Physics Simulation · polymathic-ai
rayleigh_benard
A 2D thermal convection simulation dataset for benchmarking surrogate models across varying flow regimes.
What rayleigh_benard is
The rayleigh_benard dataset is a collection of two-dimensional thermal convection simulations designed to benchmark machine learning models on non-linear fluid dynamics and heat transfer. Generated by Rudy Morel at the Flatiron Institute's Center for Computational Mathematics as part of The Well collection, it simulates fluid in a layer heated from below and cooled from above, which forms convective Bénard cells driven by buoyancy and thermal gradients.
Understanding and forecasting turbulent convective flow is critical in physics, engineering, and environmental science. Because the positioning and evolution of convective cells are highly sensitive to small perturbations in initial conditions, the dataset presents a challenging benchmark for physical surrogate architectures such as neural operators and convolutional networks.
How it was made
Simulations are generated using the spectral numerical solver Dedalus. The governing equations solve for velocity, buoyancy, and pressure in the frequency domain on a uniform Cartesian grid of 512 by 128 points spanning a spatial domain of 0 to 4 horizontally and 0 to 1 vertically. Boundaries are periodic in the horizontal direction and enforce no-slip, fixed-buoyancy Dirichlet conditions at the top and bottom plates.
The ensemble includes 1,750 distinct simulations spanning 35 parameter configurations across five Rayleigh numbers (from 10^6 to 10^10) and seven Prandtl numbers (from 0.1 to 10.0). For each physical configuration, 50 simulations are produced using perturbed initial buoyancy fields composed of a linear background combined with Gaussian white noise. Each simulation records scalar buoyancy, scalar pressure, and vector velocity over 200 uniform time steps from t = 0 to t = 50.
Key facts
- Publisher
- polymathic-ai
- Collection
- The Well
- Total simulations
- 1,750 (35 parameter combinations × 50 initial conditions)
- Total dataset size
- 358.4 GB
- Spatial resolution
- 512 × 128 grid points
- Temporal resolution
- 200 time steps (dt = 0.25, t from 0 to 50)
- Physical parameters
- Rayleigh numbers (1e6 to 1e10), Prandtl numbers (0.1 to 10.0)
- Output fields
- Buoyancy (scalar), pressure (scalar), velocity (vector)
- Numerical solver
- Dedalus (single precision)
What you can use it for
- Surrogate model benchmarking
- Evaluate the predictive accuracy of architectures such as Fourier Neural Operators (FNO, TFNO) and U-Net variants on multi-field partial differential equation forecasts.
- Turbulence and heat transfer modelling
- Train data-driven models to predict thermal convection, vortex generation, and boundary-layer behaviour under varying Rayleigh and Prandtl numbers.
- Sensitivity and bifurcation analysis
- Examine how predictive models handle trajectories that diverge due to small variations in initial buoyancy perturbations.
Explore the data
No queryable preview
This dataset is not available in a queryable form — usually an unusual file format or a repository too large to convert. The original source may still be readable.Strengths and limits
Good at
- Covers a wide non-dimensional parameter space spanning five orders of magnitude in Rayleigh number and two orders in Prandtl number.
- Provides complete physical states by outputting buoyancy, velocity vector components, and pressure fields.
- Offers standardised baselines with reported variance-scaled root-mean-square error (VRMSE) metrics for FNO, TFNO, Unet, and CNextU-net.
Watch out for
- Simulations are restricted to two-dimensional geometry, excluding three-dimensional turbulent dynamics.
- Data generation was performed in single precision rather than double precision.
- Simulations are bound to a fixed horizontal aspect ratio of 4:1 with horizontally periodic conditions.
Questions
Can I look inside rayleigh_benard without downloading it?
Not here: it is not available in a queryable form. Its description and statistics are still shown.
What licence is rayleigh_benard under?
Its authors declare cc-by-4.0. Read the terms on the original page before reusing the data.
What variables are stored in each simulation snapshot?
Each snapshot contains a scalar buoyancy field, a scalar pressure field, and a two-component velocity vector field on a 512 by 128 Cartesian grid.
How are initial conditions set for each run?
The initial velocity and pressure fields are set to zero, while the initial buoyancy field combines a damped linear background with scaled Gaussian white noise across ten random seeds and five background scaling values.
Which baseline models have been evaluated on this dataset?
Reported baselines include Fourier Neural Operators (FNO, achieving 0.8395 VRMSE), Tensorized FNO (TFNO, achieving 0.6566 VRMSE), standard U-Net (1.4860 VRMSE), and CNextU-net (0.6699 VRMSE).
How to cite it
Burns, Keaton J and Vasil, Geoffrey M and Oishi, Jeffrey S and Lecoanet, Daniel and Brown, Benjamin P. (2020). Dedalus: A flexible framework for numerical simulations with spectral methods. Physical Review Research, 2(2), 023068.
Written from rayleigh_benard'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.