Echo State network for coarsening dynamics of charge density waves

TL;DR

This paper demonstrates that an echo state network can effectively model the coarsening dynamics of charge density waves in a lattice system, offering a scalable and transferable approach for simulating complex pattern evolutions.

Contribution

It introduces a specialized ESN architecture that incorporates lattice symmetries to accurately predict charge density wave dynamics, enabling scalable modeling across different system sizes.

Findings

ESN successfully predicts CDW evolution in the Holstein model.

Model trained on small systems applies to larger lattices.

Incorporating lattice symmetries improves prediction accuracy.

Abstract

An echo state network (ESN) is a type of reservoir computer that uses a recurrent neural network with a sparsely connected hidden layer. Compared with other recurrent neural networks, one great advantage of ESN is the simplicity of its training process. Yet, despite the seemingly restricted learnable parameters, ESN has been shown to successfully capture the spatial-temporal dynamics of complex patterns. Here we build an ESN to model the coarsening dynamics of charge-density waves (CDW) in a semi-classical Holstein model, which exhibits a checkerboard electron density modulation at half-filling stabilized by a commensurate lattice distortion. The inputs to the ESN are local CDW order-parameters in a finite neighborhood centered around a given site, while the output is the predicted CDW order of the center site at the next time step. Special care is taken in the design of couplings between hidden layer and input nodes to ensure lattice symmetries are properly incorporated into the ESN model. Since the model predictions depend only on CDW configurations of a finite domain, the ESN is scalable and transferrable in the sense that a model trained on dataset from a small system can be directly applied to dynamical simulations on larger lattices. Our work opens a new avenue for efficient dynamical modeling of pattern formations in functional electron materials.