From Obstacle Problems to Neural Insights: Feed Forward Neural Network Modeling of Ice Thickness

TL;DR

This paper combines obstacle problem formulations with deep learning to improve ice thickness predictions for the Greenland ice sheet, demonstrating enhanced accuracy through numerical simulations and dataset integration.

Contribution

It introduces a novel approach that integrates mathematical obstacle problems with neural network energy minimization frameworks for ice sheet modeling.

Findings

Improved prediction accuracy on Greenland ice sheet data.

Successful application of 1D and 2D numerical simulations.

Effective use of bedrock topography for model pre-training.

Abstract

In this study, we integrate the established obstacle problem formulation from ice sheet modeling with cutting-edge deep learning methodologies to enhance ice thickness predictions, specifically targeting the Greenland ice sheet. By harmonizing the mathematical structure with an energy minimization framework tailored for neural network approximations, our method's efficacy is confirmed through both 1D and 2D numerical simulations. Utilizing the NSIDC-0092 dataset for Greenland and incorporating bedrock topography for model pre-training, we register notable advances in prediction accuracy. Our research underscores the potent combination of traditional mathematical models and advanced computational techniques in delivering precise ice thickness estimations.