Shock Caps (shock-caps)

One line description of the data: 500 shallow-water simulations on the sphere initialized with random spherical caps.

Longer description of the data: Shock Caps solves the rotation-free shallow-water equations on the unit sphere. Each simulation starts from randomly placed geodesic caps with piecewise-constant fluid depth and horizontal velocity, surrounded by a similarly randomized background state. Discontinuities at cap boundaries produce expanding bores, multi-shock collisions, and antipodal convergence as fronts propagate around the sphere. We vary the number of caps $KK$ and the initial velocity scaling $\delta \backslash delta$. Depth jumps are independent of $\delta \backslash delta$, so pressure imbalances drive shock dynamics even when the initial velocities vanish. The dataset captures interactions between discontinuities on a curved, closed domain, with cap boundaries that are not aligned with the computational grid.

Code or software used to generate the data: Clawpack/PyClaw, using the riemann.shallow_sphere_2D Riemann kernel and the classic2_sw_sphere Fortran time-step module. The solver uses high-resolution finite-volume wave propagation with an MC limiter and transverse-wave corrections.

Visualization:

About the data

Dimension of discretized data: 101 snapshots per trajectory (1.5 non-dimensional time units, sampled every 0.015) on a $256\times 512256\; \backslash times\; 512$ (lat × lon) grid.

Fields available in the data:

HDF5 path	Shape	Units	Description
t0_fields/height	(1, 101, 256, 512)	dimensionless	Fluid depth $hh$
t1_fields/momentum	(1, 101, 256, 512, 2)	dimensionless	Depth-integrated momentum; last axis is [hu, hv] (eastward, northward)
scalars/{K, delta, seed}	()	—	Run parameters (stored as floats)
dimensions/{time, lat, lon}	(101,), (256,), (512,)	—, °, °	Coordinates

All fields are stored as float32; the time coordinate is stored as float64. Cartesian momentum components are remapped to the output grid before projection onto its local east/north basis.

Number of trajectories: 500: $5\times 55\; \backslash times\; 5$ parameter combinations, each with 20 seeds. 400/50/50 train/validation/test split in data/{train,valid,test}/, stratified jointly on $(K,\delta )(K,\; \backslash delta)$.

Estimated size of the ensemble of all simulations: 63 GB (gzip-compressed HDF5).

Storage format: One HDF5 file per run, chunked as (1, 7, 32, 64) in (trajectory, time, lat, lon). Normalization statistics computed on the train split are in stats.yaml.

Grid type: $256\times 512256\; \backslash times\; 512$ equiangular, pole-excluding latitude–longitude grid.

Initial conditions: $KK$ geodesic caps with centers drawn uniformly on the sphere and angular radii drawn uniformly from $[0.3,1.0][0.3,\; 1.0]$ rad. Each cap and the background receive independently sampled primitive states with $h\in [0.5,2.0]h\; \backslash in\; [0.5,\; 2.0]$ and $u,v\in [-0.5\delta ,0.5\delta ]u,\; v\; \backslash in\; [-0.5\backslash delta,\; 0.5\backslash delta]$, all sampled uniformly. Higher-index caps overwrite lower-index caps where they overlap. Initial conditions use $4\times 44\; \backslash times\; 4$ sub-cell sampling to reduce staircase artifacts at cap boundaries.

Boundary conditions: Spherical.

Simulation time-step $(\mathrm{\Delta }t)(\backslash Delta\; t)$: Adaptive, controlled internally by Clawpack with a target CFL of 0.45 and a maximum permitted CFL of 0.9.

Data are stored separated by $(\delta t)(\backslash delta\; t)$: 0.015 non-dimensional time units.

Total time range $(t_{\text{min}}(t\_\backslash textup\{min\}$ to $t_{\text{max}})t\_\backslash textup\{max\})$: $00$ to $1.51.5$, including the initial condition.

Set of coefficients or non-dimensional parameters evaluated:

• K $\in \{1,2,4,8,16\}\backslash in\; \backslash \{1,\; 2,\; 4,\; 8,\; 16\backslash \}$, the number of spherical caps
• delta $=\delta \in \{0.0,0.25,0.5,0.75,1.0\}=\; \backslash delta\; \backslash in\; \backslash \{0.0,\; 0.25,\; 0.5,\; 0.75,\; 1.0\backslash \}$, the initial velocity scaling; depth jumps are not scaled
• seed $\in \{0,\dots ,19\}\backslash in\; \backslash \{0,\; \backslash ldots,\; 19\backslash \}$, determining cap centers, radii, cap states, and the background state

The sphere radius is fixed at $R=1R\; =\; 1$ and gravitational acceleration at $g=9.80616g\; =\; 9.80616$, both non-dimensional. No Coriolis term is included.

Approximate time to generate the data: Approximately 20 minutes per run.

Hardware used to generate the data: One sciCORE compute node at the University of Basel per run, using OpenMP-parallel Clawpack with 16 threads.

Loading

Download a single run (≈125 MB) and read it with h5py:

import h5py
from huggingface_hub import hf_hub_download

path = hf_hub_download("sada-group/shock-caps", "data/test/run_0008.h5", repo_type="dataset")
with h5py.File(path, "r") as f:
    h = f["t0_fields/height"][0]                          # (101, 256, 512)
    hu, hv = f["t1_fields/momentum"][0].transpose(3, 0, 1, 2)
    params = {k: f["scalars"][k][()] for k in f["scalars"]}

To download a whole split (or the full 63 GB dataset), use snapshot_download with allow_patterns:

from huggingface_hub import snapshot_download

root = snapshot_download(
    "sada-group/shock-caps",
    repo_type="dataset",
    allow_patterns=["data/test/*", "stats.*"],  # drop allow_patterns for everything
)

Please cite the associated paper if you use this data in your research:

@misc{muser2026dandelionsphericalflowerneural,
      title={Dandelion: A Spherical Flower for Neural Simulation of Planetary Dynamics},
      author={Till Muser and Giovanni Abati and Ivan Dokmanić},
      year={2026},
      eprint={2608.27521},
      archivePrefix={arXiv},
      primaryClass={cs.LG},
      url={https://arxiv.org/abs/2608.27521},
}

as well as the solver and the spherical finite-volume method:

@article{mandli2016clawpack,
  title={Clawpack: building an open source ecosystem for solving hyperbolic PDEs},
  author={Mandli, Kyle T and Ahmadia, Aron J and Berger, Marsha and Calhoun, Donna and George, David L and Hadjimichael, Yiannis and Ketcheson, David I and Lemoine, Grady I and LeVeque, Randall J},
  journal={PeerJ Computer Science},
  volume={2},
  pages={e68},
  year={2016},
  publisher={PeerJ Inc.}
}

@article{calhoun2008logically,
  title={Logically rectangular grids and finite volume methods for {PDE}s in circular and spherical domains},
  author={Calhoun, Donna A and Helzel, Christiane and LeVeque, Randall J},
  journal={SIAM Review},
  volume={50},
  number={4},
  pages={723--752},
  year={2008},
  publisher={SIAM}
}