Gaussian Process Emulation for Mathematical Models of the Heart

Mathematical models of the heart can help us understand how the heart functions and provide us with valuable insights into how we can treat patients or diagnose disease. Previous and ongoing work has looked at how we can use statistical and machine learning emulation strategies to speed up inference and make the mathematical models applicable within a clinical setting. The aim of this project is to further develop these methods through the application of Gaussian Processes and apply them to different mathematical problems with higher dimensional inputs than what has been previously feasible to work with. In many of the possible applications, the mathematical models will often have high dimensional and potentially correlated parameter inputs, as well as highly correlated outputs. The initial aim of this work will be to further develop the emulation methods to deal with these problems and look at how we can more effectively select the parameter inputs for the simulations we choose to generate output for. Further work will then look at how these models can potentially be combined with other techniques such as automated annotation, accelerating the construction of our emulator, or through the combination of other emulators, which would allow for the modelling of a more global system.