directed local search of suitable parameters rather than estimation via black-box sampling. In this study, we investigate the feasibility of using similar reparameterization tricks to fit sLMs through backpropagation of approximate gradients. We consider four common scenarios: fitting to single-state transitions, fitting to trajectories, inference of lattice states, and identification of stable lattice configurations. We demonstrate that all tasks can be solved by AD using four example sLMs from sociology, biophysics, image processing, and physical chemistry. Our results show that AD via approximate gradients is a promising method to fit sLMs to data for a wide variety of models and tasks.