Mass Conservation on Rails -- Rethinking Physics-Informed Learning of Ice Flow Vector Fields
This work addresses the need for physically accurate ice sheet models to project future sea level rise, offering a domain-specific incremental improvement over existing methods.
The paper tackled the problem of interpolating Antarctic ice flow vector fields from sparse, noisy measurements by enforcing exact mass conservation, resulting in more reliable estimates and improved performance across models, particularly with the addition of directional guidance.
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.