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Case study · AI emulation

Brest FNO surrogate: emulating CROCO surface currents

A Fourier neural operator evaluates the surface currents of a 250 m CROCO model over multi-start time windows, from an initial state supplied by the physical model.

All case studiesBy Matthieu Caillaud · Published on August 4, 2026 · Updated on September 12, 2026
Measured results

The figures that summarize the study

15.54%Median L2, lead 50, seed 0
32.56%B1a harmonic baseline
31.00%Harmonic init., 237 windows
32.57%B1a, 237 windows

Test temporal emulation without confusing speed with fidelity

A coastal hydrodynamic model resolves rich physics, but its cost limits scenario iteration. The project tests whether an autoregressive 2D FNO can reproduce a 250 m CROCO surface current field.

The surface run covers 570 days; relative L2 error is measured at lead 50 (12.5 h) across 238 multi-start windows, with the exact CROCO state as the initial condition.

Method

A verifiable computation chain

01

Build the numerical reference

Surface outputs from a 250 m CROCO model of the Brest roadstead over 570 days provide training and evaluation sequences.

02

Learn the operator

The 2D FNO learns spatial field evolution in the spectral domain, then generates following steps autoregressively.

03

Evaluate a fixed lead

Relative L2 error is aggregated at lead 50 (12.5 h) across 238 multi-start windows rather than retaining only the best sequence.

04

Compare with a simple reference

The B1a harmonic reconstruction acts as the baseline. A separate 237-window experiment starts from a harmonic condition to expose the limit of missing exact CROCO state.

Validation

What the comparisons show

The result depends on the initial state

With the exact CROCO state, the surface run gives 15.54% against 32.56% for B1a at lead 50 across 238 windows. A separate harmonic experiment gives 31.00% against 32.57% across 237 windows: the emulator is not an autonomous forecast.

Dispersion remains a central result

Rollout dispersion must be tracked alongside the median; a central value alone does not qualify the emulator.

Inference is measured, not the overall speed-up

Inference and simulation costs are comparable only under the same protocol; no overall acceleration factor is claimed here.

Validity domain

What this study does not claim

  • Current validation measures fidelity to CROCO, not yet agreement with independent in-situ observations.
  • Several quantiles are needed to monitor rollout dispersion alongside the median.
  • This FNO addresses temporal emulation; it must not be conflated with a UNet used for spatial downscaling.

Do you need to reduce the cost of a scenario ensemble?

We define the metric, baseline and validity domain before selecting a surrogate architecture.

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