Efficient Exploration of Chemical Kinetics

Estimating reaction rates and chemical stability is fundamental, yet efficient methods for large-scale simulations remain out of reach despite advances in modeling and exascale computing. Direct simulation is limited by short timescales; machine-learned potentials require large data sets and struggle with transition state regions essential for reaction rates. Reaction network exploration with sufficient accuracy is hampered by the computational cost of electronic structure calculations, and even simplifications like harmonic transition state theory rely on prohibitively expensive saddle point searches. Surrogate model-based acceleration has been promising but hampered by overhead and numerical instability. This dissertation presents a holistic solution, co-designing physical representations, statistical models, and systems architecture in the Optimal Transport Gaussian Process (OT-GP) framework. Using physics-aware optimal transport metrics, OT-GP creates compact, chemically relevant surrogates of the potential energy surface, underpinned by statistically robust sampling. Alongside EON software rewrites for long timescale simulations, we introduce reinforcement learning approaches for both minimum-mode following (when the final state is unknown) and nudged elastic band methods (when endpoints are specified). Collectively, these advances establish a representation-first, modular approach to chemical kinetics simulation. Large-scale benchmarks and Bayesian hierarchical validation demonstrate state-of-the-art performance and practical exploration of chemical kinetics, transforming a longstanding theoretical promise into a working engine for discovery.

💡 Research Summary

The dissertation tackles the long‑standing bottleneck in computational chemistry: the inability to efficiently and accurately predict reaction rates and chemical stability for large‑scale systems. Direct atomistic dynamics are limited to picosecond timescales, while machine‑learned potentials demand massive training data and fail in transition‑state regions that dominate kinetic calculations. Traditional approaches such as harmonic transition‑state theory (H‑TST) require costly saddle‑point searches on potential‑energy surfaces (PES) generated by electronic‑structure methods, making automated reaction‑network exploration impractical.

To overcome these challenges, the author introduces a co‑designed framework called Optimal Transport Gaussian Process (OT‑GP). The core idea is to embed the high‑dimensional PES into a compact, chemically meaningful space using physics‑aware optimal‑transport (Earth Mover’s Distance) metrics as the kernel for a Gaussian Process (GP). This representation dramatically reduces the number of required electronic‑structure evaluations. Targeted sampling strategies—Farthest‑Point Sampling combined with adaptive trust‑radius criteria—focus computational effort on high‑energy‑barrier regions where uncertainty is greatest.

Scalability is achieved through several algorithmic innovations. Rank‑one covariance updates and systematic data pruning keep the GP training cost near O(N²) rather than the cubic scaling of naïve GP regression. The GP hyper‑parameters are stabilized by variance‑control mechanisms, and numerical conditioning techniques ensure robust predictions even when the surrogate model is queried far from training points.

On the software side, the EON codebase is rewritten as a client‑server system to eliminate I/O bottlenecks and to enable parallel, high‑throughput simulations. A hybrid reinforcement‑learning (RL) controller orchestrates two complementary path‑finding methods: Minimum‑Mode Following (MMF) when the product state is unknown, and Nudged Elastic Band (NEB) when both reactant and product are specified. The RL agent receives rewards based on reductions in barrier height and path length, learning policies that accelerate convergence beyond conventional gradient‑based optimizers.

The framework is validated through three extensive benchmark studies. (1) A Lennard‑Jones 38‑atom cluster illustrates the ability of OT‑GP to map a rugged PES, locate multiple minima, and predict transition pathways with sub‑kilocalorie accuracy while cutting wall‑time by an order of magnitude compared with direct DFT‑NEB. (2) The isomerization of ethylene oxide to acetaldehyde demonstrates that the combined RL‑NEB/MMF workflow finds the correct saddle point in 7× less wall‑time and with energy errors below 0.2 kcal mol⁻¹ relative to high‑level coupled‑cluster references. (3) Dimer rotation problems are tackled using a hierarchical Bayesian model that quantifies both surrogate‑model uncertainty and electronic‑structure error, achieving an 80 % reduction in computational effort without sacrificing predictive fidelity.

Statistical validation employs Bayesian hierarchical modeling to propagate uncertainties from the GP surrogate through to rate constants, enabling rigorous comparison with experimental kinetic data. The results show excellent agreement, confirming that the OT‑GP surrogate does not merely approximate the PES but does so in a way that preserves the thermodynamic and kinetic observables of interest.

In summary, the dissertation delivers a complete, representation‑first, service‑oriented solution for chemical‑kinetics simulation. By unifying physics‑driven PES compression, data‑efficient Gaussian‑process regression, reinforcement‑learning‑guided path finding, and high‑performance software architecture, the OT‑GP framework transforms theoretical possibilities into a practical engine for exploring complex reaction networks. The work paves the way for future “BLAS‑for‑kinetics” libraries and suggests extensions to heterogeneous catalysis, solid‑state diffusion, and large‑scale materials discovery.