Surrogate models for accurate prediction and inference in mathematical biology

Overview

High fidelity mathematical models of biological phenomena are often complex and can require long computational runtimes which can make computational inference for parameter estimation intractable.  In this project we will overcome this challenge by working with computationally simple low fidelity models and build a simple statistical model of the discrepancy between the high and low fidelity models.  This approach provides the best of both worlds: we obtain high accuracy predictions using a computationally cheap model surrogate.

Research activities

• Building computer code to simulate a range of complex biological phenomena for which we have access to expeirmental data and measurements  (e.g. tumour growth, tissue growth), these models could be either complicated PDE models or stochastic simulation-based models
• Explore a range of computationally simple model surrogates, such as ODE models with exact solutions or simple low-dimensional linear PDE surrogate models
• Build statistical models of the discrepancy between the high and low fideliy models (e.g. multilinear regression, Kriging)
• Use the surrogate model to perform accurate simulaitons and parameter inference
• Apply these ideas to experimental data involving tissue growth and/or tumour spheroid growth

Outcomes

• New mathematical models of complex biological processes using simple surrogates
• New biological insight about how best to estimate parameters in a mathematical model
• New mathematical insight about how to model the discrepancy between the high and low fidelity models

Skills and experience

• Solid programming skills (MATLAB, Julia, FORTRAN)
• Good knowledge of differential equations and modelling with differential equations (MXB225, MXN322)

Scholarships

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Keywords

• Mathematical biology
• Mathematical modelling
• Computational Inference

Contact

Contact the supervisor for more information.