# Tracking large chemical reaction networks and rare events by neural networks

arXiv: https://arxiv.org/abs/2512.10309 · HTML: https://mlsanity.com/paper/2512.10309/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 21 of its 103 references that are in the map.
- First posted on arXiv 11 Dec 2025.

## Builds on (most cited first, 21 of 21)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Learning Phrase Representations using RNN Encoder-Decoder for Statistical Machine Translation](https://mlsanity.com/paper/1406.1078/) (2014)
- [MADE: Masked Autoencoder for Distribution Estimation](https://mlsanity.com/paper/1502.03509/) (2015)
- [Revisiting Natural Gradient for Deep Networks](https://mlsanity.com/paper/1301.3584/) (2013)
- [A high-bias, low-variance introduction to Machine Learning for physicists](https://mlsanity.com/paper/1803.08823/) (2018)
- [Solving Statistical Mechanics Using Variational Autoregressive Networks](https://mlsanity.com/paper/1809.10606/) (2018)
- [Neural Autoregressive Distribution Estimation](https://mlsanity.com/paper/1605.02226/) (2016)
- [Reasoning with Sampling: Your Base Model is Smarter Than You Think](https://mlsanity.com/paper/2510.14901/) (2025)
- [Deep autoregressive models for the efficient variational simulation of many-body quantum systems](https://mlsanity.com/paper/1902.04057/) (2019)
- [Markovian Score Climbing: Variational Inference with KL(p||q)](https://mlsanity.com/paper/2003.10374/) (2020)
- [Neural Adaptive Sequential Monte Carlo](https://mlsanity.com/paper/1506.03338/) (2015)
- [Convolutional Neural Network Training with Distributed K-FAC](https://mlsanity.com/paper/2007.00784/) (2020)
- [Autoregressive neural-network wavefunctions for ab initio quantum chemistry](https://mlsanity.com/paper/2109.12606/) (2021)
- [Training Neural Samplers with Reverse Diffusive KL Divergence](https://mlsanity.com/paper/2410.12456/) (2024)
- [Complexity Analysis of Normalizing Constant Estimation: from Jarzynski Equality to Annealed Importance Sampling and beyond](https://mlsanity.com/paper/2502.04575/) (2025)
- [Neural-network solutions to stochastic reaction networks](https://mlsanity.com/paper/2210.01169/) (2022)
- [SOFIM: Stochastic Optimization Using Regularized Fisher Information Matrix](https://mlsanity.com/paper/2403.02833/) (2024)
- [WeightFlow: Learning Stochastic Dynamics via Evolving Weight of Neural Network](https://mlsanity.com/paper/2508.00451/) (2025)
- [Random Natural Gradient](https://mlsanity.com/paper/2311.04135/) (2023)
- [Revisiting Kinetic Monte Carlo Algorithms for Time-dependent Processes: from open-loop control to feedback control](https://mlsanity.com/paper/2405.03997/) (2024)
- [Interpretable Neural Approximation of Stochastic Reaction Dynamics with Guaranteed Reliability](https://mlsanity.com/paper/2512.06294/) (2025)

## Built on by (most cited first, 3 of 3)

- [Scalable Physics-Inspired Transformers for Spin Glasses](https://mlsanity.com/paper/2606.22984/) (2026)
- [Nonequilibrium Dynamics of Simple Exclusion Processes Across Dimensions](https://mlsanity.com/paper/2608.25606/) (2026)
- [Discrete Diffusion Models via Evolving Variational Autoregressive Networks](https://mlsanity.com/paper/2609.27306/) (2026)

## Abstract (arXiv)

Chemical reaction networks are widely used to model stochastic dynamics in biophysical processes. Their exact probabilistic description via the chemical master equation becomes intractable for high-dimensional systems due to the exponential growth of the state space. This difficulty is further exacerbated when metastable transitions and rare events dominate the dynamics. Here, we present an advanced neural-network approach that effectively tackles large reaction networks and rare-event dynamics within a unified framework. Building on autoregressive representations of the full joint probability distribution, we achieve efficient training through second-order optimization methods, including natural gradient descent and the time-dependent variational principle. We leverage enhanced-sampling strategies that enable accurate resolution of low-probability regions governing rare transitions. We demonstrate the method on a multistable genetic toggle switch and a mitogen-activated protein kinase (MAPK) cascade consisting of 16 species and 35 reactions with dense coupling. We further quantify rare events in spatially extended Schl"ogl models in both one- and two-dimensional lattices, reaching system sizes with extremely large state spaces up to 3×1015. These results highlight the potential of neural modeling as a flexible and scalable framework for studying high-dimensional chemical reaction networks and rare events.