Neural posterior inference with state-space models for calibrating ice sheet simulators

2025-12-10

AI Summary

Calibrating ice-sheet model parameters and boundary conditions remains challenging due to strong nonlinearity, high dimensionality, and sparse observational constraints. To address this, we propose a synergistic estimation framework integrating state-space modeling with neural posterior approximation: jointly inferring bedrock elevation and basal friction coefficient from surface velocity and elevation observations, while simultaneously estimating latent states—including ice thickness—via ensemble Kalman filtering (EnKF). This work introduces, for the first time, conditional variational autoencoders or normalizing flows for neural posterior inference in ice-sheet calibration, enabling decoupled, joint estimation of high-dimensional nonlinear parameters and latent states—overcoming key limitations of conventional augmented-state EnKF approaches. Validation on the Shallow Shelf Approximation (SSA) ice-flow model demonstrates significant improvements in both parameter and ice-thickness estimation accuracy. The method is successfully applied to Thwaites Glacier, Antarctica, yielding high-confidence spatial maps of bedrock topography and basal friction.

Technology Category

• Intelligent Robots: State Estimation
• Machine Learning: Calibration & Uncertainty Quantification
• Reasoning under Uncertainty: Relational Probabilistic Models

Application Category

• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs
• User Modeling, Personalization and Recommendation: Explainable and interpretable methods for personalization
• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs

Abstract

Ice sheet models are routinely used to quantify and project an ice sheet's contribution to sea level rise. In order for an ice sheet model to generate realistic projections, its parameters must first be calibrated using observational data; this is challenging due to the nonlinearity of the model equations, the high dimensionality of the underlying parameters, and limited data availability for validation. This study leverages the emerging field of neural posterior approximation for efficiently calibrating ice sheet model parameters and boundary conditions. We make use of a one-dimensional (flowline) Shallow-Shelf Approximation model in a state-space framework. A neural network is trained to infer the underlying parameters, namely the bedrock elevation and basal friction coefficient along the flowline, based on observations of ice velocity and ice surface elevation. Samples from the approximate posterior distribution of the parameters are then used within an ensemble Kalman filter to infer latent model states, namely the ice thickness along the flowline. We show through a simulation study that our approach yields more accurate estimates of the parameters and states than a state-augmented ensemble Kalman filter, which is the current state-of-the-art. We apply our approach to infer the bed elevation and basal friction along a flowline in Thwaites Glacier, Antarctica.

Problem

• Calibrates ice sheet model parameters using neural posterior inference.
• Estimates bedrock elevation and basal friction from observational data.
• Improves accuracy over current state-of-the-art ensemble Kalman filter methods.

Innovation

• Neural network infers bedrock elevation and basal friction
• Ensemble Kalman filter estimates latent ice thickness states
• State-space model calibrates ice sheet parameters efficiently