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.gitattributes

@@ -56,3 +56,34 @@ saved_model/**/* filter=lfs diff=lfs merge=lfs -text
 # Video files - compressed
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MHD_64.yaml

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+dataset_name: MHD_64
+n_spatial_dims: 3
+spatial_resolution:
+- 64
+- 64
+- 64
+scalar_names: []
+constant_scalar_names:
+- Ma
+- Ms
+field_names:
+  0:
+  - density
+  1:
+  - magnetic_field_x
+  - magnetic_field_y
+  - magnetic_field_z
+  - velocity_x
+  - velocity_y
+  - velocity_z
+  2: []
+constant_field_names:
+  0: []
+  1: []
+  2: []
+boundary_condition_types:
+- PERIODIC
+n_simulations: 10
+n_steps_per_simulation:
+- 100
+- 100
+- 100
+- 100
+- 100
+- 100
+- 100
+- 100
+- 100
+- 100
+grid_type: cartesian

README.md

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+---
+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:
+
+```python
+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\\) for `MHD_256` and \\(64^3\\) for `MHD_64`. The data was first generated at \\(256^3\\) and then downsampled to \\(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\\) and then downsampled to \\(64^3\\) after anti-aliasing with an ideal low-pass filter. This dataset is the downsampled version.
+
+**Associated paper**: [Paper](https://iopscience.iop.org/article/10.3847/1538-4357/abc484/pdf)
+
+**Domain expert**: [Blakesley Burkhart](https://www.bburkhart.com/), CCA, Flatiron Institute & Rutgers University.
+
+**Code or software used to generate the data**: Fortran + MPI.
+
+**Equation**:
+```math
+\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\\) is the density, \\(\mathbf{v}\\) is the velocity, \\(\mathbf{B}\\) is the magnetic field, \\(\mathbf{I}\\) the identity matrix and \\(p\\) is the gas pressure.
+
+![Gif](https://users.flatironinstitute.org/~polymathic/data/the_well/datasets/MHD_64/gif/density_unnormalized.gif)
+
+| 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\\) 64 \\(\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\_{max}\\)):** \\(t\_{min} = 0\\), \\(t\_{max} = 1\\).
+
+**Spatial domain size (\\(L_x\\), \\(L_y\\), \\(L_z\\)):** dimensionless so 64 pixels.
+
+**Set of coefficients or non-dimensional parameters evaluated:** all combinations of \\(\mathcal{M}_s=\\){0.5, 0.7, 1.5, 2.0 7.0} and \\(\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}
+}
+```

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stats.yaml

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+mean:
+  density: 0.9653607914644455
+  magnetic_field:
+  - 0.5146667018354735
+  - 8.502926743613606e-10
+  - 1.9217535158110976e-08
+std:
+  density: 0.8951430295818846
+  magnetic_field:
+  - 0.5285708137815139
+  - 0.31148932676110025
+  - 0.3143722294873327