Surrogate modelling for complex physical systems

Ryan, William (2026) Surrogate modelling for complex physical systems. PhD thesis, University of Glasgow.

Abstract

Mathematical models of complex physical systems typically require numerically solving computationally expensive partial differential equations where a single simulation can take minutes to hours. When these models must be calibrated to experimental or clinical data, the problem becomes apparent. Bayesian parameter inference demands thousands of forward evaluations of the numerical solver, or simulator, rendering traditional methods of inference, such as Markov Chain Monte Carlo, intractable for time-sensitive applications such as surgical planning. Surrogate models, or emulators, are fast, learned approximations to expensive simulators and offer a compelling solution. However, the effectiveness of these emulators is often limited by the choice of architecture, which must balance predictive accuracy with the data efficiency required for real-world application.

This thesis develops surrogate models designed to emulate complex dynamics across a variety of problems. The work begins with Gaussian process emulation applied to multiexponential fluorescence decay models, demonstrating that emulation-based Bayesian inference can reliably perform parameter inference and model selection. This establishes the reliability of surrogate-assisted inference in a biophysical problem, providing a benchmark for the development of more complex architectures required for larger scale physical systems. The primary application focus is on cardiovascular haemodynamics, where clinical decision-making for patients with congenital heart defects requires patient-specific predictive models that current computational tools cannot deliver in tractable time frames. Physics-informed neural networks are developed for a realistic 17-vessel model of systemic circulation, where, by embedding conservation laws and bifurcation conditions into the training objective, they achieve improved accuracy over purely data-driven alternatives while requiring up to eight times fewer training simulations. When applied to data from patients with Fontan circulation the framework infers vessel wall stiffness parameters within three hours and produces non-invasive pressure waveform predictions aligned with clinical measurements to within ±3 mmHg. However, at application time, the process requires transfer-learning the learned weights from one patient to the next. Building on the physics-informed emulation framework, the approach is extended to neural operators, which learn mappings between function spaces. This enables the model to accept patient-specific time-varying inflow boundary conditions as functional inputs, on top of physiological parameters, effectively working as a surrogate model generalisable to any patient and avoiding the transfer-learning step. Physics-informed variants of Deep Operator Networks and Fourier Neural Operator architectures demonstrate improved accuracy and parameter recovery across diverse test cases. Additionally, a generative model is developed to ensure physiologically realistic boundary conditions are used for training the neural operators. The final contribution introduces a probabilistic surrogate architecture designed for systems with sparse or irregularly sampled observations. The proposed Variational Set Operator Network combines a permutation-invariant neural operator architecture with variational inference to produce calibrated predictive distributions without assuming Gaussian outputs. Evaluated on regression, image completion, and Bayesian optimization benchmarks, this approach achieves state-of-the-art uncertainty quantification while maintaining computational efficiency that scales linearly with the number of query points, compared to the quadratic scaling of transformer-based alternatives. Collectively, this work demonstrates that tailored surrogate architectures can bridge the gap between high-fidelity simulation and real-time decision-making. While validated primarily in cardiovascular and biophysical contexts, these surrogate strategies are applicable to any parametric system requiring fast evaluation from sparse data.

• Item Type: Thesis (PhD)
• Additional Information: Supported by funding from the Engineering and Physical Sciences Research Council (EPSRC).
• Subjects: Q Science > QA Mathematics
• Colleges/Schools: College of Science and Engineering > School of Mathematics and Statistics
• Funder's Name: Engineering and Physical Sciences Research Council (EPSRC)
• Supervisor's Name: Vyshemirsky, Dr. Vladislav and Husmeier, Professor Dirk
• Date of Award: 2026
• Depositing User: Theses Team
• Unique ID: glathesis:2026-86113
• Copyright: Copyright of this thesis is held by the author.
• Date Deposited: 14 Jul 2026 15:25
• Last Modified: 14 Jul 2026 15:25
• Thesis DOI: 10.5525/gla.thesis.86113
• URI: https://theses.gla.ac.uk/id/eprint/86113

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