# Variational Inference at Glacier Scale

arXiv: https://arxiv.org/abs/2108.07263 · HTML: https://mlsanity.com/paper/2108.07263/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 10 of its 72 references that are in the map.
- First posted on arXiv 16 Aug 2021.

## Builds on (most cited first, 10 of 10)

- [Variational Inference: A Review for Statisticians](https://mlsanity.com/paper/1601.00670/) (2016)
- [Weight Uncertainty in Neural Networks](https://mlsanity.com/paper/1505.05424/) (2015)
- [B-PINNs: Bayesian Physics-Informed Neural Networks for Forward and Inverse PDE Problems with Noisy Data](https://mlsanity.com/paper/2003.06097/) (2020)
- [Automatic Differentiation Variational Inference](https://mlsanity.com/paper/1603.00788/) (2016)
- [Hilbert Space Methods for Reduced-Rank Gaussian Process Regression](https://mlsanity.com/paper/1401.5508/) (2014)
- [Natural Gradients in Practice: Non-Conjugate Variational Inference in Gaussian Process Models](https://mlsanity.com/paper/1803.09151/) (2018)
- [A computational framework for infinite-dimensional Bayesian inverse problems: Part II. Stochastic Newton MCMC with application to ice sheet flow inverse problems](https://mlsanity.com/paper/1308.6221/) (2013)
- [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](https://mlsanity.com/paper/1410.1221/) (2014)
- [Approximate Bayesian Model Inversion for PDEs with Heterogeneous and State-Dependent Coefficients](https://mlsanity.com/paper/1902.06718/) (2019)
- [Sparse Variational Bayesian Approximations for Nonlinear Inverse Problems: applications in nonlinear elastography](https://mlsanity.com/paper/1412.0473/) (2014)

## Built on by (most cited first, 1 of 1)

- [A Hybrid Deep Neural Operator/Finite Element Method for Ice-Sheet Modeling](https://mlsanity.com/paper/2301.11402/) (2023)

## Abstract (arXiv)

We characterize the complete joint posterior distribution over spatially-varying basal traction and and ice softness parameters of an ice sheet model from observations of surface speed by using stochastic variational inference combined with natural gradient descent to find an approximating variational distribution. By placing a Gaussian process prior over the parameters and casting the problem in terms of eigenfunctions of a kernel, we gain substantial control over prior assumptions on parameter smoothness and length scale, while also rendering the inference tractable. In a synthetic example, we find that this method recovers known parameters and accounts for mutual indeterminacy, both of which can influence observed surface speed. In an application to Helheim Glacier in Southeast Greenland, we show that our method scales to glacier-sized problems. We find that posterior uncertainty in regions of slow flow is high regardless of the choice of observational noise model.