---
license: cc-by-4.0
pretty_name: "Heterogeneous Waves Conditional Forecasting"
tags:
  - physics
  - wave-equation
  - probabilistic-forecasting
  - generative-models
viewer: false
---

# Heterogeneous Waves Conditional Forecasting

This dataset contains conditional ensembles of trajectories from a linear wave equation in a heterogeneous medium. Each ensemble shares the same observed coarse initial state but differs in its hidden fine-scale initial conditions, producing multiple possible future trajectories.

The dataset accompanies an anonymous research submission.

## Dataset

The observed state consists of 392 real-valued Fourier coefficients: 196 of the displacement \(u\), followed by 196 of the finite-difference velocity, recorded at 41 time points between \(t=0\) and \(t=1\).

The main file, `data/trajectories_fine.npz`, contains:

| Array | Shape | Description |
|---|---|---|
| `vecs_train` | (80, 200, 41, 392) | Training ensembles |
| `vecs_eval` | (10, 200, 41, 392) | Validation ensembles |

The main experiments used the 80 initial conditions in `vecs_train` (200 realizations each).

The file also contains group identifiers and time coordinates. All trajectory arrays are stored in float64.

Train, validation, and test conditions are specified in `data/split.json` and are disjoint. The released data contain 80 training, 10 validation, and 10 test conditions.

## Test reference ensembles

`truth_bank/` contains 10,000 reference trajectories for each of the 10 test conditions. These are used to evaluate the predicted conditional distributions.

The test conditions are stored only in `truth_bank/`; their shared initial state is the first time point of any of their trajectories. The reference trajectories are stored in float32.

## Files and usage

- `data/trajectories_fine.npz` — coarse trajectories
- `data/split.json` — group-level data splits
- `data/normalization.npz` — training-derived normalization parameters
- `data/u_norm/normalization.npz`, `data/v_norm/normalization.npz` — displacement and velocity normalization
- `truth_bank/group_<gid>.npz` — test reference ensembles
- `SHA256SUMS` — file checksums

Download using:

```bash
hf download coarse-grained-forecasting-benchmark/het-waves --repo-type dataset --local-dir het-waves
```

For the accompanying evaluation code, set `WAVES_DATA` to `het-waves/data` and `WAVES_TRUTH_BANK` to `het-waves/truth_bank`.

## License

Creative Commons Attribution 4.0 International (CC BY 4.0).