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Stochastic lattice models (sLMs) are computational tools for simulatingspatiotemporal dynamics in physics, computational biology, chemistry, ecology,and other fields. Despite their widespread use, it is challenging to fit sLMsto data, as their likelihood function is commonly intractable and the modelsnon-differentiable. The adjacent field of agent-based modelling (ABM), facedwith similar challenges, has recently introduced an approach to approximategradients in network-controlled ABMs via reparameterization tricks. Thisapproach enables efficient gradient-based optimization with automaticdifferentiation (AD), which allows for a directed local search of suitableparameters rather than estimation via black-box sampling. In this study, weinvestigate the feasibility of using similar reparameterization tricks to fitsLMs through backpropagation of approximate gradients. We consider four commonscenarios: fitting to single-state transitions, fitting to trajectories,inference of lattice states, and identification of stable latticeconfigurations. We demonstrate that all tasks can be solved by AD using fourexample sLMs from sociology, biophysics, image processing, and physicalchemistry. Our results show that AD via approximate gradients is a promisingmethod to fit sLMs to data for a wide variety of models and tasks.

Fitting Stochastic Lattice Models Using Approximate Gradients