Four Gyre Rom Eval

four-gyre-rom-eval

Extreme learning machine for reduced order modeling of turbulent geophysical flows — San et al. (2018) (arXiv:1803.00222, 2018)

What this evaluates

Evaluates the ability of a machine learning closure model to stabilize reduced-order models for turbulent geophysical fluid dynamics. Specifically, it probes whether an extreme learning machine can predict mode-dependent eddy viscosities to maintain long-time integration accuracy and statistical steady-state behavior in coarse-grained ocean circulation simulations.

Datasets

• Four-gyre barotropic circulation problem — total ?; splits: train (900), test (-1)

Metrics

• L2-norm error (primary) — range: other
  • L2-norm of the difference between the ROM-predicted mean vorticity or streamfunction fields and the Full Order Model (FOM) reference fields over the assessment window.

Input / output format

Input: Time-series snapshots of the barotropic vorticity equation (BVE) at Re=450, Ro=3.6e-3, used to construct POD basis and train the ELM closure.

Output: Predicted mode-dependent eddy viscosities and the resulting ROM state variables (mean vorticity and streamfunction fields) over the integration window.

Scoring recipe

def compute_l2_error(rom_pred, fom_ref):
    # rom_pred, fom_ref: arrays of mean vorticity or streamfunction fields
    return np.linalg.norm(rom_pred - fom_ref)

Common pitfalls

• The FOM baseline uses a very small time step (Δt=2.5e-5) for stability, so CPU time comparisons heavily favor the stabilized ROM without normalization.
• Out-of-sample testing uses different physical parameters (Re=200, Ro=1.6e-3) than training, which tests generalization but requires separate L2 error reporting.
• The metric is computed on mean fields over a steady-state window, not instantaneous snapshots, which masks short-term transient errors.

Evidence (verbatim from paper)

Table 1: L2-norm errors of the reduced order models (with respect to FOM) for the mean vorticity and streamfunction fields. Note that the ROM-ANN retains only M=10 modes.

Citation

@misc{san2018extreme,
  title={Extreme learning machine for reduced order modeling of turbulent geophysical flows},
  author={San et al. (2018)},
  year={2018},
  note={arXiv:1803.00222}
}

• arXiv: 1803.00222