Scalable and efficient algorithms for the propagation of uncertainty from data through inference to prediction for large-scale problems, with application to flow of the Antarctic ice sheet

Journal Article · Tue Sep 01 04:00:00 EDT 2015 · Journal of Computational Physics

DOI:https://doi.org/10.1016/j.jcp.2015.04.047· OSTI ID:1565299

Isaac, Tobin ^[1]; Petra, Noemi ^[2]; Stadler, Georg ^[3]; Ghattas, Omar ^[4]

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1. Univ. of Texas, Austin, TX (United States). Inst. for Computational Engineering & Sciences
2. Univ. of California, Merced, CA (United States). School of Natural Sciences, Applied Mathematics
3. New York Univ., New York, NY (United States). Courant Inst. of Mathematical Sciences
4. Univ. of Texas, Austin, TX (United States). Inst. for Computational Engineering & Sciences, and Dept. of Mechanical Engineering, and Jackson School of Geosciences

The majority of research on efficient and scalable algorithms in computational science and engineering has focused on the forward problem: given parameter inputs, solve the governing equations to determine output quantities of interest. In contrast, in this paper, we consider the broader question: given a (large-scale) model containing uncertain parameters, (possibly) noisy observational data, and a prediction quantity of interest, how do we construct efficient and scalable algorithms to (1) infer the model parameters from the data (the deterministic inverse problem), (2) quantify the uncertainty in the inferred parameters (the Bayesian inference problem), and (3) propagate the resulting uncertain parameters through the model to issue predictions with quantified uncertainties (the forward uncertainty propagation problem)? We present efficient and scalable algorithms for this end-to-end, data-to-prediction process under the Gaussian approximation and in the context of modeling the flow of the Antarctic ice sheet and its effect on loss of grounded ice to the ocean. The ice is modeled as a viscous, incompressible, creeping, shear-thinning fluid. The observational data come from satellite measurements of surface ice flow velocity, and the uncertain parameter field to be inferred is the basal sliding parameter, represented by a heterogeneous coefficient in a Robin boundary condition at the base of the ice sheet. The prediction quantity of interest is the present-day ice mass flux from the Antarctic continent to the ocean. We show that the work required for executing this data-to-prediction process—measured in number of forward (and adjoint) ice sheet model solves—is independent of the state dimension, parameter dimension, data dimension, and the number of processor cores. The key to achieving this dimension independence is to exploit the fact that, despite their large size, the observational data typically provide only sparse information on model parameters. This property can be exploited to construct a low rank approximation of the linearized parameter-to-observable map via randomized SVD methods and adjoint-based actions of Hessians of the data misfit functional.

• Research Organization: Oak Ridge National Laboratory (ORNL), Oak Ridge, TN (United States). Oak Ridge Leadership Computing Facility (OLCF); UT-Battelle LLC/ORNL, Oak Ridge, TN (Unted States); Univ. of Texas, Austin, TX (United States)
• Sponsoring Organization: USDOE Office of Science (SC)
• Grant/Contract Number: AC05-00OR22725; SC0009286; SC0010518; SC0009286
• OSTI ID: 1565299
• Alternate ID(s): OSTI ID: 1359273
• Journal Information: Journal of Computational Physics, Journal Name: Journal of Computational Physics Journal Issue: C Vol. 296; ISSN 0021-9991
• Publisher: Elsevier
• Country of Publication: United States
• Language: English

Related Subjects

54 ENVIRONMENTAL SCIENCES
97 MATHEMATICS AND COMPUTING
Antarctic ice sheet
Bayesian inference
Nonlinear Stroke equations
adjoint-based Hessian
computer science
data-to-prediction
ice sheet flow modeling
inexact Newton-Krylov method
inverse problems
low-rank approximation
physics
preconditioning
uncertainty quantification