Gaussian Process Emulation for Mathematical Models of the Heart

心脏的数学模型可以帮助我们了解心脏的功能，并为我们如何治疗病人或诊断疾病提供有价值的见解。之前和正在进行的工作研究了我们如何使用统计和机器学习仿真策略来加速推理，并使数学模型适用于临床环境。这个项目的目的是通过应用高斯过程进一步发展这些方法，并将它们应用于不同的数学问题，这些问题具有比以前可行的更高的维度输入。在许多可能的应用中，数学模型通常具有高维和潜在相关的参数输入，以及高度相关的输出。这项工作的最初目的是进一步发展仿真方法来处理这些问题，并研究如何更有效地为我们选择生成输出的仿真选择参数输入。然后，进一步的工作将着眼于如何将这些模型与其他技术相结合，例如自动注释，加速我们的模拟器的构建，或者通过其他模拟器的组合，这将允许对更全局的系统进行建模。

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.