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

TL;DR

This paper develops scalable algorithms for uncertainty propagation from data through inference to prediction in large-scale models, demonstrated on Antarctic ice sheet flow, achieving dimension-independent computational work.

Contribution

It introduces efficient algorithms for the entire data-to-prediction process, leveraging low rank approximations to handle high-dimensional problems.

Findings

Work is independent of model, data, and parameter dimensions.

Low rank approximation exploits sparse observational data.

Algorithms are applied to Antarctic ice sheet flow modeling.

Abstract

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.