# 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

arXiv: https://arxiv.org/abs/1410.1221 · HTML: https://mlsanity.com/paper/1410.1221/

## Key facts

- Cited by 13 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 5 Oct 2014.

## Built on by (most cited first, 13 of 13)

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- [A Hybrid Deep Neural Operator/Finite Element Method for Ice-Sheet Modeling](https://mlsanity.com/paper/2301.11402/) (2023)
- [Differentiable modeling to unify machine learning and physical models and advance Geosciences](https://mlsanity.com/paper/2301.04027/) (2023)
- [Solving High-Dimensional Inverse Problems with Auxiliary Uncertainty via Operator Learning with Limited Data](https://mlsanity.com/paper/2303.11379/) (2023)
- [Stratospheric aerosol source inversion: Noise, variability, and uncertainty quantification](https://mlsanity.com/paper/2409.06846/) (2024)
- [Variational Inference at Glacier Scale](https://mlsanity.com/paper/2108.07263/) (2021)
- [Adaptive Sensor Steering Strategy Using Deep Reinforcement Learning for Dynamic Data Acquisition in Digital Twins](https://mlsanity.com/paper/2504.10248/) (2025)
- [Stochastic Learning Approach to Binary Optimization for Optimal Design of Experiments](https://mlsanity.com/paper/2101.05958/) (2021)
- [Domain-Decomposed Graph Neural Network Surrogate Modeling for Ice Sheets](https://mlsanity.com/paper/2512.01888/) (2025)

## Abstract (arXiv)

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.