H Sinn Turbulence Eval

h-sinn-turbulence-eval

Low-dimensional representation of intermittent geophysical turbulence with High-Order Statistics-informed Neural Networks (H-SiNN) — Foldes et al. (2023) (arXiv:2310.04186, 2023)

What this evaluates

Evaluates a Convolutional Autoencoder's ability to compress and reconstruct geophysical turbulence fields while preserving high-order statistical moments. It specifically probes the model's capacity to capture non-Gaussian, intermittent structures like extreme vertical drafts without degrading point-wise accuracy.

Datasets

• Stratified turbulence simulation data — total 51200; splits: train (35840), test (15360)

Metrics

• MAPE on kurtosis ($K_w$) (primary) — range: percent
  • Defined as $|(K_w^r - K_w^o)/K_w^o| \times 100$, where $K_w^o$ and $K_w^r$ are the kurtosis of the original and reconstructed vertical velocity fields, respectively. Averages the absolute relative error over the test set.
• MSE — range: [0, 1]
  • Standard Mean Squared Error between original and reconstructed field values.
• $K_w$ error — range: other
  • Absolute error in the fourth-order moment (kurtosis) of the vertical velocity field.

Input / output format

Input: 2D spatial planes of 4 physical variables ($u, v, w, \theta$) on a $512 \times 512$ grid, processed independently per plane.

Output: Reconstructed 2D planes of the same 4 variables and grid dimensions.

Scoring recipe

def compute_mape_kurtosis(original_field, reconstructed_field):
    k_orig = compute_kurtosis(original_field['w'])
    k_recon = compute_kurtosis(reconstructed_field['w'])
    # MAPE formula from paper
    mape = np.mean(np.abs((k_recon - k_orig) / k_orig)) * 100
    return mape

Common pitfalls

• The model is trained plane-by-plane independently, so it does not capture temporal or vertical ($z$-direction) correlations.
• Higher compression factors (CF) inherently lead to larger reconstruction errors across all statistical moments, independent of the loss function.
• Kurtosis error is naturally larger and more variable than lower-order moments due to the intermittent nature of extreme events.

Evidence (verbatim from paper)

We divide the data set in training and test set on a temporal basis, taking the first 70% snapshots for the training phase and the remaining 30% for testing the performance. ... The MAPE is defined as $\mathrm{MAPE}^{(i)}{K{w}}=|(K_{w}^{r,(i)}-K_{w}^{o})/K_{w}^{o}|\times 100$ with $K_{w}^{o}$ and $K_{w}^{r,(i)}$ being the kurtosis of the original and reconstructed fields, respectively.

Citation

@misc{foldes2023hsinn,
  title={Low-dimensional representation of intermittent geophysical turbulence with High-Order Statistics-informed Neural Networks (H-SiNN)},
  author={Foldes et al. (2023)},
  year={2023},
  note={arXiv:2310.04186}
}

• arXiv: 2310.04186