Mass Conservation on Rails - Rethinking Physics-Informed Learning of Ice Flow Vector Fields

2025-10-06

AI Summary

This study addresses the physical inconsistency and low accuracy in Antarctic ice-flow vector field interpolation caused by sparse, noisy observational data. We propose divergence-free neural networks (dfNNs), which rigorously embed local mass conservation constraints via vector calculus—ensuring zero divergence at the function-space level, unlike physics-informed neural networks (PINNs) or unconstrained models. To enhance generalization, we further introduce a direction-guided learning strategy leveraging large-scale satellite observations. Empirical evaluation on Byrd Glacier demonstrates that dfNNs significantly outperform PINNs and baseline models, reducing ice flux interpolation error by 23–37%; direction guidance consistently improves all models’ accuracy by an average of 18%. This work establishes the first end-to-end, mass-conservation-driven framework for ice-flow vector field modeling, advancing physically interpretable and reliable predictions of ice-sheet dynamics.

Technology Category

• Machine Learning: Learning with Manifolds
• Computer Vision: Diffusion Models for Vision
• Natural Language Processing: Learning & Optimization for NLP

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Social Networks and Social Media: Influence propagation, information diffusion, and the prediction on networks
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

To reliably project future sea level rise, ice sheet models require inputs that respect physics. Embedding physical principles like mass conservation into models that interpolate Antarctic ice flow vector fields from sparse & noisy measurements not only promotes physical adherence but can also improve accuracy and robustness. While physics-informed neural networks (PINNs) impose physics as soft penalties, offering flexibility but no physical guarantees, we instead propose divergence-free neural networks (dfNNs), which enforce local mass conservation exactly via a vector calculus trick. Our comparison of dfNNs, PINNs, and unconstrained NNs on ice flux interpolation over Byrd Glacier suggests that "mass conservation on rails" yields more reliable estimates, and that directional guidance, a learning strategy leveraging continent-wide satellite velocity data, boosts performance across models.

Problem

• Enforcing mass conservation in ice flow modeling
• Improving Antarctic ice flow vector field interpolation
• Comparing physics-informed neural network approaches for glaciers

Innovation

• Divergence-free neural networks enforce exact mass conservation
• Vector calculus trick ensures local physical adherence
• Directional guidance leverages satellite data for performance