Learning stochastic dynamics and predicting emergent behavior using transformers

TL;DR

This paper demonstrates that transformers can learn the underlying stochastic dynamics of a physical system from a single observed trajectory and accurately predict emergent behaviors like phase separation under unseen conditions.

Contribution

It introduces a method where transformers are used to learn complex dynamical rules from minimal data, enabling prediction of nonequilibrium phenomena without explicit rate enumeration.

Findings

Transformers successfully learned the dynamics of a lattice active matter model.

The trained model predicted phase separation at untrained densities.

The approach is applicable to complex physical systems with nonlocal and numerous dynamical processes.

Abstract

We show that a neural network originally designed for language processing can learn the dynamical rules of a stochastic system by observation of a single dynamical trajectory of the system, and can accurately predict its emergent behavior under conditions not observed during training. We consider a lattice model of active matter undergoing continuous-time Monte Carlo dynamics, simulated at a density at which its steady state comprises small, dispersed clusters. We train a neural network called a transformer on a single trajectory of the model. The transformer, which we show has the capacity to represent dynamical rules that are numerous and nonlocal, learns that the dynamics of this model consists of a small number of processes. Forward-propagated trajectories of the trained transformer, at densities not encountered during training, exhibit motility-induced phase separation and so predict the existence of a nonequilibrium phase transition. Transformers have the flexibility to learn dynamical rules from observation without explicit enumeration of rates or coarse-graining of configuration space, and so the procedure used here can be applied to a wide range of physical systems, including those with large and complex dynamical generators.