# Learning chemical reaction networks from trajectory data

## TL;DR

This paper introduces a data-driven approach to infer chemical reaction networks from trajectory data by modeling them as continuous-time Markov chains and employing sparse regularization to learn propensity functions.

## Contribution

The paper presents a novel method for learning reaction networks from trajectory data using likelihood maximization and $l^1$ regularization, with theoretical analysis and numerical validation.

## Key findings

- Effective learning of propensity functions from synthetic data
- Asymptotic analysis confirms method's consistency in infinite-data limit
- Demonstrated applicability to fully observed reaction systems

## Abstract

We develop a data-driven method to learn chemical reaction networks from trajectory data. Modeling the reaction system as a continuous-time Markov chain and assuming the system is fully observed, our method learns the propensity functions of the system with predetermined basis functions by maximizing the likelihood function of the trajectory data under $l^1$ sparse regularization. We demonstrate our method with numerical examples using synthetic data and carry out an asymptotic analysis of the proposed learning procedure in the infinite-data limit.