Seismic Response Eval

---
name: seismic-response-eval
description: Evaluates a neural operator's ability to map high-frequency seismic wave excitations to building displacement responses across multiple floors. It specifically probes the model's capacity to capture oscillatory function spaces and handle amplitude-frequency disparities between different structural floors. Use when the user wants to benchmark on Custom seismic building response dataset, or asks about evaluating this task. Reports mean relative L2 error.
metadata:
  skill_kind: dataset_eval
  source_arxiv: 2111.04860
  bibtex_key: [REDACTED]
  confidence: medium
---

# seismic-response-eval

> Multiscale DeepONet for Nonlinear Operators in Oscillatory Function Spaces for Building Seismic Wave Responses — Liu et al. (2021) (arXiv:2111.04860, 2021)

## What this evaluates

Evaluates a neural operator's ability to map high-frequency seismic wave excitations to building displacement responses across multiple floors. It specifically probes the model's capacity to capture oscillatory function spaces and handle amplitude-frequency disparities between different structural floors.

## Datasets

- **Custom seismic building response dataset** — total ?; splits: train (-1), test (-1)

## Metrics

- `mean relative L2 error` **(primary)** — range: other
  - Computed as the mean over test cases of the relative L2 norm: (1/N) * Σ ||x_pred - x_true||_2 / ||x_true||_2.

## Input / output format

**Input**: Seismic wave excitation time series [P(t_1), ..., P(t_m)] and time points t.

**Output**: Building displacement response x(t) as a time series or array.

## Scoring recipe

```python
relative_l2 = np.linalg.norm(y_pred - y_true, axis=-1) / np.linalg.norm(y_true, axis=-1)
mean_relative_l2 = np.mean(relative_l2)
return mean_relative_l2
```

## Common pitfalls

- Requires MSE loss to reach O(10^-6) to capture high-frequency oscillations satisfactorily.
- Trunk net must use multiscale architecture to handle high frequencies; standard fully connected trunk nets fail to capture them.
- Amplitude separation across floors is necessary to handle the disparity between high-frequency/small-amplitude (lower floors) and low-frequency/large-amplitude (higher floors) responses.

## Evidence (verbatim from paper)

> The mean relative L2 error for testing cases at last is 0.13. ... We could conclude that the amplitude separation idea indeed have some contributions even though the data augmentation is also applied during training procedure of multiscale DeepONet without amplitude separation.

## Citation

```bibtex
@misc{liu2021multiscaledeeponet,
  title={Multiscale DeepONet for Nonlinear Operators in Oscillatory Function Spaces for Building Seismic Wave Responses},
  author={Liu et al. (2021)},
  year={2021},
  note={arXiv:2111.04860}
}
```

- arXiv: 2111.04860