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Fitting stochastic lattice models using approximate gradients

• Jan Schering
• Sander Keemink
• Johannes Textor

(2024). ECMS 2024, 38th Proceedings
Edited by: Daniel Grzonka, Natalia Rylko, Grazyna Suchacka, Vladimir Mityushev, European Council for Modelling and Simulation.
DOI: http://doi.org/10.7148/2024
ISSN: 2522-2422 (ONLINE)
ISSN: 2522-2414 (PRINT)
ISSN: 2522-2430 (CD-ROM)
ISBN: 978-3-937436-84-5
ISBN: 978-3-937436-83-8 (CD) Communications of the ECMS Volume 38, Issue 1, June 2024, Cracow, Poland June 4th – June 7th, 2024

https://doi.org/10.7148/2024-0366

Jan schering, Sander keemink, Johannes textor (2024). Fitting Stochastic Lattice Models using Approximate Gradients, ECMS 2024, Proceedings Edited by: Daniel Grzonka, Natalia Rylko, Grazyna Suchacka, Vladimir Mityushev, European Council for Modelling and Simulation. doi:10.7148/2024-0366

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 three common scenarios: fitting to single-state transitions, fitting to trajectories, and identification of stable lattice configurations. We demonstrate that all tasks can be solved by AD using three example sLMs from sociology, biophysics, 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.