# Estimating Committor Functions via Deep Adaptive Sampling on Rare Transition Paths

arXiv: https://arxiv.org/abs/2501.15522 · HTML: https://mlsanity.com/paper/2501.15522/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 23 of its 68 references that are in the map.
- First posted on arXiv 26 Jan 2025.

## Builds on (most cited first, 23 of 23)

- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [UMAP: Uniform Manifold Approximation and Projection for Dimension Reduction](https://mlsanity.com/paper/1802.03426/) (2018)
- [Density estimation using Real NVP](https://mlsanity.com/paper/1605.08803/) (2016)
- [Glow: Generative Flow with Invertible 1x1 Convolutions](https://mlsanity.com/paper/1807.03039/) (2018)
- [DGM: A deep learning algorithm for solving partial differential equations](https://mlsanity.com/paper/1708.07469/) (2017)
- [The Deep Ritz method: A deep learning-based numerical algorithm for solving variational problems](https://mlsanity.com/paper/1710.00211/) (2017)
- [DAS-PINNs: A deep adaptive sampling method for solving high-dimensional partial differential equations](https://mlsanity.com/paper/2112.14038/) (2021)
- [Failure-informed adaptive sampling for PINNs](https://mlsanity.com/paper/2210.00279/) (2022)
- [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)
- [Adaptive deep density approximation for Fokker-Planck equations](https://mlsanity.com/paper/2103.11181/) (2021)
- [Interpolating between BSDEs and PINNs: deep learning for elliptic and parabolic boundary value problems](https://mlsanity.com/paper/2112.03749/) (2021)
- [Adversarial Adaptive Sampling: Unify PINN and Optimal Transport for the Approximation of PDEs](https://mlsanity.com/paper/2305.18702/) (2023)
- [Variational approach to rare event simulation using least-squares regression](https://mlsanity.com/paper/1901.09195/) (2019)
- [VAE-KRnet and its applications to variational Bayes](https://mlsanity.com/paper/2006.16431/) (2020)
- [Inexact iterative numerical linear algebra for neural network-based spectral estimation and rare-event prediction](https://mlsanity.com/paper/2303.12534/) (2023)
- [Bounded KRnet and its applications to density estimation and approximation](https://mlsanity.com/paper/2305.09063/) (2023)
- [GAS: A Gaussian Mixture Distribution-Based Adaptive Sampling Method for PINNs](https://mlsanity.com/paper/2303.15849/) (2023)
- [Supervised Learning and the Finite-Temperature String Method for Computing Committor Functions and Reaction Rates](https://mlsanity.com/paper/2107.13522/) (2021)
- [Deep adaptive sampling for surrogate modeling without labeled data](https://mlsanity.com/paper/2402.11283/) (2024)
- [Deep Learning Method for Computing Committor Functions with Adaptive Sampling](https://mlsanity.com/paper/2404.06206/) (2024)
- [A semigroup method for high dimensional committor functions based on neural network](https://mlsanity.com/paper/2012.06727/) (2020)

## Built on by (most cited first, 4 of 4)

- [Rare Event Analysis via Stochastic Optimal Control](https://mlsanity.com/paper/2604.13213/) (2026)
- [Deep Adaptive Dimension Reduction for Bayesian Inference in Inverse Problems](https://mlsanity.com/paper/2605.29373/) (2026)
- [Commitment Before Realization: When Classifier-Free Guidance Becomes Unnecessary in Masked Diffusion Language Models](https://mlsanity.com/paper/2608.08082/) (2026)
- [Machine learning kinetics from molecular dynamics data](https://mlsanity.com/paper/2609.17736/) (2026)

## Abstract (arXiv)

The committor functions are central to investigating rare but important events in molecular simulations. It is known that computing the committor function suffers from the curse of dimensionality. Recently, using neural networks to estimate the committor function has gained attention due to its potential for high-dimensional problems. Training neural networks to approximate the committor function needs to sample transition data from straightforward simulations of rare events, which is very inefficient. The scarcity of transition data makes it challenging to approximate the committor function. To address this problem, we propose an efficient framework to generate data points in the transition state region that helps train neural networks to approximate the committor function. We design a Deep Adaptive Sampling method for TRansition paths (DASTR), where deep generative models are employed to generate samples to capture the information of transitions effectively. In particular, we treat a non-negative function in the integrand of the loss functional as an unnormalized probability density function and approximate it with the deep generative model. The new samples from the deep generative model are located in the transition state region and fewer samples are located in the other region. This distribution provides effective samples for approximating the committor function and significantly improves the accuracy. We demonstrate the effectiveness of the proposed method through both simulations and realistic examples.