Red Diffeq Fwi Eval

---
name: red-diffeq-fwi-eval
description: Evaluates the ability of a diffusion-based regularization framework to reconstruct high-resolution subsurface velocity models from seismic data. It probes robustness under varying data conditions, including clean recordings, Gaussian noise contamination, and missing traces. The benchmark also tests out-of-distribution generalization on complex geological structures. Use when the user wants to benchmark on OpenFWI, Marmousi, or asks about evaluating this task. Reports RMSE.
metadata:
  skill_kind: dataset_eval
  source_arxiv: 2509.21659
  bibtex_key: shan2025reddiffeq
  confidence: high
---

# red-diffeq-fwi-eval

> RED-DiffEq: Regularization by denoising diffusion models for solving inverse PDE problems with application to full waveform inversion — Shan et al. (2025) (arXiv:2509.21659, 2025)

## What this evaluates

Evaluates the ability of a diffusion-based regularization framework to reconstruct high-resolution subsurface velocity models from seismic data. It probes robustness under varying data conditions, including clean recordings, Gaussian noise contamination, and missing traces. The benchmark also tests out-of-distribution generalization on complex geological structures.

## Datasets

- **OpenFWI** — total 400; splits: test (400)
- **Marmousi** — total ?; splits: test (-1)

## Metrics

- `RMSE` **(primary)** — range: other
  - Root Mean Squared Error: square root of the average of squared differences between predicted and ground truth velocity values.
- `MAE` — range: other
  - Mean Absolute Error: average of absolute differences between predicted and ground truth velocity values.
- `SSIM` — range: [0, 1]
  - Structural Similarity Index: measures perceived change in structural information, luminance, and contrast between two images.

## Input / output format

**Input**: Seismic wavefield data (potentially noisy or with missing traces) and an initial velocity model (ground truth filtered with a Gaussian kernel).

**Output**: Reconstructed subsurface velocity model grid.

## Scoring recipe

```python
def compute_metrics(pred, gt):
    rmse = np.sqrt(np.mean((pred - gt) ** 2))
    mae = np.mean(np.abs(pred - gt))
    ssim = compute_ssim(pred, gt)
    return {'rmse': rmse, 'mae': mae, 'ssim': ssim}

# Average metrics across all test cases (e.g., 400 samples from OpenFWI families)
```

## Common pitfalls

- Initialization sensitivity: Results heavily depend on the initial velocity model (Gaussian filtered ground truth with specific sigma), which is often not disclosed in other FWI papers.
- Metric vs. Qualitative trade-off: Numerical metrics (RMSE/MAE) may not capture geological interpretability, especially in missing trace scenarios where metrics stay stable but visual fidelity degrades.

## Evidence (verbatim from paper)

> We first evaluated various methods on clean seismic data using 100 previously unseen samples from each of the four chosen geological families in the OpenFWI dataset, and all the quantitative metrics are the average of these 400 test cases. The convergence analysis (Fig.[4]b, top row) reveals that RED-DiffEq consistently achieves the lowest RMSE and MAE, and highest SSIM throughout the optimization process.

## Citation

```bibtex
@misc{shan2025reddiffeq,
  title={RED-DiffEq: Regularization by denoising diffusion models for solving inverse PDE problems with application to full waveform inversion},
  author={Shan et al. (2025)},
  year={2025},
  note={arXiv:2509.21659}
}
```

- arXiv: 2509.21659