Learned data assimilation: what can be learned in the analysis
esmax · ocean · 6 · Eleven ways to learn a piece of the analysis: the objective, its gradient, the solver, the output, or the whole inverse
Abstract¶
The taxonomy page took the model apart, and this page takes the assimilation apart: the objective, its gradient, the solver, the output, and whether the answer is computed per window or learned across windows. We give eleven ways to learn one of those pieces, on the same Gulf Stream QG example and the same 10-day window of SSH maps.
Where it sits. Boxes 4 and 5 taken apart: what can be learned in the assimilation itself. The full page is a self-contained document with operator boxes (inputs, outputs, shapes and units), figures and code sketches, which opens on its own and links back here.
TL;DR: One analysis operator, eleven insides¶
Every type is box 2’s operator: maps, masks, errors, background, covariates and forcing go in, and a state window and its uncertainty come out. What changes is the inside, the training data it needs, and whether the output is a point, an ensemble or a density.
The training signal matters more than the network. Simulated truth (OSSE) learns the QG model’s ocean, whereas the ELBO and held-out observations learn the real one but never see the unobserved scales.
Mean, mode or sample. 4D-Var returns a mode, an MSE-trained network returns a mean and VI returns a density, so benchmarks must compare the same statistic.
Teal types fail loudly, because the classical cost or solver is still there to check the answer. Amber types fail silently, which means an unusual window gets a confident wrong field. Scoring any output with the classical cost and its innovations turns most of the silent failures into loud ones.
On the page¶
Notation
The master equation
Training signals
The eleven types
Model type × assimilation type
What the structure implies
Where each type lives