Accelerating Monte Carlo Simulation of Rare Events by Importance Sampling using Neural Network

Monte Carlo simulation is a widely used method, especially for atomistic simulations. However, at low temperatures, the system becomes trapped in metastable states; hence, transitions between these metastable states become "rare events". We introduce a machine learning approach for importance sampling of rare events in Monte Carlo simulations within the discrete domain. Our method employs a neural network to determine the optimal bias potential, which is proportional to the logarithm of the optimal importance function. This importance sampling strategy effectively increases the probability of sampling successful transition events between meta-stable states, while maintaining relative transition probabilities among various transition paths. To demonstrate the robustness and efficacy of our approach, we applied it to both 2-dimensional and 14-dimensional systems at low temperature. Furthermore, we developed a rigorous formulation for calculating transition rates between meta-stable states using importance sampling. Our rate predictions are in strong agreement with classical transition rate theories (e.g., Kramers reaction rate theory), confirming the validity of our methodology. This advancement contributes to the acceleration of Monte Carlo simulation of rare events for low-temperature, complex, and high-dimensional systems.