Recurrent convolutional neural networks for modeling non-adiabatic dynamics of quantum-classical systems

TL;DR

This paper introduces a physics-aware recurrent convolutional neural network designed to model the complex non-adiabatic dynamics of quantum-classical systems, capturing both deterministic and chaotic behaviors effectively.

Contribution

The paper presents a novel PARC-CNN architecture that incorporates physics principles to accurately model quantum-classical dynamics, including chaotic regimes.

Findings

Single-CNN recurrent network accurately models shallow quenches.

PARC-CNN effectively captures the statistical behavior under deep quenches.

Model demonstrates ability to learn complex spatiotemporal quantum dynamics.

Abstract

Recurrent neural networks (RNNs) have recently been extensively applied to model the time-evolution in fluid dynamics, weather predictions, and even chaotic systems thanks to their ability to capture temporal dependencies and sequential patterns in data. Here we present a RNN model based on convolution neural networks for modeling the nonlinear non-adiabatic dynamics of hybrid quantum-classical systems. The dynamical evolution of the hybrid systems is governed by equations of motion for classical degrees of freedom and von Neumann equation for electrons. The physics-aware recurrent convolution (PARC) neural network structure incorporates a differentiator-integrator architecture that inductively models the spatiotemporal dynamics of generic physical systems. We apply our RNN approach to learn the space-time evolution of a one-dimensional semi-classical Holstein model after an interaction quench. For shallow quenches (small changes in electron-lattice coupling), the deterministic dynamics can be accurately captured using a single-CNN-based recurrent network. In contrast, deep quenches induce chaotic evolution, making long-term trajectory prediction significantly more challenging. Nonetheless, we demonstrate that the PARC-CNN architecture can effectively learn the statistical climate of the Holstein model under deep-quench conditions.