Integral chemical reaction neural networks
Abstract
Discovering the structure and kinetics of chemical reaction networks (CRNs) from time-series concentration data is a fundamental challenge in chemical kinetics, with existing approaches relying on prior mechanistic assumptions or suffering from high computational cost and noise sensitivity. In this work, we present integral chemical reaction neural networks (iCRNNs), a framework that combines the interpretable, physics-constrained, architecture of chemical reaction neural networks (CRNNs) with an integral collocation formulation of the governing dynamics. Rather than solving ODEs forward in time at each training step, we approximate the integral of the learned rate functions directly using numerical quadrature. This yields an entirely algebraic forward pass consisting only of matrix operations, eliminating the repeated adaptive ODE solves of standard CRNN and producing smoother, more predictable training. We provide a recovery error analysis characterising the structural sources of ill-conditioning (conservation laws, reaction reversibility, and shared reactant sets) that limit network identifiability. On two benchmark CRNs, iCRNN trains in roughly half the wall-clock time of the baseline CRNN method on a four-species mechanism and between three and four times faster on a five-species mechanism, while completing every training run reliably and attaining comparable or lower loss.
Related
- Joint Neural Posterior Estimation and Model Selection for Chemical Reaction Networks
- Bulk stability of bimolecular stochastic chemical reaction networks
- Input-to-state stability of chemical reaction networks with application to molecular computation
- Optimal Control of Chemical Reaction Networks with Thermodynamic Cost
- Solving Fredholm Integral Equations with Physics-Informed Neural Networks: Single-and double-network approaches
BibTeX
@misc{reyesvelazquez2026integral,
title = {{Integral chemical reaction neural networks}},
author = {Abraham Reyes-Velázquez and Stefan Güttel},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.21715},
eprint = {2609.21715},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.21715},
}
RIS
TY - UNPB
TI - Integral chemical reaction neural networks
AU - Abraham Reyes-Velázquez
AU - Stefan Güttel
PY - 2026
DA - 2026/09/18
PB - arXiv
DO - 10.48550/arxiv.2609.21715
UR - https://arxiv.org/abs/2609.21715
AB - Discovering the structure and kinetics of chemical reaction networks (CRNs) from time-series concentration data is a fundamental challenge in chemical kinetics, with existing approaches relying on prior mechanistic assumptions or suffering from high computational cost and noise sensitivity. In this work, we present integral chemical reaction neural networks (iCRNNs), a framework that combines the interpretable, physics-constrained, architecture of chemical reaction neural networks (CRNNs) with an integral collocation formulation of the governing dynamics. Rather than solving ODEs forward in time at each training step, we approximate the integral of the learned rate functions directly using numerical quadrature. This yields an entirely algebraic forward pass consisting only of matrix operations, eliminating the repeated adaptive ODE solves of standard CRNN and producing smoother, more predictable training. We provide a recovery error analysis characterising the structural sources of ill-conditioning (conservation laws, reaction reversibility, and shared reactant sets) that limit network identifiability. On two benchmark CRNs, iCRNN trains in roughly half the wall-clock time of the baseline CRNN method on a four-species mechanism and between three and four times faster on a five-species mechanism, while completing every training run reliably and attaining comparable or lower loss.
ER -