Accelerated Sampling of Rare Events using a Neural Network Bias Potential

TL;DR

The paper tackles efficient sampling of rare molecular transitions by learning a variance-free bias potential with a deep neural network to guide biased Langevin dynamics. It casts rare-event probabilities as a variational optimization, uses a smooth indicator and likelihood-ratio framework, and trains the network via KL-divergence constraints while learning from successful trajectories. The approach yields robust estimators with favorable variance and effective-sample-size properties and demonstrates substantial speedups over naive Monte Carlo in a 2D testbed, with clear pathways to higher dimensions. This method holds promise for scalable, data-efficient rare-event estimation in materials science and biochemistry, offering a practical alternative to solving high-dimensional committor PDEs or relying solely on traditional sampling techniques.

Abstract

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.

Figures (6)

• Figure 1: Full details of training are described in Algorithm \ref{['alg:bias']} in Sec. \ref{['sec:algorithm']}. Our method adopts a Reinforcement Learning approach: it samples trajectories and subsequently learns from them.
• Figure 2: Plot of the 2D energy function in eq. \ref{['eq:dynamics']}. A and B represent the two minima of the energy.
• Figure 3: Trajectories at temperature 1000K and 1200K obtained by traditional Monte Carlo sampling method. The molecules escape at a higher rate at the elevated temperature of 1200K. However, the two channels of transition are more precise and refined at the lower temperature.
• Figure 4: Left: Bias potential functions generated by our method in mode A. Right: Bias potential generated by the PDE's numerical solution. The shapes of two functions are very similar, although our optimization process does not involve solving the PDE.
• Figure 5: Mode B of our method at temperature 1200K. Training in mode A sometimes suffers from mode collapse as other generative methods. In this case, we only need the positions of the successful paths, and we minimize \ref{['eq:exist_loss']} to train a new bias potential that can sample paths that are similar to all the past training examples. The sampled trajectories are also similar to the Monte Carlo's in Fig. \ref{['fig:traj']}.