The Conserving Emulator

Sea ice models in global climate simulations are expensive — tracking ice thickness distributions, snow layers, and thermodynamic budgets at every ocean grid cell requires solving coupled conservation equations at sub-daily timesteps. Machine learning emulators can be faster, but standard neural networks don't conserve mass. A sea ice emulator that creates or destroys ice mass at every timestep will drift, accumulating errors that corrupt the climate state over decades of simulation.

Cheng et al. (arXiv:2603.12449) build FloeNet, a mass-conserving sea ice emulator trained on GFDL's SIS2 model. Instead of predicting ice states directly, FloeNet predicts budget tendencies — the rates of change for ice mass and area from growth, melt, and advection — and then updates the state by integrating these rates. Conservation is enforced architecturally: the predicted tendencies are constrained to satisfy the mass budget exactly, not approximately.

The conservation constraint does double duty. Obviously, it prevents drift. Less obviously, it forces the emulator to correctly separate thermodynamic from dynamic responses to climate forcing. When CO2 quadruples, a non-conservative emulator can reproduce the right total ice loss by any combination of melting and advection errors that happen to cancel. A conservative emulator can't — the mass budget forces it to get the partition right. FloeNet trained on reanalysis-forced data generalizes to pre-industrial and 4xCO2 climates, correctly predicting that the Arctic ice loss is primarily thermodynamic (more melting) while Antarctic changes involve more dynamic redistribution.

The broader point: conservation laws aren't just physics constraints — they're regularizers that force the model to learn the right decomposition of the signal.