Dataset Viewer
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The dataset viewer is not available for this split.
Cannot load the dataset split (in streaming mode) to extract the first rows.
Error code:   StreamingRowsError
Exception:    CastError
Message:      Couldn't cast
batch: int64
state_shape: list<item: int64>
  child 0, item: int64
dtype: string
device: string
saved_steps: list<item: int64>
  child 0, item: int64
note: string
initial_step: int64
saved_for: string
num_samples: int64
dim: int64
dynamics_type: string
to
{'batch': Value('int64'), 'state_shape': List(Value('int64')), 'dtype': Value('string'), 'device': Value('string'), 'saved_steps': List(Value('int64')), 'dynamics_type': Value('string'), 'dim': Value('int64'), 'num_samples': Value('int64'), 'saved_for': Value('string'), 'initial_step': Value('int64')}
because column names don't match
Traceback:    Traceback (most recent call last):
                File "/src/services/worker/src/worker/utils.py", line 99, in get_rows_or_raise
                  return get_rows(
                         ^^^^^^^^^
                File "/src/libs/libcommon/src/libcommon/utils.py", line 272, in decorator
                  return func(*args, **kwargs)
                         ^^^^^^^^^^^^^^^^^^^^^
                File "/src/services/worker/src/worker/utils.py", line 77, in get_rows
                  rows_plus_one = list(itertools.islice(ds, rows_max_number + 1))
                                  ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
                File "/usr/local/lib/python3.12/site-packages/datasets/iterable_dataset.py", line 2690, in __iter__
                  for key, example in ex_iterable:
                                      ^^^^^^^^^^^
                File "/usr/local/lib/python3.12/site-packages/datasets/iterable_dataset.py", line 2227, in __iter__
                  for key, pa_table in self._iter_arrow():
                                       ^^^^^^^^^^^^^^^^^^
                File "/usr/local/lib/python3.12/site-packages/datasets/iterable_dataset.py", line 2251, in _iter_arrow
                  for key, pa_table in self.ex_iterable._iter_arrow():
                                       ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
                File "/usr/local/lib/python3.12/site-packages/datasets/iterable_dataset.py", line 494, in _iter_arrow
                  for key, pa_table in iterator:
                                       ^^^^^^^^
                File "/usr/local/lib/python3.12/site-packages/datasets/iterable_dataset.py", line 384, in _iter_arrow
                  for key, pa_table in self.generate_tables_fn(**gen_kwags):
                                       ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
                File "/usr/local/lib/python3.12/site-packages/datasets/packaged_modules/json/json.py", line 299, in _generate_tables
                  self._cast_table(pa_table, json_field_paths=json_field_paths),
                  ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
                File "/usr/local/lib/python3.12/site-packages/datasets/packaged_modules/json/json.py", line 128, in _cast_table
                  pa_table = table_cast(pa_table, self.info.features.arrow_schema)
                             ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
                File "/usr/local/lib/python3.12/site-packages/datasets/table.py", line 2321, in table_cast
                  return cast_table_to_schema(table, schema)
                         ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
                File "/usr/local/lib/python3.12/site-packages/datasets/table.py", line 2249, in cast_table_to_schema
                  raise CastError(
              datasets.table.CastError: Couldn't cast
              batch: int64
              state_shape: list<item: int64>
                child 0, item: int64
              dtype: string
              device: string
              saved_steps: list<item: int64>
                child 0, item: int64
              note: string
              initial_step: int64
              saved_for: string
              num_samples: int64
              dim: int64
              dynamics_type: string
              to
              {'batch': Value('int64'), 'state_shape': List(Value('int64')), 'dtype': Value('string'), 'device': Value('string'), 'saved_steps': List(Value('int64')), 'dynamics_type': Value('string'), 'dim': Value('int64'), 'num_samples': Value('int64'), 'saved_for': Value('string'), 'initial_step': Value('int64')}
              because column names don't match

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1. Kolmogorov Flow Dataset

Pre-generated Kolmogorov flow simulation datasets.

Datasets are indexed by:

  • spatial resolution (dim)
  • number of samples (num_samples)
  • initial timestep (step)

The simulator implementation follows the MASF project: https://github.com/tcnllab-oss/masf

The Kolmogorov dynamics implementation is adapted from: https://github.com/francois-rozet/sda


2. Dataset Structure

Repository layout:

dim{DIM}/
└── num_samples{N}/
    ├── meta.json
    └── step_XXXXXX.pt

Example:

dim64/
└── num_samples1000/
    ├── meta.json
    └── step_000050.pt

3. Loading Data

This loads the prior state at step, num_samples samples on a dim × dim spatial grid.

3.1. Option 1 — MASF API

Parameter Description
dim spatial grid resolution
num_samples number of generated samples
step simulation timestep
from dynamics import kolmogorov_flow

x = kolmogorov_flow(
    dim=64,
    num_samples=1000,
    step=50,
)

# x.shape = [num_samples, 2, dim, dim]

The API automatically:

  • checks the Hugging Face dataset repository
  • downloads existing datasets
  • generates missing configurations when unavailable

3.2. Option 2 — Direct Hugging Face Download

Without using the MASF API.

Available configurations:

  • dim ∈ {64, 128, 256, 512}
  • num_samples ∈ {10, 100}
  • step ∈ {50}
from huggingface_hub import hf_hub_download
import torch

dim = 64
num_samples = 10
step = 50

filename = (
    f"dim{dim}/"
    f"num_samples{num_samples}/"
    f"step_{step:06d}.pt"
)

path = hf_hub_download(
    repo_id="eunbii1/Kolmogorov_flow",
    repo_type="dataset",
    filename=filename,
)

x = torch.load(path)

# print(x.keys()) = ["step","state"]
# x["state"].shape = [num_samples, 2, dim, dim]

4. File Description

4.1. step_XXXXXX.pt

PyTorch serialized tensor containing simulation states.

Example:

import torch

x = torch.load("step_000050.pt")

4.2. meta.json

Metadata associated with a dataset configuration.

Example:

{"dim": 64, "num_samples": 1000, "step": 50}

5. Reference

Implementation adapted from:

@inproceedings{rozet2023sda,
  title={Score-based Data Assimilation},
  author={Fran{\c{c}}ois Rozet and Gilles Louppe},
  booktitle={Thirty-seventh Conference on Neural Information Processing Systems},
  year={2023},
  url={https://openreview.net/forum?id=VUvLSnMZdX},
}

MASF project:

@article{yoon2026masf,
  title={Rethinking Forward Processes for Score-Based Nonlinear Data Assimilation in High Dimensions},
  author={Yoon, Eunbi and Chang, Won and Kim, Donghan and Kim, Dae Wook},
  journal={arXiv preprint},
  year={2026}
}
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