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

Controlling relative rates of competing reactions has driven chemistry for centuries. Despite advances in mathematical modeling and exascale computing, efficient determination of reaction rates in large-scale simulations has remained out of reach. Surrogate-model acceleration of saddle point searches has looked promising for a decade, but in practice has been limited by computational overhead and numerical instabilities that wipe out the wall-time advantage.

This dissertation co-designs the physical representation, the statistical model, and the systems architecture into a single framework rather than treating them as independent layers. The result is the Optimal Transport Gaussian Process (OT-GP) framework, which uses optimal transport metrics as a physics-aware representation of molecular configurations to produce a compact, chemically relevant surrogate of the potential energy surface. Alongside the OT-GP framework, the thesis presents rewrites of the EON software for long-timescale simulations and a reinforcement-learning approach to the minimum-mode following method (for unknown final states) and to the nudged elastic band method (for known endpoints).

Structure

The thesis is a monograph (not a paper collection) with original narrative connecting the published work. Each chapter is tagged with the research thread it develops, so a reader who lands here from a thread page can jump to the chapter that builds it out.

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

Connected research threads

• Transition State Methods (Ch. 2, 4)
• GP-Accelerated Searches (Ch. 5, 7, 8)
• Bayesian Statistical Methods (Ch. 6)
• Scientific Software Interoperability (Ch. 3)

Read the thesis

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