# Synergizing Physically Constrained MCMC and Chemical-Informed Gaussian Processes for Reaction Network Discovery

arXiv: https://arxiv.org/abs/2606.23757 · HTML: https://mlsanity.com/paper/2606.23757/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 8 of its 56 references that are in the map.
- First posted on arXiv 22 Jun 2026.

## Builds on (most cited first, 8 of 8)

- [Machine Learning of Linear Differential Equations using Gaussian Processes](https://mlsanity.com/paper/1701.02440/) (2017)
- [Cautious Model Predictive Control using Gaussian Process Regression](https://mlsanity.com/paper/1705.10702/) (2017)
- [Stiff Neural Ordinary Differential Equations](https://mlsanity.com/paper/2103.15341/) (2021)
- [Sparsity information and regularization in the horseshoe and other shrinkage priors](https://mlsanity.com/paper/1707.01694/) (2017)
- [A spectrum of physics-informed Gaussian processes for regression in engineering](https://mlsanity.com/paper/2309.10656/) (2023)
- [Physics-Informed Gaussian Process Regression for Probabilistic States Estimation and Forecasting in Power Grids](https://mlsanity.com/paper/2010.04591/) (2020)
- [A hybrid data driven-physics constrained Gaussian process regression framework with deep kernel for uncertainty quantification](https://mlsanity.com/paper/2205.06494/) (2022)
- [Finding Thermodynamically Favorable Pathways in Chemical Reaction Networks Using Flows in Hypergraphs and Mixed-Integer Linear Programming](https://mlsanity.com/paper/2411.15900/) (2024)

## Abstract (arXiv)

Extracting interpretable governing equations from sparse, noisy chemical time-series data remains difficult because discrete reaction topology and continuous kinetic parameters are tightly coupled. We present PC-MCMC-CIGP, a reproducible gray-box workflow that combines spike-and-slab topology sampling, hard conservation and thermodynamic screening, and a Chemical-Informed Gaussian Process (CIGP) residual model for parameter calibration and experimental design. The methodological contribution is not a new MCMC or GP family in isolation; rather, it is the integration of these components into a physically constrained workflow with explicit uncertainty-aware acquisition choices. On the H2 + Br2 benchmark, the constrained sampler distinguishes elementary radical pathways from deceptive phenomenological fits in our experiments. On styrene epoxidation, the CIGP optimization loop improves final yield by 12.5% over the reported GP-BO baseline. A new 10-seed acquisition study shows that EI, GWU, PC-EI, uncertainty sampling, discrepancy hunting, and random search have different trade-offs: PC-EI substantially reduces low-yield BO suggestions, while EI-style criteria give the strongest final-yield performance.