Accelerated Markov Chain Monte Carlo Simulation via Neural Network-Driven Importance Sampling

TL;DR

This paper introduces a neural network-based importance sampling method to accelerate Markov chain Monte Carlo simulations, enabling efficient observation of rare transition events in high-dimensional systems.

Contribution

It presents a novel neural network-driven bias potential for importance sampling in MCMC, improving the sampling of rare events and accurately estimating transition rates in complex systems.

Findings

Successfully accelerated simulations of 2D and 14D systems.

Accurately estimated transition rates between metastable states.

Demonstrated scalability and efficiency of the method.

Abstract

Atomistic simulations provide valuable insights into the physical processes governing material behavior. However, their applicability is fundamentally constrained by the limited time scales accessible to brute-force simulations. This bottleneck often stems from complex energy landscapes where the systems stay trapped in metastable states for long periods of time. Yet, the long-term evolution is controlled by the transitions between the metastable states, which are rare events and difficult to observe. We present an importance sampling method designed to accelerate the time scale of Markov chain Monte Carlo (MCMC) simulations. By employing a bias potential, our approach enhances the sampling of rare transition events while preserving the relative probabilities of distinct transition pathways. The bias potential is represented by a neural network which enables the flexibility needed for high-dimensional systems. We propose a rigorous formulation to obtain the original transition rates between metastable states using transition paths obtained from the biased simulation. We further use a branching random walk (BRW) technique to enhance efficiency and to reduce variance. The proposed methodology is validated on 2-dimensional and 14-dimensional systems, demonstrating its accuracy and scalability.