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

Extracting interpretable chemical kinetics from sparse, noisy time-series data is an ill-posed problem because discrete reaction topologies and continuous kinetic parameters are tightly coupled. Standard black-box machine learning models often sacrifice physical interpretability for predictive accuracy, while unconstrained symbolic regression can produce mathematically valid but physically impossible models. The authors propose PC-MCMC-CIGP, a gray-box workflow that treats structural inference and parameter estimation as a cooperative task.

The approach consists of two main stages:

1. Physically Constrained MCMC (PC-MCMC): A spike-and-slab sampler identifies the reaction topology. It enforces hard constraints—specifically mass conservation, charge conservation, and thermodynamic consistency (detailed balance)—to prune the search space and eliminate spurious mechanisms.
2. Chemical-Informed Gaussian Process (CIGP): The identified mechanistic ODE model is embedded as the prior mean function of a Gaussian Process. This allows the model to capture dominant kinetic trends while using the non-parametric GP component to model systematic structural discrepancies.

The authors demonstrate the framework's efficacy on two benchmarks: the H2 + Br2 radical chain system and styrene epoxidation. In the H2 + Br2 case, the PC-MCMC sampler successfully identified the correct elementary radical pathways, whereas unconstrained sparse regression (SINDy) produced models that diverged numerically, and symbolic regression (PySR) produced purely phenomenological fits that failed to capture the underlying radical intermediates.

In the styrene epoxidation task, the CIGP optimization loop improved the final yield by 12.5% compared to a standard GP-based Bayesian optimization baseline. The study also compared various acquisition functions, finding that the proposed Physically Constrained Expected Improvement (PC-EI) significantly reduced the number of low-yield experimental suggestions compared to standard EI.

This work bridges the gap between purely data-driven discovery and mechanistic chemical modeling. By embedding physical laws directly into the Bayesian inference loop, the framework ensures that the resulting models are not only predictive but also scientifically valid. This is particularly valuable for complex chemical systems where experimental data is expensive and sparse, as it enables autonomous, physics-aware experimental design that avoids unphysical regimes.