# Neural-network solutions to stochastic reaction networks

arXiv: https://arxiv.org/abs/2210.01169 · HTML: https://mlsanity.com/paper/2210.01169/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- Builds on 11 of its 72 references that are in the map.
- First posted on arXiv 29 Sep 2022.

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

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [On the Properties of Neural Machine Translation: Encoder-Decoder Approaches](https://mlsanity.com/paper/1409.1259/) (2014)
- [Pixel Recurrent Neural Networks](https://mlsanity.com/paper/1601.06759/) (2016)
- [MADE: Masked Autoencoder for Distribution Estimation](https://mlsanity.com/paper/1502.03509/) (2015)
- [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)
- [Deep autoregressive models for the efficient variational simulation of many-body quantum systems](https://mlsanity.com/paper/1902.04057/) (2019)
- [Variational Neural Annealing](https://mlsanity.com/paper/2101.10154/) (2021)
- [Autoregressive neural-network wavefunctions for ab initio quantum chemistry](https://mlsanity.com/paper/2109.12606/) (2021)
- [Automated Deep Abstractions for Stochastic Chemical Reaction Networks](https://mlsanity.com/paper/2002.01889/) (2020)

## Built on by (most cited first, 8 of 8)

- [Learning noise-induced transitions by multi-scaling reservoir computing](https://mlsanity.com/paper/2309.05413/) (2023)
- [Tracking large chemical reaction networks and rare events by neural networks](https://mlsanity.com/paper/2512.10309/) (2025)
- [Scalable Physics-Inspired Transformers for Spin Glasses](https://mlsanity.com/paper/2606.22984/) (2026)
- [Language models as master equation solvers](https://mlsanity.com/paper/2308.02514/) (2023)
- [Explainable Learning Rate Regimes for Stochastic Optimization](https://mlsanity.com/paper/2508.13639/) (2025)
- [Data-driven Effective Modeling of Stochastic Chemical Reaction Networks](https://mlsanity.com/paper/2608.25421/) (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)

The stochastic reaction network in which chemical species evolve through a set of reactions is widely used to model stochastic processes in physics, chemistry and biology. To characterize the evolving joint probability distribution in the state space of species counts requires solving a system of ordinary differential equations, the chemical master equation, where the size of the counting state space increases exponentially with the type of species, making it challenging to investigate the stochastic reaction network. Here, we propose a machine-learning approach using the variational autoregressive network to solve the chemical master equation. Training the autoregressive network employs the policy gradient algorithm in the reinforcement learning framework, which does not require any data simulated in prior by another method. Different from simulating single trajectories, the approach tracks the time evolution of the joint probability distribution, and supports direct sampling of configurations and computing their normalized joint probabilities. We apply the approach to representative examples in physics and biology, and demonstrate that it accurately generates the probability distribution over time. The variational autoregressive network exhibits a plasticity in representing the multimodal distribution, cooperates with the conservation law, enables time-dependent reaction rates, and is efficient for high-dimensional reaction networks with allowing a flexible upper count limit. The results suggest a general approach to investigate stochastic reaction networks based on modern machine learning.