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Learning stochastic dynamics and predicting emergent behavior using transformers

Author

Listed:
  • Corneel Casert

    (Lawrence Berkeley National Laboratory
    Ghent University)

  • Isaac Tamblyn

    (Cash App, Block
    Vector Institute for Artificial Intelligence
    University of Ottawa)

  • Stephen Whitelam

    (Lawrence Berkeley National Laboratory)

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.

Suggested Citation

  • Corneel Casert & Isaac Tamblyn & Stephen Whitelam, 2024. "Learning stochastic dynamics and predicting emergent behavior using transformers," Nature Communications, Nature, vol. 15(1), pages 1-7, December.
  • Handle: RePEc:nat:natcom:v:15:y:2024:i:1:d:10.1038_s41467-024-45629-w
    DOI: 10.1038/s41467-024-45629-w
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    References listed on IDEAS

    as
    1. Sun-Ting Tsai & En-Jui Kuo & Pratyush Tiwary, 2020. "Learning molecular dynamics with simple language model built upon long short-term memory neural network," Nature Communications, Nature, vol. 11(1), pages 1-11, December.
    2. Andreas Mardt & Luca Pasquali & Hao Wu & Frank Noé, 2018. "Author Correction: VAMPnets for deep learning of molecular kinetics," Nature Communications, Nature, vol. 9(1), pages 1-1, December.
    3. Andreas Mardt & Luca Pasquali & Hao Wu & Frank Noé, 2018. "VAMPnets for deep learning of molecular kinetics," Nature Communications, Nature, vol. 9(1), pages 1-11, December.
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