Calibration and uncertainty quantification of computationally expensive simulations, with applications to nuclear fusion systems
File(s)
Author(s)
Crovini, Enrico
Type
Thesis
Abstract
Bayesian inverse problems aim to infer a posterior distribution of parameters that generated observed data through a forward model. When the computational cost of evaluating the forward model is high, standard methodologies must be adapted or replaced with novel approaches. Inspired by a nuclear fusion calibration problem, this thesis develops new methodologies to address these challenges. Specifically, Bayesian inverse problems are solved using Bayesian optimal design in two ways. First, we frame the task as a maximum a posteriori problem and propose a novel batch Bayesian optimization (BO) method to estimate the maximum of the inverse density. This approach extends standard batch BO by constructing a new acquisition functional based on multipoint expected improvement, which is concave over probability measures. Practical schemes for solving the inner BO optimization are derived using gradient flows of this objective function. The method’s efficacy is demonstrated on benchmark functions and compared with state-of-the-art batch BO methods. Second, we develop a method for posterior inference using Bayesian optimal design to sequentially select points over the parameter domain, utilizing Fisher information gain. Model evaluations at these points construct a surrogate of the inverse posterior density, and the methodology is applied to various examples. We apply the methodologies we derived to the motivating calibration problem, where we target an expensive numerical solver of the magnetohydrodynamics equations, JOREK, and develop a framework for its automatic calibration with respect to some physical output data. We highlight challenges and show that the calibration is possible, albeit demanding.
Version
Open Access
Date Issued
2024-03-31
Date Awarded
01/01/2025
License URL
Advisor
Duncan, Andrew
Sponsor
EUROfusion (Firm)
Grant Number
101052200
Publisher Department
Mathematics
Publisher Institution
Imperial College London
Qualification Level
Doctoral
Qualification Name
Doctor of Philosophy (PhD)