[Paper Review] Data-driven discovery of chemical reaction networks

Abraham Reyes-Velázquez, Stefan Güttel+2 more|arXiv (Cornell University)|Feb 12, 2026

Gene Regulatory Network Analysis0 citations

TL;DR

A unified SINDy-based framework automatically reconstructs full chemical reaction networks from concentration data using integral formulations, with theoretical error bounds and improved noise robustness.

ABSTRACT

We propose a unified framework that allows for the full mechanistic reconstruction of chemical reaction networks (CRNs) from concentration data. The framework utilizes an integral formulation of the differential equations governing the chemical reactions, followed by an automatic procedure to recover admissible mass-action mechanisms from the equations. We provide theoretical justification for the use of integral formulations using analytical and numerical error bounds. The integral formulation is demonstrated to offer superior robustness to noise and improved accuracy in both rate-law and graph recovery when compared to other commonly used formulations. Together, our developments advance the goal of fully automated, data-driven chemical mechanism discovery.

Motivation & Objective

• Motivate the automatic discovery of chemical reaction networks (CRNs) from time-series concentration data.
• Develop a SINDy-based pipeline that links inferred ODEs to admissible mass-action CRNs.
• Compare differential and integral SINDy formulations and provide error analysis for each.
• Automate the graph-recovery step to obtain a chemically valid network from data.
• Assess robustness to noise and the effect of conservation laws on identifiability.

Proposed method

• Formulate CRNs with mass-action kinetics and express dynamics as an ODE or its Picard integral form.
• Construct a sparse dictionary of monomial terms up to a chosen degree (p ≤ 2 commonly sufficient).
• Apply SINDy to identify coefficient matrices linking dictionary terms to concentration dynamics.
• Introduce two formulations: differentiate data (differential SINDy) or integrate dictionary terms (integral SINDy) after spline interpolation.
• Automate reconstruction of admissible CRN graphs from the inferred ODEs via a convex optimization post-processing step.
• Provide theoretical error bounds for differentiation vs integration and analyze how noise, sampling, and rank deficiencies affect recovery.

Experimental results

Research questions

• RQ1 Can a data-driven framework recover both the rate laws and the underlying CRN graph from concentration time series?
• RQ2 Does an integral formulation offer advantages over differentiation in robustness to noise and in reconstruction accuracy?
• RQ3 How can a sparse ODE model be transformed into an admissible mass-action CRN automatically?
• RQ4 What are the error bounds for using differential vs integral SINDy under noise and discretization?
• RQ5 How do conservation laws and multi-experiment data affect identifiability and rank of the reconstruction problem?

Key findings

• The integral SINDy formulation yields superior robustness to noise and more accurate recovery of both rate laws and network structure compared to the differential formulation.
• An automated post-processing step maps sparse ODE models to admissible mass-action CRNs using convex optimization, fully automated for closed networks and requiring minimal user input for open systems.
• The paper provides analytical and numerical error bounds for both differential and integral formulations, showing integral formulation lowers accumulated numerical and regression error.
• Using multi-experiment data increases dictionary rank and helps mitigate rank deficiencies caused by conservation laws.
• The framework integrates sparse system identification, chemical-network reconstruction, and rigorous error analysis within a single unified approach.