# Accelerated Sampling of Rare Events using a Neural Network Bias Potential

arXiv: https://arxiv.org/abs/2401.06936 · HTML: https://mlsanity.com/paper/2401.06936/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 11 of its 38 references that are in the map.
- First posted on arXiv 13 Jan 2024.

## Builds on (most cited first, 11 of 11)

- [An overview of gradient descent optimization algorithms](https://mlsanity.com/paper/1609.04747/) (2016)
- [A systematic study of the class imbalance problem in convolutional neural networks](https://mlsanity.com/paper/1710.05381/) (2017)
- [What Neural Networks Memorize and Why: Discovering the Long Tail via Influence Estimation](https://mlsanity.com/paper/2008.03703/) (2020)
- [Likelihood Ratios for Out-of-Distribution Detection](https://mlsanity.com/paper/1906.02845/) (2019)
- [Deep Long-Tailed Learning: A Survey](https://mlsanity.com/paper/2110.04596/) (2021)
- [Solving for high dimensional committor functions using artificial neural networks](https://mlsanity.com/paper/1802.10275/) (2018)
- [Computing Committor Functions for the Study of Rare Events Using Deep Learning](https://mlsanity.com/paper/1906.06285/) (2019)
- [Reinforced dynamics for enhanced sampling in large atomic and molecular systems](https://mlsanity.com/paper/1712.03461/) (2017)
- [Optimal control for sampling the transition path process and estimating rates](https://mlsanity.com/paper/2305.17112/) (2023)
- [Transition path theory for Langevin dynamics on manifold: optimal control and data-driven solver](https://mlsanity.com/paper/2010.09988/) (2020)
- [Optimal importance sampling for overdamped Langevin dynamics](https://mlsanity.com/paper/2307.11744/) (2023)

## Built on by (most cited first, 2 of 2)

- [Transition Path Sampling with Improved Off-Policy Training of Diffusion Path Samplers](https://mlsanity.com/paper/2405.19961/) (2024)
- [Improving Flow Matching by Aligning Flow Divergence](https://mlsanity.com/paper/2602.00869/) (2026)

## Abstract (arXiv)

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.