Dynamical Large Deviations of Two-Dimensional Kinetically Constrained Models Using a Neural-Network State Ansatz

Casert, Corneel; Vieijra, Tom; Whitelam, Stephen; Tamblyn, Isaac

doi:10.1103/physrevlett.127.120602

Cited by 17 publications

(17 citation statements)

References 67 publications

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“…Although the sets of forbidden and allowed transitions are the same for both W and W doob s , the transition rates of W doob s depend on the entire lattice configuration. Recently, the conditioned dynamics of several prototypical dynamical systems have been uncovered using neural-network methods [48,49] and reinforcement learning [50,51].…”

Section: S5 Learning a Nonlocal Dynamicsmentioning

confidence: 99%

Learning stochastic dynamics and predicting emergent behavior using transformers

Casert¹,

Tamblyn²,

Whitelam³

2022

Preprint

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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.

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Section: S5 Learning a Nonlocal Dynamicsmentioning

confidence: 99%

Learning stochastic dynamics and predicting emergent behavior using transformers

Casert¹,

Tamblyn²,

Whitelam³

2022

Preprint

Self Cite

View full text Add to dashboard Cite

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“…Neural networks have recently been used to detect local structure in colloidal systems 46 , 47 , define a structural order parameter which correlates strongly with dynamical heterogeneities in supercooled liquids 48 , and have helped in uncovering the critical behavior of a Gardner transition in hard-sphere glasses 49 . Neural network-based variational methods have also been introduced to study the large deviations of kinetically constrained models, which are lattice-based systems displaying glassy dynamics 50 , 51 . Graph neural networks, which operate on the elements of arbitrary graphs and their respective connectivity, have proven successful in predicting quantum-mechanical molecular properties 52 , describing the dynamics of complex physical materials 53 , or providing structural predictors for the long-term dynamics of glassy systems without the need for human-defined features 54 .…”

Section: Introductionmentioning

confidence: 99%

Robust prediction of force chains in jammed solids using graph neural networks

2022

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Force chains are quasi-linear self-organised structures carrying large stresses and are ubiquitous in jammed amorphous materials like granular materials, foams or even cell assemblies. Predicting where they will form upon deformation is crucial to describe the properties of such materials, but remains an open question. Here we demonstrate that graph neural networks (GNN) can accurately predict the location of force chains in both frictionless and frictional materials from the undeformed structure, without any additional information. The GNN prediction accuracy also proves to be robust to changes in packing fraction, mixture composition, amount of deformation, friction coefficient, system size, and the form of the interaction potential. By analysing the structure of the force chains, we identify the key features that affect prediction accuracy. Our results and methodology will be of interest for granular matter and disordered systems, e.g. in cases where direct force chain visualisation or force measurements are impossible.

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“…Examples of recent progress in direct sampling are flow models [36,37] and autoregressive neural networks [38,39] in the context of generative machine learning. These have recently been used in a physical context, such as for sampling classical many-body systems [40], in the context of lattice field theories [41] and optimization of variational states for many-body systems [42][43][44].…”

Section: Introductionmentioning

confidence: 99%

Direct sampling of projected entangled-pair states

et al. 2021

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Variational Monte Carlo studies employing projected entangled-pair states (PEPS) have recently shown that they can provide answers to long-standing questions such as the nature of the phases in the two-dimensional J 1 -J 2 model. The sampling in these Monte Carlo algorithms is typically performed with Markov chain Monte Carlo algorithms employing local update rules, which often suffer from long autocorrelation times and interdependent samples. We propose a sampling algorithm that generates independent samples from a PEPS, bypassing all problems related to finite autocorrelation times. This algorithm is a generalization of an existing direct sampling algorithm for unitary tensor networks. We introduce an auxiliary probability distribution from which independent samples can be drawn, and combine it with importance sampling in order to evaluate expectation values accurately. We benchmark our algorithm on the classical Ising model and on variational optimization of two-dimensional quantum spin models.

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Dynamical Large Deviations of Two-Dimensional Kinetically Constrained Models Using a Neural-Network State Ansatz

Cited by 17 publications

References 67 publications

Learning stochastic dynamics and predicting emergent behavior using transformers

Learning stochastic dynamics and predicting emergent behavior using transformers

Robust prediction of force chains in jammed solids using graph neural networks

Direct sampling of projected entangled-pair states

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