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

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.