Flatvela Fwi Eval

---
name: flatvela-fwi-eval
description: Evaluates the ability of quantum and classical models to perform full-waveform inversion (FWI) by predicting subsurface velocity maps from scaled seismic waveform data. It probes the effectiveness of physics-guided data scaling and layer-wise variational quantum circuit designs in geophysical imaging tasks. Use when the user wants to benchmark on FlatVelA, or asks about evaluating this task. Reports SSIM.
metadata:
  skill_kind: dataset_eval
  source_arxiv: 2311.12333
  bibtex_key: jiang2023qugeo
  confidence: high
---

# flatvela-fwi-eval

> QuGeo: An End-to-end Quantum Learning Framework for Geoscience -- A Case Study on Full-Waveform Inversion — Jiang et al. (2023) (arXiv:2311.12333, 2023)

## What this evaluates

Evaluates the ability of quantum and classical models to perform full-waveform inversion (FWI) by predicting subsurface velocity maps from scaled seismic waveform data. It probes the effectiveness of physics-guided data scaling and layer-wise variational quantum circuit designs in geophysical imaging tasks.

## Datasets

- **FlatVelA** — total 500; splits: train (400), test (100)

## Metrics

- `SSIM` **(primary)** — range: [0, 1]
  - Structural Similarity Image Metric, measuring perceptual similarity between predicted and ground-truth velocity maps. Values closer to 1 indicate higher similarity.
- `MSE` — range: other
  - Mean Squared Error, calculating the average squared difference between predicted and true velocity values.

## Input / output format

**Input**: Scaled seismic waveform data (dimension 256) for inference; scaled seismic data and ground-truth 8x8 velocity maps for training.

**Output**: Predicted 8x8 velocity map.

## Scoring recipe

```python
For each of the 100 test samples:
  pred = model(input_seismic_data)
  ssim_val = compute_ssim(pred, ground_truth_velocity_map)
  mse_val = compute_mse(pred, ground_truth_velocity_map)
Return mean(ssim_val) and mean(mse_val) across the test set.
```

## Common pitfalls

- Naive downsampling (D-Sample) loses critical physical information, drastically degrading SSIM/MSE compared to physics-guided or CNN-based scaling.
- Models must be compared with matched parameter counts; quantum and classical baselines differ by only 40-60 parameters.
- Metrics are computed on the downsampled 8x8 velocity maps, not the original 70x70 resolution, so absolute error magnitudes are scale-dependent.

## Evidence (verbatim from paper)

> To support training, we split the FlatVelA dataset with 500 samples into a training set (size of 400) and a test set (size of 100). Figure 5(a) is a VQC model obtained in training, where the x-axis and y-axis stand for Structural Similarity Image Metric (SSIM) and Mean Squared Error (MSE), respectively.

## Citation

```bibtex
@misc{jiang2023qugeo,
  title={QuGeo: An End-to-end Quantum Learning Framework for Geoscience -- A Case Study on Full-Waveform Inversion},
  author={Jiang et al. (2023)},
  year={2023},
  note={arXiv:2311.12333}
}
```

- arXiv: 2311.12333