Uncertainty Quantification for Numerical Models with two Regions of Solution

在科学和政策中使用复杂的数值模型现在是无处不在。在实际应用中，这种模型的预测需要伴随着对不确定性的估计。提供这些估计数是一个难题。高斯过程仿真器是一种数字代码的统计模型，运行速度快，因此可用于计算不确定性估计，例如通过蒙特卡洛方法，使用完整模型在计算上是不可能的。仿真器已被用于各种各样的应用，从气候和空气污染到工程和地质学到系统生物学。然而，也有数值模型，其中有两个或两个以上的解决方案分开的分叉或临界点。气候科学的一个简单例子是Stommel模型，它对翻转环流何时打开或关闭有不同的解决方案。我们还有气候、油藏建模和生物学方面的其他例子。这个博士将着眼于这个问题的开发方法，以确定每个解决方案的模型输入空间的区域，以及如何为每个解决方案构建单独但链接的仿真器。逆问题，我们有真实的世界的一些模型输出的观察，这些被用来对模型的输入进行推断，实际上运行模型“向后”，也将被考虑。此外，学生将研究实验设计问题，在有限的计算机预算下最好运行模型，开发新的顺序方法。虽然学生将开发一个通用的方法，它将被应用到整个博士学位的真实的世界的应用数量。

The use of complex numerical models in science and policy is now ubiquitous. For practical application predictions from such models need to be accompanied by estimates of uncertainty. Supplying these estimates is a difficult problem. Gaussian process emulation has proved to be a very effective solution A Gaussian process emulator is a statistical model of the numerical code that is fast to run so can be used to calculate uncertainty estimates, for example by Monte Carlo methods that are computationally impossible with the full model. Emulators have been used across a wide variety of applications from climate and air pollution through engineering and geology to systems biology. However there are numerical models where there are two or more solutions separated by bifurcations or tipping points. A simple example from climate science is the Stommel model which has a different solution for when the overturning circulation is turned on or off. We have other examples from climate, oil reservoir modelling and biology. This PhD will look at this problem developing methods to identify the areas of model input space where each solution holds and how to build separate, but linked, emulators for each solutions. The inverse problem where we have real world observations of some of the model outputs and these are used to make inferences about the model inputs, in effect running the model 'backwards', will also be considered. In addition the student will look at the problem of experimental design, where best to run the model with a limited computer budget, developing new sequential methods. Although the student will develop a general methodology it will be applied to a number of real world applications throughout the PhD.