Data-Driven Parallel Scientific Computing: Multi-Fidelity Information Fusion Algorithms and Applications to Physical and Biological Systems

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Overview

Title
Data-Driven Parallel Scientific Computing: Multi-Fidelity Information Fusion Algorithms and Applications to Physical and Biological Systems
Contributors
Perdikaris, Paris (creator)
Karniadakis, George (Director)
Royset, Johannes (Reader)
Venturi, Daniele (Reader)
Brown University. Applied Mathematics (sponsor)
Doi
10.7301/Z03N21S1
Copyright Date
2015
Abstract
This thesis takes aim at two directions. The first direction involves setting the foundations for a new type of data-driven scientific computing, essentially creating a platform for blending multiple information sources of variable fidelity, e.g., experimental data, high-fidelity numerical simulations, expert opinion, etc., towards creating tractable paths to analyzing the response of complex physical and biological systems. Standing on the verge of traditional scientific computing and contemporary statistical learning techniques, we elaborate on a novel multi-fidelity information fusion framework that allows for the seamless integration of surrogate-based optimization and uncertainty quantification, and enables the development of efficient algorithms for data assimilation, design optimization, model inversion, and beyond. The second direction is focused on addressing open questions in the modeling of the human circulatory system, especially the interplay between blood flow and biomechanics in the brain Despite great growth in computing power and algorithmic sophistication, in-silico modeling of blood flow and arterial mechanics is still limited to truncated arterial domains, a fact that introduces the need for reduced-order models and parametric representations to account for the neglected mesoscale dynamics. The implicit need of such simplified representations gives rise to a series of open questions in cardiovascular mathematics, three of which will be at the focal point of our attention. To this end, we will introduce robust fractional-order constitutive laws for arterial biomechanics, we will address the closure problem for hemodynamic simulations in truncated arterial domains by coupling terminal outlet vessels to nonlinear 1D blood flow models in fractal arterial trees, and we will propose a model inversion technique via multi-fidelity surrogates that enables the efficient solution of parameter calibration problems.
Keywords
Multi-fidelity modeling
High performance scientific computing
Design optimization
Uncertainty quantification
Arterial biomechanics
Inverse problems
Machine learning
Big data
Blood flow
Notes
Thesis (Ph.D. -- Brown University (2015)
Extent
xxi, 236 p.

Citation

Perdikaris, Paris, "Data-Driven Parallel Scientific Computing: Multi-Fidelity Information Fusion Algorithms and Applications to Physical and Biological Systems" (2015). Applied Mathematics Theses and Dissertations. Brown Digital Repository. Brown University Library. https://doi.org/10.7301/Z03N21S1

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