A generalized multi-resolution expansion for uncertainty propagation with application to cardiovascular modeling
- Univ. of Notre Dame, IN (United States). Dept. of Applied and Computational Mathematics and Statistics
- Univ. of Colorado, Boulder, CO (United States). Aerospace Engineering Sciences
- Stanford Univ., CA (United States). Dept. of Mechanical Engineering and Inst. for Computational and Mathematical Engineering (ICME)
- Stanford Univ., CA (United States). Dept. of Pediatrics and Inst. for Computational and Mathematical Engineering (ICME)
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.
- Research Organization:
- Univ. of Colorado, Boulder, CO (United States)
- Sponsoring Organization:
- USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR); American Heart Association (AHA); Burroughs Wellcome Fund (BWF); National Science Foundation (NSF); National Institutes of Health (NIH)
- Grant/Contract Number:
- SC0006402; 15POST23010012; OCI-1150184; R01HL123689; R01 PA16285; ACI-1053575; CMMI-145460
- OSTI ID:
- 1463087
- Alternate ID(s):
- OSTI ID: 1413548
- Journal Information:
- Computer Methods in Applied Mechanics and Engineering, Vol. 314, Issue C; ISSN 0045-7825
- Publisher:
- ElsevierCopyright Statement
- Country of Publication:
- United States
- Language:
- English
Web of Science
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journal | March 2017 |
Performance of preconditioned iterative linear solvers for cardiovascular simulations in rigid and deformable vessels
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journal | February 2019 |
| Performance of preconditioned iterative linear solvers for cardiovascular simulations in rigid and deformable vessels | preprint | January 2019 |
| Multi-fidelity estimators for coronary circulation models under clinically-informed data uncertainty | preprint | January 2019 |
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