Thesis

Efficient Exploration of Chemical Kinetics

Development and application of tractable Gaussian Process Models

Ph.D. Dissertation in Physical Chemistry, University of Iceland, October 2025.

Supervised by Prof. Hannes Jonsson (with Prof. Birgir Hrafnkelsson as co-supervisor). Committee: Morris Riedel, Egill Skulason, Thomas Bligaard. Opponents: Sigurdur I. Erlingsson, Normand Mousseau.

Abstract

Spatio-temporal control of chemical systems to tune relative rates of competing reactions has been the goal of chemistry since early alchemy. Despite leaps in mathematical modeling and exascale computing, efficient methods for determining reaction rates in large scale simulations has remained out of reach. Surrogate model based acceleration of saddle point searches have been described as promising for almost a decade now, but in practical terms have remained crippled by large computational overhead and numerical instabilities that negate the advantage in wall time.

This dissertation presents a solution based on a holistic approach that co-designs the physical representation, statistical model, and systems architecture. This philosophy is embodied in the Optimal Transport Gaussian Process (OT-GP) framework, which uses a physics-aware representation based on optimal transport metrics to create a compact and chemically relevant surrogate of the potential energy surface. Alongside rewrites for the EON software for long timescale simulations, we present a reinforcement-learning approach for the minimum-mode following method when final state is not known and nudged elastic band method when both initial and final state are specified.

Structure

The thesis is a monograph (not a paper collection) with original narrative connecting the published work:

1. Introduction: Chemistry for computers – space, time, and temperature
2. Theory: Minimum mode following, NEB, GP regression, acceleration strategies
3. Electronic structure: FEM for atomic structure (the Certik collaboration)
4. Software design: eOn architecture, client-server model, CI-NEB-MMF hybrid, concurrency
5. Efficient GP regression: Surface systems, data dredging, performance, cataloging saddles
6. Dimer rotations and Bayesian models: CG vs L-BFGS benchmarking with brms/Stan
7. Data efficiency: Rank-one covariance updates, pruning strategies, variance control
8. Optimal Transport GP: Earth Mover’s Distance, farthest point sampling, hyperparameter stability
9. Summary
10. Conclusions: Scientific software, statistics vs physics, future outlook – “A BLAS for Chemical Kinetics”

Connected research threads

• Transition State Methods (Ch. 2, 4)
• GP-Accelerated Searches (Ch. 5, 7, 8)
• Bayesian Statistical Methods (Ch. 6)

Read the thesis

Two versions are available: