Physics Simulation · polymathic-ai
MHD_64
A 3D compressible magnetohydrodynamics turbulence dataset at 64³ resolution for neural operator benchmarking.
What MHD_64 is
MHD_64 is a dataset of three-dimensional compressible magnetohydrodynamic (MHD) turbulence simulations published by polymathic-ai and developed with domain expertise from Blakesley Burkhart. It models isothermal fluid flows without self-gravity, capturing turbulent physical dynamics that occur in environments such as the diffuse interstellar medium, the solar wind, and galaxy formation.
The dataset is designed to train and benchmark physics-informed machine learning models, including neural operators. It covers compressible MHD flow across multiple physical regimes, spanning subsonic, supersonic, sub-Alfvénic, and super-Alfvénic turbulence.
How it was made
The underlying simulations solve the compressible, isothermal magnetohydrodynamic equations for mass continuity, momentum conservation, and magnetic induction using Fortran and MPI. The computational setup uses a uniform Cartesian grid with periodic boundary conditions and uniform initial conditions.
Simulations were initially run at a higher spatial resolution of 256³ and subsequently downsampled to 64³ cubes using an ideal low-pass filter to prevent aliasing. The complete dataset contains 100 trajectories, formed by combining 10 initial conditions with 10 pairs of sonic Mach numbers (0.5, 0.7, 1.5, 2.0, 7.0) and Alfvénic Mach numbers (0.7, 2.0). Each trajectory is recorded over 100 timesteps from t = 0 to t = 1 at uniform intervals of Δt = 0.01.
Key facts
- Domain expert
- Blakesley Burkhart (CCA, Flatiron Institute & Rutgers University)
- Spatial resolution
- 64 × 64 × 64
- Temporal resolution
- 100 timesteps (t = 0 to 1, Δt = 0.01)
- Ensemble size
- 71.6 GB (100 trajectories)
- Fields
- Density (scalar), velocity (3D vector), magnetic field (3D vector)
- Grid type
- Uniform Cartesian grid
- Boundary conditions
- Periodic
- Simulation software
- Fortran + MPI
What you can use it for
- Neural operator benchmarking
- Test and compare deep learning architectures, such as Fourier Neural Operators and U-Nets, on predicting non-linear plasma dynamics.
- Astrophysical plasma research
- Analyse compressible magnetohydrodynamic flow regimes representing diffuse interstellar medium environments.
- Surrogate simulator evaluation
- Assess generative or surrogate physical models against target data using power spectra and two-point correlation functions.
Explore the data
No licence declared
The authors have not published a licence, which means no permission to redistribute the data has been granted to anyone. The rows are not served here; read them on the original dataset page.Strengths and limits
Good at
- Spans diverse turbulent regimes across combinations of subsonic, supersonic, sub-Alfvénic, and super-Alfvénic parameters.
- Provides complete physical states including scalar density, vector velocity, and vector magnetic field components.
- Applies an ideal low-pass anti-aliasing filter during downsampling from the original 256³ simulation to preserve spectral accuracy.
Watch out for
- Does not include self-gravity or non-isothermal equations of state.
- Coarsened to 64³ resolution, omitting sub-grid turbulence details present in the 256³ parent simulation.
Questions
Can I look inside MHD_64 without downloading it?
Not here: it declares no licence, so no permission to redistribute its rows has been granted. Its description and statistics are still shown.
What licence is MHD_64 under?
Its authors have not declared a licence, which means no permission to reuse or redistribute it has been granted.
What equations are solved in the simulation?
The data is generated from the isothermal compressible magnetohydrodynamics equations, covering the continuity equation for density, the momentum equation including magnetic and gas pressure forces, and the induction equation for the magnetic field.
What parameters vary across the trajectories?
The 100 trajectories cover 10 initial conditions across all 10 combinations of sonic Mach numbers (0.5, 0.7, 1.5, 2.0, 7.0) and Alfvénic Mach numbers (0.7, 2.0).
How have standard baseline models performed on this dataset?
In baseline tests evaluated by VRMSE, CNextU-net achieved an error of 0.1633, U-Net scored 0.1798, FNO reached 0.3605, and TFNO scored 3561.
How should new models trained on this data be evaluated?
New models can be evaluated using physical diagnostic metrics such as power spectra and two-point correlation functions.
How to cite it
Burkhart, B., Appel, S. M., Bialy, S., Cho, J., Christensen, A. J., Collins, D., Federrath, C., Fielding, D. B., Finkbeiner, D., Hill, A. S., et al. (2020). The catalogue for astrophysical turbulence simulations (cats). The Astrophysical Journal, 905(1), 14.
Written from MHD_64's own dataset card. Statements citing a figure that does not appear there are removed before publication. Licence and running details come from our registry.