Towards Bayesian inference of friction parameters in ice sheets

Abstract

This work is concerned in the inference of space dependent friction parameters in ice sheets from partial and noisy observations of ice velocity. A Bayesian framework is used to quantify the uncertainty on the inverse problem solution. A space dependent field has to be discretized for the inverse problem to be finite dimensional. Here, the friction field is described as a random field, which allows to discretize it using the Karhunen-Loève expansion. Such discretizations lead to a small dimensional inverse problem. The forward model is a finite-element implementation of an ice-sheet reduced order model. As it is computationally expensive, a polynomial chaos surrogate model is constructed. The inverse problem is solved using sampling methods and neural posterior estimation. Neural posterior estimator has been shown to require less calls to the forward model than sampling methods, for equally satisfying results. This suggests that the use of neural posterior estimator could improve the current state-of-the-art of Bayesian inverse problems in glaciology.