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
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, here we consider the broader question: given a (la...
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ftdatacite:10.48550/arxiv.1410.1221 2023-05-15T13:49:41+02:00 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 Isaac, Tobin Petra, Noemi Stadler, Georg Ghattas, Omar 2014 https://dx.doi.org/10.48550/arxiv.1410.1221 https://arxiv.org/abs/1410.1221 unknown arXiv https://dx.doi.org/10.1016/j.jcp.2015.04.047 arXiv.org perpetual, non-exclusive license http://arxiv.org/licenses/nonexclusive-distrib/1.0/ Optimization and Control math.OC Numerical Analysis math.NA Computation stat.CO Methodology stat.ME FOS Mathematics FOS Computer and information sciences 35Q62, 62F15, 35R30, 35Q93, 65C60, 49M15, 86A40 article-journal Article ScholarlyArticle Text 2014 ftdatacite https://doi.org/10.48550/arxiv.1410.1221 https://doi.org/10.1016/j.jcp.2015.04.047 2022-04-01T12:54:24Z 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, here 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 sea level. The ice is modeled as a viscous, incompressible, creeping, shear-thinning fluid. The observational data come from InSAR satellite measurements of surface ice flow velocity, and the uncertain parameter field to be inferred is the basal sliding parameter. 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 is independent of the state dimension, parameter dimension, data dimension, and number of processor cores. The key to achieving this dimension independence is to exploit the fact that 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. Text Antarc* Antarctic Ice Sheet DataCite Metadata Store (German National Library of Science and Technology) Antarctic The Antarctic |
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DataCite Metadata Store (German National Library of Science and Technology) |
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topic |
Optimization and Control math.OC Numerical Analysis math.NA Computation stat.CO Methodology stat.ME FOS Mathematics FOS Computer and information sciences 35Q62, 62F15, 35R30, 35Q93, 65C60, 49M15, 86A40 |
spellingShingle |
Optimization and Control math.OC Numerical Analysis math.NA Computation stat.CO Methodology stat.ME FOS Mathematics FOS Computer and information sciences 35Q62, 62F15, 35R30, 35Q93, 65C60, 49M15, 86A40 Isaac, Tobin Petra, Noemi Stadler, Georg Ghattas, Omar 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 |
topic_facet |
Optimization and Control math.OC Numerical Analysis math.NA Computation stat.CO Methodology stat.ME FOS Mathematics FOS Computer and information sciences 35Q62, 62F15, 35R30, 35Q93, 65C60, 49M15, 86A40 |
description |
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, here 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 sea level. The ice is modeled as a viscous, incompressible, creeping, shear-thinning fluid. The observational data come from InSAR satellite measurements of surface ice flow velocity, and the uncertain parameter field to be inferred is the basal sliding parameter. 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 is independent of the state dimension, parameter dimension, data dimension, and number of processor cores. The key to achieving this dimension independence is to exploit the fact that 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. |
format |
Text |
author |
Isaac, Tobin Petra, Noemi Stadler, Georg Ghattas, Omar |
author_facet |
Isaac, Tobin Petra, Noemi Stadler, Georg Ghattas, Omar |
author_sort |
Isaac, Tobin |
title |
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 |
title_short |
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 |
title_full |
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 |
title_fullStr |
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 |
title_full_unstemmed |
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 |
title_sort |
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 |
publisher |
arXiv |
publishDate |
2014 |
url |
https://dx.doi.org/10.48550/arxiv.1410.1221 https://arxiv.org/abs/1410.1221 |
geographic |
Antarctic The Antarctic |
geographic_facet |
Antarctic The Antarctic |
genre |
Antarc* Antarctic Ice Sheet |
genre_facet |
Antarc* Antarctic Ice Sheet |
op_relation |
https://dx.doi.org/10.1016/j.jcp.2015.04.047 |
op_rights |
arXiv.org perpetual, non-exclusive license http://arxiv.org/licenses/nonexclusive-distrib/1.0/ |
op_doi |
https://doi.org/10.48550/arxiv.1410.1221 https://doi.org/10.1016/j.jcp.2015.04.047 |
_version_ |
1766251960594333696 |