Physics-informed emulation with applications in soft-tissue mechanics

Dalton, David (2024) Physics-informed emulation with applications in soft-tissue mechanics. PhD thesis, University of Glasgow.

Abstract

The development of mathematical models in the past generation has been transformative for a number of scientific disciplines. Mathematical models allow for causal effects to be examined, relationships between variables to be quantified, and hypotheses to be explored through the generation of synthetic data. One example of particular relevance for this work is the field of soft-tissue mechanics, where recent developments in modelling theory and practice have the potential for application in quantitative personalised medicine.
The sophistication of modern mathematical models extends far beyond the limits of analytical tractability, which means that numerical physics simulators are required for solutions to be found. Computer simulation algorithms have also seen tremendous development in the past generation. However, challenges remain with traditional simulation approaches, particularly their high computational costs in certain cases. An alternative method which can alleviate some of these challenges is emulation, whereby the simulator is replaced by a cheaper, data-driven surrogate model. Emulation however has its own drawbacks, in particular lack of explicit incorporation of known physical laws. In this work we make use of a new generation of methods which incorporate aspects of both physics simulators and data-driven emulators, which we call physics-informed emulation.
We first consider a model describing the behaviour of the left-ventricle (LV) of the heart in diastole, performing emulation with a Graph Neural Network (GNN) surrogate model. In contrast to more traditional emulation approaches, a GNN allows for the exact computational mesh representation of the LV to be modelled, without any approximations. Numerical experiments are performed which demonstrate that our approach can achieve strong out of sample predictive accuracy, while offering massive savings over the simulator at prediction time. We next extend the GNN emulation framework to a range of soft-tissue mechanical models, involving varying constitutive laws, boundary conditions and geometries. Furthermore, the emulator is trained by application of the Principle of Minimum Potential Energy, which has the advantage that no simulation data is required for training. The possible significance of this work is in enabling soft-tissue mechanical models to be deployed for real-time clinical decision support. Finally, we switch focus to consider how to integrate noisy observation data, linear PDE information and boundary conditions into a Gaussian process (GP) surrogate modelling framework. We demonstrate via theoretical analysis and numerical experiments that this integration can be done seamlessly and efficiently, and is especially useful for solving inverse problems.

• Item Type: Thesis (PhD)
• Qualification Level: Doctoral
• Subjects: H Social Sciences > HA Statistics; Q Science > QA Mathematics; Q Science > QC Physics
• Colleges/Schools: College of Science and Engineering > School of Mathematics and Statistics
• Supervisor's Name: Husmeier, Professor Dirk and Gao, Dr. Hao
• Date of Award: 2024
• Depositing User: Theses Team
• Unique ID: glathesis:2024-84552
• Copyright: Copyright of this thesis is held by the author.
• Date Deposited: 13 Sep 2024 07:32
• Last Modified: 13 Sep 2024 07:34
• Thesis DOI: 10.5525/gla.thesis.84552
• URI: https://theses.gla.ac.uk/id/eprint/84552

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