---
license: cc-by-4.0
pretty_name: "2-D Euler Conditional Forecasting"
tags:
  - physics
  - fluid-dynamics
  - probabilistic-forecasting
  - generative-models
viewer: false
---

# 2-D Euler Conditional Forecasting

This dataset contains conditional ensembles of trajectories from the two-dimensional incompressible Euler equations. 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 196 real-valued Fourier coefficients of vorticity, 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, 196) | Training ensembles |
| `vecs_new` | (720, 20, 41, 196) | Additional training ensembles |
| `vecs_eval` | (20, 100, 41, 196) | Validation and test ensembles |

The main experiments used only the 80 initial conditions in `vecs_train` (200 realizations each). The additional 720 conditions in `vecs_new` were not used in these experiments.

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 dataset contains 800 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 first 100 realizations of each reference ensemble are identical to the corresponding realizations in `vecs_eval`.

## Files and usage

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

Download using:

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

For the accompanying evaluation code, set `EULER_DATA` to `euler/data` and `EULER_TRUTH_BANK` to `euler/truth_bank`.

## License

Creative Commons Attribution 4.0 International (CC BY 4.0).