Hybrid model taxonomy: what can be learned in an ocean model
esmax · ocean · 5 · Ten things that can be learned in an ocean model, from parameters to the whole rollout, and how each is glued back
Abstract¶
The physical model is not one object. It is a stack of pieces (parameters, discretisation, terms, a tendency, an integrator, a step map, a rollout), and every hybrid or emulator learns one of those pieces and glues it back in one of a few ways. In this page, we list the ten that matter, on the same Gulf Stream QG example as the state-estimation page.
Where it sits. Box 3 taken apart: which layer of the model is learned, and what each choice keeps. 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 signature, ten insides¶
Every type from T1 to T8 is the same operator: today’s state, covariates, forcing and parameters go in, and tomorrow’s state comes out. So any of them drops into the cycles, the DA and the rollouts of the last page unchanged. T9 and T10 change the signature.
Types differ in which layer is learned (the diagram below) and in how the learned piece is glued back: added, used as a coefficient, built into a conserving form, or substituted.
The training target splits them into two jobs. Emulation reproduces the physical model faster (box 3, where the ground truth is step 1), whereas correction makes the model closer to the real ocean (box 6, where the ground truth is a richer model or data).
The lower the learned layer, the more physics survives: conservation, freedom in and a trustworthy adjoint. The higher the layer, the more speed and the less structure.
On the page¶
Notation
The physical model, taken apart
Three axes
The ten types
Selection matrix
What the structure implies
Where each type lives