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International Journal for Multiscale Computational Engineering
IF: 1.016 5-Year IF: 1.194 SJR: 0.452 SNIP: 0.68 CiteScore™: 1.18

ISSN Print: 1543-1649
ISSN Online: 1940-4352

International Journal for Multiscale Computational Engineering

DOI: 10.1615/IntJMultCompEng.2017020553
pages 265-283

A STOCHASTIC INVERSE PROBLEM FOR MULTISCALE MODELS

N. Panda
Department of Statistics, Colorado State University, Fort Collins, Colorado 80523-1877, USA
Troy Butler
Department of Mathematical and Statistical Sciences, University of Colorado Denver, Colorado 80217, USA
Donald Estep
Department of Statistics, Colorado State University, Fort Collins, Colorado 80523-1877, USA
Lindley Graham
Department of Scientific Computing, Florida State University, Tallahassee, Florida 32306, USA
Clint Dawson
The Institute for Computational Engineering and Sciences, University of Texas at Austin, Austin, Texas 78712, USA

ABSTRACT

Descriptions of complex multiscaled physical systems often involve many physical processes interacting through a multitude of scales. In many cases, the primary interest lies in predicting behavior of the system at the macroscale (i.e., engineering scale) where continuum, physics-based, models such as partial differential equations provide high-fidelity descriptions. However, in multiscale systems, the behavior of continuum models can depend strongly on microscale properties and effects, which are often included in the macroscale model as a parameter field obtained by some upscaling process from a microscale model. Generally, a number of choices have to be made in choosing an upscaling procedure and the resulting representation of the parameter. These choices have a strong impact on both the fidelity and the computational efficiency of the model. Thus, choosing a good parameter representation and upscaling procedure becomes part of the uncertainty quantification and prediction problem for a multiscale model. We consider the use of output data from the macroscale model to formulate and solve a stochastic inverse problem to determine probability information about the upscaled parameter field. In particular, we extend a measure-theoretic inverse problem frame-work and non-intrusive sample-based algorithm to determine the choices of parameter representation and upscaling procedure that are most probable given uncertain data from the macroscale model.We illustrate the methodology in the context of shallow water flow and sub-surface flow.


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