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Thesis

Multilevel Monte Carlo methods for uncertainty quantification in brain simulations

Abstract:

This thesis consists of two parts. In the first, we develop two new strategies for spatial white noise and Gaussian-Mat\'ern field sampling that work within a non-nested multilevel (quasi) Monte Carlo (ML(Q)MC) hierarchy. In the second, we apply the techniques developed to quantify the level of uncertainty in a new stochastic model for tracer transport in the brain.

The new sampling techniques are based on the stochastic partial differential equation (SPDE) approach, which recast...

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Institution:
University of Oxford
Division:
MPLS
Department:
Mathematical Institute
Subgroup:
Mathematical Institute
Research group:
Numerical Analysis
Oxford college:
University College
Role:
Author
ORCID:
0000-0003-1669-9445

Contributors

Institution:
University of Oxford
Division:
MPLS
Department:
Mathematical Institute
Subgroup:
Mathematical Institute
Research group:
Mathematical and Computational Finance & Numerical Analysis
Oxford college:
St Hugh's College
Role:
Supervisor
ORCID:
0000-0002-5445-3721
Institution:
Simula Research Laboratory
Subgroup:
Mathematical Institute
Research group:
Department of Numerical Analysis and Scientific Computing
Role:
Supervisor
ORCID:
0000-0002-6872-3710
Institution:
University of Oxford
Division:
MPLS
Department:
Mathematical Institute
Subgroup:
Mathematical Institute
Research group:
Numerical Analysis
Oxford college:
Oriel College
Role:
Supervisor
ORCID:
0000-0002-1241-7060
Institution:
University of Heidelberg
Research group:
Numerical Analysis and Uncertainty Quantification
Role:
Examiner
ORCID:
0000-0001-8493-4393
Institution:
University of Oxford
Division:
MPLS
Department:
Mathematical Institute
Subgroup:
Mathematical Institute
Research group:
Numerical Analysis & Oxford Centre for Nonlinear PDE
Oxford college:
Worcester College
Role:
Examiner
ORCID:
0000-0002-0812-6105
More from this funder
Grant:
Programme:
Oxford-Radcliffe Graduate Scholarships
Funding agency for:
Croci, M
More from this funder
Grant:
EP/L015803/1
Programme:
EPSRC Centre For Doctoral Training in Industrially Focused Mathematical Modelling
Funding agency for:
Croci, M
Type of award:
DPhil
Level of award:
Doctoral
Awarding institution:
University of Oxford

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