Joint parameter and model dimension reduction for Bayesian ice sheet inverse problems governed by the nonlinear Stokes equations
Abstract
Understanding the dynamics of ice sheets play a critical role in predicting future sea level rise. However, there are several challenges when it comes to the modeling and simulation of ice sheet flow. One of these challenges stems from the need to infer for unknown/uncertain parameter fields in the model (e.g., the basal sliding coefficient field) from satellite observations of the surface ice flow velocity. The Bayesian inversion framework can be used to perform such inference and quantify the associated uncertainties. However, the exploration of the solution of the Bayesian inverse problem (i.e., the posterior) suffers from the twin difficulties of high dimensionality of the uncertain parameters and computationally expensive forward models. In this talk, we discuss an effective approach to tackle these challenges in the context of a large-scale ice sheet inverse problem governed by the nonlinear Stokes equations. In particular, we exploit the underlying problem structure (e.g., local sensitivity of the data to parameters, the smoothing properties of the forward model, and the covariance structure of the prior) to identify a likelihood-informed parameter subspace where the change from prior to posterioris most significant. This approach allows us to construct a parameter-reduced posterior. We also employ a proper orthogonal decomposition (POD) to establish a low-dimensional manifold for the forward state space and the discrete empirical interpolation method (DEIM) to approximate the nonlinearity inherent in the forward model. This approach enables us to obtain the forward solution without significant loss of accuracy at a cost that is independent of the original full dimension of the forward state space. The resulting joint parameter and state dimension reduction leads to a scalable and efficient scheme that has the potential to make the exploration of the full posterior distribution of the parameter or subsequent predictions tractable. We illustrate our approach with the Arolla ice sheet inverse problem governed by the nonlinear Stokes equations for which the basal sliding coefficient field is inferred from surface velocities.
- Publication:
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AGU Fall Meeting Abstracts
- Pub Date:
- December 2021
- Bibcode:
- 2021AGUFMNG21A..06P