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Title: A generalized multi-resolution expansion for uncertainty propagation with application to cardiovascular modeling

Computational models are used in a variety of fields to improve our understanding of complex physical phenomena. Recently, the realism of model predictions has been greatly enhanced by transitioning from deterministic to stochastic frameworks, where the effects of the intrinsic variability in parameters, loads, constitutive properties, model geometry and other quantities can be more naturally included. A general stochastic system may be characterized by a large number of arbitrarily distributed and correlated random inputs, and a limited support response with sharp gradients or event discontinuities. This motivates continued research into novel adaptive algorithms for uncertainty propagation, particularly those handling high dimensional, arbitrarily distributed random inputs and non-smooth stochastic responses. Here, we generalize a previously proposed multi-resolution approach to uncertainty propagation to develop a method that improves computational efficiency, can handle arbitrarily distributed random inputs and non-smooth stochastic responses, and naturally facilitates adaptivity, i.e., the expansion coefficients encode information on solution refinement. Our approach relies on partitioning the stochastic space into elements that are subdivided along a single dimension, or, in other words, progressive refinements exhibiting a binary tree representation. We also show how these binary refinements are particularly effective in avoiding the exponential increase in the multi-resolution basis cardinality andmore » significantly reduce the regression complexity for moderate to high dimensional random inputs. The performance of the approach is demonstrated through previously proposed uncertainty propagation benchmarks and stochastic multi-scale finite element simulations in cardiovascular flow.« less
Authors:
 [1] ;  [2] ;  [3] ;  [4]
  1. Univ. of Notre Dame, IN (United States). Dept. of Applied and Computational Mathematics and Statistics
  2. Univ. of Colorado, Boulder, CO (United States). Aerospace Engineering Sciences
  3. Stanford Univ., CA (United States). Dept. of Mechanical Engineering and Inst. for Computational and Mathematical Engineering (ICME)
  4. Stanford Univ., CA (United States). Dept. of Pediatrics and Inst. for Computational and Mathematical Engineering (ICME)
Publication Date:
Grant/Contract Number:
SC0006402; 15POST23010012; OCI-1150184; R01HL123689; R01 PA16285; ACI-1053575; CMMI-145460
Type:
Accepted Manuscript
Journal Name:
Computer Methods in Applied Mechanics and Engineering
Additional Journal Information:
Journal Volume: 314; Journal Issue: C; Journal ID: ISSN 0045-7825
Publisher:
Elsevier
Research Org:
Univ. of Colorado, Boulder, CO (United States)
Sponsoring Org:
USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR) (SC-21); American Heart Association (AHA); Burroughs Wellcome Fund (BWF); National Science Foundation (NSF); National Institutes of Health (NIH)
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICS AND COMPUTING; 59 BASIC BIOLOGICAL SCIENCES; Uncertainty quantification; Multi-resolution stochastic expansion; Cardiovascular simulation; Sparsity-promoting regression; Relevance vector machines; Multi-scale models for cardiovascular flow
OSTI Identifier:
1463087
Alternate Identifier(s):
OSTI ID: 1413548

Schiavazzi, D. E., Doostan, A., Iaccarino, G., and Marsden, A. L.. A generalized multi-resolution expansion for uncertainty propagation with application to cardiovascular modeling. United States: N. p., Web. doi:10.1016/j.cma.2016.09.024.
Schiavazzi, D. E., Doostan, A., Iaccarino, G., & Marsden, A. L.. A generalized multi-resolution expansion for uncertainty propagation with application to cardiovascular modeling. United States. doi:10.1016/j.cma.2016.09.024.
Schiavazzi, D. E., Doostan, A., Iaccarino, G., and Marsden, A. L.. 2016. "A generalized multi-resolution expansion for uncertainty propagation with application to cardiovascular modeling". United States. doi:10.1016/j.cma.2016.09.024. https://www.osti.gov/servlets/purl/1463087.
@article{osti_1463087,
title = {A generalized multi-resolution expansion for uncertainty propagation with application to cardiovascular modeling},
author = {Schiavazzi, D. E. and Doostan, A. and Iaccarino, G. and Marsden, A. L.},
abstractNote = {Computational models are used in a variety of fields to improve our understanding of complex physical phenomena. Recently, the realism of model predictions has been greatly enhanced by transitioning from deterministic to stochastic frameworks, where the effects of the intrinsic variability in parameters, loads, constitutive properties, model geometry and other quantities can be more naturally included. A general stochastic system may be characterized by a large number of arbitrarily distributed and correlated random inputs, and a limited support response with sharp gradients or event discontinuities. This motivates continued research into novel adaptive algorithms for uncertainty propagation, particularly those handling high dimensional, arbitrarily distributed random inputs and non-smooth stochastic responses. Here, we generalize a previously proposed multi-resolution approach to uncertainty propagation to develop a method that improves computational efficiency, can handle arbitrarily distributed random inputs and non-smooth stochastic responses, and naturally facilitates adaptivity, i.e., the expansion coefficients encode information on solution refinement. Our approach relies on partitioning the stochastic space into elements that are subdivided along a single dimension, or, in other words, progressive refinements exhibiting a binary tree representation. We also show how these binary refinements are particularly effective in avoiding the exponential increase in the multi-resolution basis cardinality and significantly reduce the regression complexity for moderate to high dimensional random inputs. The performance of the approach is demonstrated through previously proposed uncertainty propagation benchmarks and stochastic multi-scale finite element simulations in cardiovascular flow.},
doi = {10.1016/j.cma.2016.09.024},
journal = {Computer Methods in Applied Mechanics and Engineering},
number = C,
volume = 314,
place = {United States},
year = {2016},
month = {10}
}