README.md

metadata

language:
  - en
license: cc-by-4.0
tags:
  - physics
task_categories:
  - time-series-forecasting
  - other
task_ids:
  - multivariate-time-series-forecasting

How To Load from HuggingFace Hub

1. Be sure to have the_well installed (pip install the_well)
2. Use the WellDataModule to retrieve data as follows:

from the_well.benchmark.data import WellDataModule

# The following line may take a couple of minutes to instantiate the datamodule
datamodule = WellDataModule(
    "hf://datasets/polymathic-ai/",
    "MHD_64",
)
train_dataloader = datamodule.train_dataloader()

for batch in dataloader:
    # Process training batch
    ...

Magnetohydrodynamics (MHD) compressible turbulence

NOTE: This dataset is available in two different resolutions $256^{3}256^3$ for MHD_256 and $64^{3}64^3$ for MHD_64. The data was first generated at $256^{3}256^3$ and then downsampled to $64^{3}64^3$ after anti-aliasing with an ideal low-pass filter. The data is available in both resolutions.

One line description of the data: This is an MHD fluid flows in the compressible limit (subsonic, supersonic, sub-Alfvenic, super-Alfvenic).

Longer description of the data: An essential component of the solar wind, galaxy formation, and of interstellar medium (ISM) dynamics is magnetohydrodynamic (MHD) turbulence. This dataset consists of isothermal MHD simulations without self-gravity (such as found in the diffuse ISM) initially generated with resolution $256^{3}256^3$ and then downsampled to $64^{3}64^3$ after anti-aliasing with an ideal low-pass filter. This dataset is the downsampled version.

Associated paper: Paper

Domain expert: Blakesley Burkhart, CCA, Flatiron Institute & Rutgers University.

Code or software used to generate the data: Fortran + MPI.

Equation:

\begin{align}
\frac{\partial \rho}{\partial t} + \nabla \cdot (\rho \mathbf{v}) &= 0 \nonumber\\
\frac{\partial \rho \mathbf{v}}{\partial t} + \nabla \cdot (\rho \mathbf{v} \mathbf{v} - \mathbf{B} \mathbf{B}) + \nabla p &= 0 \nonumber\\
\frac{\partial \mathbf{B}}{\partial t} - \nabla \times (\mathbf{v} \times \mathbf{B}) &= 0 \nonumber\\
\end{align}

where $\rho \backslash rho$ is the density, $\mathbf{v}\backslash mathbf\{v\}$ is the velocity, $\mathbf{B}\backslash mathbf\{B\}$ is the magnetic field, $\mathbf{I}\backslash mathbf\{I\}$ the identity matrix and $pp$ is the gas pressure.

Dataset	FNO	TFNO	Unet	CNextU-net
MHD_64	0.3605	3561	0.1798	\(\mathbf{0.1633}\)

Table: VRMSE metrics on test sets (lower is better). Best results are shown in bold. VRMSE is scaled such that predicting the mean value of the target field results in a score of 1.

About the data

Dimension of discretized data: 100 timesteps of 64 $\times \backslash times$ 64 $\times \backslash times$ 64 cubes.

Fields available in the data: Density (scalar field), velocity (vector field), magnetic field (vector field).

Number of trajectories: 10 Initial conditions x 10 combination of parameters = 100 trajectories.

Estimated size of the ensemble of all simulations: 71.6 GB.

Grid type: uniform grid, cartesian coordinates.

Initial conditions: uniform IC.

Boundary conditions: periodic boundary conditions.

Data are stored separated by (\(\Delta t\)): 0.01 (arbitrary units).

Total time range (\(t_{min}\) to $t\mathrm{\_}maxt\backslash \_\{max\}$): $t\mathrm{\_}min=0t\backslash \_\{min\}\; =\; 0$, $t\mathrm{\_}max=1t\backslash \_\{max\}\; =\; 1$.

Spatial domain size (\(L_x\), $L_{y}L\_y$, $L_{z}L\_z$): dimensionless so 64 pixels.

Set of coefficients or non-dimensional parameters evaluated: all combinations of ${\mathcal{M}}_s=\backslash mathcal\{M\}\_s=${0.5, 0.7, 1.5, 2.0 7.0} and ${\mathcal{M}}_A=\backslash mathcal\{M\}\_A\; =${0.7, 2.0}.

Approximate time and hardware used to generate the data: Downsampled from MHD_256 after applying ideal low-pass filter.

What is interesting and challenging about the data:

What phenomena of physical interest are catpured in the data: MHD fluid flows in the compressible limit (sub and super sonic, sub and super Alfvenic).

How to evaluate a new simulator operating in this space: Check metrics such as Power spectrum, two-points correlation function.

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

@article{burkhart2020catalogue,
  title={The catalogue for astrophysical turbulence simulations (cats)},
  author={Burkhart, B and Appel, SM and Bialy, S and Cho, J and Christensen, AJ and Collins, D and Federrath, Christoph and Fielding, DB and Finkbeiner, D and Hill, AS and others},
  journal={The Astrophysical Journal},
  volume={905},
  number={1},
  pages={14},
  year={2020},
  publisher={IOP Publishing}
}