For scientists to be able to trust their own research results, it is imperative to map the uncertainty in the models they use. However, this is often numerically resource intensive. This thesis introduce polynomial chaos expansions, a completely new research tool to map uncertainty in numerical models. The thesis makes uncertainty quantification easier and more accessible to researchers.
The research is split into three papers. The first paper shows that polynomials chaos expansions are applicable in an bio-mechanics model simulating blood flow simulation, out-competing alternative approaches. In the second paper a software toolbox was developed to give researches easy access to polynomial chaos expansions. And lastly, in the third paper, the theoretical framework for polynomial chaos expansions to show that it can be effective for problems previously known to be problematic.
The thesis is written within the field of uncertainty quantification. The work has been conducted at Simula Research Laboratory.
Prior to the defense, at 10:15, Jonathan Feinberg presented his trial lecture "A critical review of numerical methods for stochastic Langevin equations".
The adjudication committee
• Professor Daniel Tartakovsky, University of California, San Diego
• Professor Håvard Rue, Norwegian University of Science and Technology
• Professor Erik Bølviken, University of Oslo
Chair of the disputation
• Professor, Ørnulf Borgan University of Oslo
• Professor Hans Petter Langtangen, University of Oslo
• Professor Arne Bang Huseby, University of Oslo
• Doctor Stuart Clark, Simula Research Laboratory