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MHD_64.yaml

@@ -25,8 +25,19 @@ constant_field_names:
   2: []
 boundary_condition_types:
 - PERIODIC
-n_simulations: 10
-n_steps_per_simulation:
+n_files: 10
+n_trajectories_per_file:
+- 1
+- 1
+- 1
+- 1
+- 1
+- 1
+- 1
+- 1
+- 1
+- 1
+n_steps_per_trajectory:
 - 100
 - 100
 - 100

README.md

@@ -1,46 +1,10 @@
----
-language:
-- en
-license: cc-by-4.0
-tags:
-- physics
-
-task_categories:
-- time-series-forecasting
-- other
-task_ids:
-- multivariate-time-series-forecasting
----
-
-This Dataset is part of <a href="arxiv.org/abs/2412.00568">The Well Collection</a>.
-
-# 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.
+**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.
+**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)
 
@@ -49,27 +13,28 @@ for batch in dataloader:
 **Code or software used to generate the data**: Fortran + MPI.
 
 **Equation**:
+
 $$
-\begin{align}
-\frac{\partial \rho}{\partial t} + \nabla \cdot (\rho \mathbf{v}) &= 0 \nonumber\\
-\frac{\partial \rho \mathbf{v}}{\partial t} + \nabla \cdot (\rho \mathbf{v} \mathbf{v} - \mathbf{B} \mathbf{B}) + \nabla p &= 0 \nonumber\\
-\frac{\partial \mathbf{B}}{\partial t} - \nabla \times (\mathbf{v} \times \mathbf{B}) &= 0 \nonumber\\
-\end{align}
+\begin{align*}
+\frac{\partial \rho}{\partial t} + \nabla \cdot (\rho \mathbf{v}) &= 0 \\
+\frac{\partial \rho \mathbf{v}}{\partial t} + \nabla \cdot (\rho \mathbf{v} \mathbf{v} - \mathbf{B} \mathbf{B}) + \nabla p &= 0 \\
+\frac{\partial \mathbf{B}}{\partial t} - \nabla \times (\mathbf{v} \times \mathbf{B}) &= 0
+\end{align*}
 $$
 
-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.
+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|**0.1633**|
+| `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
+## About the data
 
-**Dimension of discretized data:** 100 timesteps of 64 \\(\times\\) 64 \\(\times\\) 64 cubes.
+**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).
 
@@ -83,17 +48,17 @@ Table: VRMSE metrics on test sets (lower is better). Best results are shown in b
 
 **Boundary conditions:** periodic boundary conditions.
 
-**Data are stored separated by ( \\(\Delta t\\)):** 0.01 (arbitrary units).
+**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\\).
+**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.
+**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}.
+**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 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).
 

data/stats.yaml

@@ -0,0 +1,20 @@
+mean:
+  density: 1.0015409125682395
+  magnetic_field:
+  - 0.533287413173605
+  - 8.496519008201078e-10
+  - 1.9938109340438524e-08
+  velocity:
+  - 0.0096151666910381
+  - 0.06783284226761686
+  - 0.01931474557406926
+std:
+  density: 0.8922789419164839
+  magnetic_field:
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+  - 0.31708956322212195
+  - 0.32008268824591013
+  velocity:
+  - 0.4851500418364637
+  - 0.43813973615708446
+  - 0.4785808622773084

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full_stats.yaml

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+mean:
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+mean_delta:
+  density: 1.9139367447387947e-06
+  magnetic_field:
+  - 9.954447885797118e-07
+  - -1.3963002451010604e-11
+  - 2.4057991715067304e-11
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+  - 5.5438619323951735e-05
+  - 0.00016727280948930295
+  - 6.947009005609897e-06
+rms:
+  density: 1.3413597242110717
+  magnetic_field:
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+  - 0.31708956322212195
+  - 0.3200826882459108
+  velocity:
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+  - 0.44335958644186657
+  - 0.47897045956372203
+rms_delta:
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stats.yaml

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 mean:
-  density: 1.0015E+00
+  density: 1.0015
   magnetic_field:
-  - 5.3329E-01
-  - 8.4965E-10
-  - 1.9938E-08
+  - 0.5333
+  - 0.0
+  - 0.0
   velocity:
-  - 9.6152E-03
-  - 6.7833E-02
-  - 1.9315E-02
+  - 0.0096
+  - 0.0678
+  - 0.0193
 mean_delta:
-  density: 1.9139E-06
+  density: 0.0
   magnetic_field:
-  - 9.9544E-07
-  - -1.3963E-11
-  - 2.4058E-11
+  - 0.0
+  - -0.0
+  - 0.0
   velocity:
-  - 5.5439E-05
-  - 1.6727E-04
-  - 6.9470E-06
+  - 0.0001
+  - 0.0002
+  - 0.0
 rms:
-  density: 1.3414E+00
+  density: 1.3414
   magnetic_field:
-  - 7.5093E-01
-  - 3.1709E-01
-  - 3.2008E-01
+  - 0.7509
+  - 0.3171
+  - 0.3201
   velocity:
-  - 4.8525E-01
-  - 4.4336E-01
-  - 4.7897E-01
+  - 0.4852
+  - 0.4434
+  - 0.479
 rms_delta:
-  density: 5.6639E-01
+  density: 0.5664
   magnetic_field:
-  - 1.4292E-01
-  - 1.4945E-01
-  - 1.4937E-01
+  - 0.1429
+  - 0.1495
+  - 0.1494
   velocity:
-  - 1.4390E-01
-  - 1.4259E-01
-  - 1.4304E-01
+  - 0.1439
+  - 0.1426
+  - 0.143
 std:
-  density: 8.9228E-01
+  density: 0.8923
   magnetic_field:
-  - 5.2867E-01
-  - 3.1709E-01
-  - 3.2008E-01
+  - 0.5287
+  - 0.3171
+  - 0.3201
   velocity:
-  - 4.8515E-01
-  - 4.3814E-01
-  - 4.7858E-01
+  - 0.4852
+  - 0.4381
+  - 0.4786
 std_delta:
-  density: 5.6639E-01
+  density: 0.5664
   magnetic_field:
-  - 1.4292E-01
-  - 1.4945E-01
-  - 1.4937E-01
+  - 0.1429
+  - 0.1495
+  - 0.1494
   velocity:
-  - 1.4390E-01
-  - 1.4259E-01
-  - 1.4304E-01
+  - 0.1439
+  - 0.1426
+  - 0.143