  In the field of computational physics and material science, the efficient
sampling of rare events occurring at atomic scale is crucial. It aids in
understanding mechanisms behind a wide range of important phenomena, including
protein folding, conformal changes, chemical reactions and materials diffusion
and deformation. Traditional simulation methods, such as Molecular Dynamics and
Monte Carlo, often prove inefficient in capturing the timescale of these rare
events by brute force. In this paper, we introduce a practical approach by
combining the idea of importance sampling with deep neural networks (DNNs) that
enhance the sampling of these rare events. In particular, we approximate the
variance-free bias potential function with DNNs which is trained to maximize
the probability of rare event transition under the importance potential
function. This method is easily scalable to high-dimensional problems and
provides robust statistical guarantees on the accuracy of the estimated
probability of rare event transition. Furthermore, our algorithm can actively
generate and learn from any successful samples, which is a novel improvement
over existing methods. Using a 2D system as a test bed, we provide comparisons
between results obtained from different training strategies, traditional Monte
Carlo sampling and numerically solved optimal bias potential function under
different temperatures. Our numerical results demonstrate the efficacy of the
DNN-based importance sampling of rare events.
