Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

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

Kim Bente, Roman Marchant, Fabio Ramos

TL;DR

Mass-conservation is essential for reliable AIS flux interpolation from sparse data. The paper introduces divergence-free neural networks (dfNNs) that enforce $\nabla \cdot \mathbf{v}=0$ exactly via a stream-function representation, and compares them to PINNs and unconstrained nets on Byrd Glacier data. It further augments learning with directional guidance derived from continent-wide velocity observations and evaluates performance with RMSE, MAE, and a mass-conservation metric MAD. Results show dfNNs outperform all baselines in both accuracy and physics adherence, with the best dfNN + dir achieving zero mass-divergence on test data; directional guidance improves even hard-constrained models while auxiliary surface predictors can degrade performance. The findings advocate a hard-constrained 'models on rails' paradigm for physics-informed learning in climate applications and suggest directional guidance as a practical enhancement.

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.

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

TL;DR

Mass-conservation is essential for reliable AIS flux interpolation from sparse data. The paper introduces divergence-free neural networks (dfNNs) that enforce exactly via a stream-function representation, and compares them to PINNs and unconstrained nets on Byrd Glacier data. It further augments learning with directional guidance derived from continent-wide velocity observations and evaluates performance with RMSE, MAE, and a mass-conservation metric MAD. Results show dfNNs outperform all baselines in both accuracy and physics adherence, with the best dfNN + dir achieving zero mass-divergence on test data; directional guidance improves even hard-constrained models while auxiliary surface predictors can degrade performance. The findings advocate a hard-constrained 'models on rails' paradigm for physics-informed learning in climate applications and suggest directional guidance as a practical enhancement.

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.

Paper Structure

This paper contains 9 sections, 2 equations, 4 figures, 3 tables.

Table of Contents

  1. Introduction & Background
  2. Exact mass conservation with dfNNs
  3. Experiments & Results
  4. Conclusion
  5. Results Table
  6. Training details
  7. Mean Absolute Divergence (MAD)
  8. Training and testing data
  9. Emissions

Figures (4)

  • Figure 1: Diagram of the divergence-free NN (dfNN) model architecture and directional guidance learning strategy (left). The quiver plot (right) shows an on-grid ice flux reconstruction by the dfNN with directional guidance (best model) for a subset of the experimental region over Byrd Glacier.
  • Figure 2: Test RMSE ($\downarrow$) comparison across all model variants, averaged over five runs. Boxed values indicate mean RMSE, with error bars showing $\pm$ std. MAD (top) denotes the Mean Absolute Divergence. dfNNs (proposed, in bold) outperform PINNs & NNs, while directional guidance (proposed, in bold) improves all models and yields the best-performing variant, dfNN + dir (underlined).
  • Figure 3: Gridded predictions of models + dir (best variant per model) for a small test region (white).
  • Figure 4: Train-Test chequerboard over Byrd Glacier, Antarctica. Training regions are shown in grey and test regions are shown in white. Points indicate locations with ice flux observations, collected mainly through airborne geophysical surveys, highlighting the anisotropic nature of the 'flight line' data. The Antarctic Polar stereographic coordinate system is used (ESPG:3031, https://epsg.io/3031). The selected region (purple frame) corresponds to the region shown in \ref{['fig:preds']}.