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Case study · AI emulation

Brest FNO surrogate: emulating a CROCO tidal cycle

A Fourier neural operator reproduces the barotropic currents of a 250 m CROCO model with 17% median error over a full tidal cycle.

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

The figures that summarize the study

17%Median FNO error
29%M2+S2 baseline
42%FNO error at p90
250 mCROCO resolution

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 CROCO current field over a complete tidal cycle.

The criterion is not a successful snapshot at a favourable time: error is measured across multiple rollout windows, then summarized by its median and 90th percentile. Performance is also compared with an M2+S2 harmonic baseline.

Method

A verifiable computation chain

01

Build the ground truth

Barotropic outputs from a 250 m CROCO model of the Brest roadstead over 90 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 full cycle

Rollouts cover a complete tidal period. The metric is aggregated across several windows rather than retaining only the best sequence.

04

Compare with a simple reference

An M2+S2 harmonic reconstruction acts as the baseline, testing whether the network adds more than elementary tidal periodicity.

Validation

What the comparisons show

The FNO beats the harmonic baseline

Median error reaches 17% over a full tidal cycle, against 29% for the M2+S2 reconstruction. Both are evaluated over the same domain and time horizon.

Dispersion remains a central result

The 90th percentile error reaches 42%. The model cannot therefore be summarized by its median alone: some rollout windows remain substantially less faithful.

Inference is measured, not the overall speed-up

One M2 period is inferred in 1.9 s on CPU. Because the reference CROCO runtime was not timed under the same protocol, no acceleration factor is claimed.

Validity domain

What this study does not claim

  • Current validation measures fidelity to CROCO, not yet agreement with independent in-situ observations.
  • A p90 of 42% means rollout dispersion must be monitored alongside median error.
  • 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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