Physics Simulation · polymathic-ai
planetswe
Spherical rotating shallow-water simulations with Earth-like topography and periodic forcings for atmospheric surrogate models.
What planetswe is
PlanetSWE is a physics simulation dataset generated by Polymathic AI as part of The Well collection. It simulates forced hyperviscous rotating shallow-water equations on a sphere, incorporating Earth-like topography along with diurnal and seasonal periodic forcings. The shallow-water equations act as a two-dimensional depth-integrated approximation of three-dimensional incompressible fluid flow, providing an established analogue for single pressure-level atmospheric circulation.
Initialised from the 500 hPa pressure level of the ERA5 reanalysis dataset, this benchmark presents an atmosphere-like environment where the underlying dynamical equations are fully known. It serves researchers developing machine learning surrogate models for weather and climate dynamics, testing their ability to manage spherical coordinates, handle multi-scale periodic patterns, and maintain autoregressive rollout stability over long horizons.
How it was made
Simulations are generated using the Dedalus solver framework on a spherical domain spanning longitude phi in [0, 2pi] and latitude theta in [0, pi]. The governing equations couple two-dimensional velocity and the height deviation of the pressure surface, incorporating hyperviscosity, Coriolis acceleration, and an explicit daily-plus-annual forcing term based on solar declination and diurnal cycles.
Data are integrated across an equiangular polar grid of 256 by 512 points using a Courant–Friedrichs–Lewy (CFL) adaptive time-step with a safety factor of 0.4. Initial conditions derived from ERA5 500 hPa fields are filtered for numerical stability and burned in for half a simulation year before trajectory recording begins. Snapshots are recorded hourly in model time, covering 40 distinct trajectories of three model years each (3,024 timesteps per trajectory).
Key facts
- Part of
- The Well Collection
- Domain
- Physics simulation, Earth science
- Total ensemble size
- 185.8 GB
- Trajectories
- 40 trajectories
- Timesteps per trajectory
- 3,024 steps (1 hour interval, 24 steps/day, 1,008 steps/year)
- Spatial resolution
- 256 x 512 (equiangular polar grid)
- Fields available
- Height (scalar field), velocity (vector field)
- Boundary conditions
- Spherical
- Generation software
- Dedalus
- Generation hardware
- 64 Icelake CPU cores
What you can use it for
- Surrogate Weather and Climate Modelling
- Benchmarking data-driven models, such as neural operators and U-Nets, to predict planetary atmospheric dynamics on spherical topologies.
- Evaluating Autoregressive Rollout Stability
- Assessing the long-term numerical stability and drift of autoregressive neural forecasting models across multi-year continuous rollouts.
- Multi-Frequency Periodicity Learning
- Testing whether machine learning architectures can resolve combined daily and seasonal atmospheric cycles using context length or explicit temporal conditioning.
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
- Ground-truth dynamics are precisely determined by closed partial differential equations, unlike observational atmospheric data.
- Incorporates realistic Earth-like topography, Coriolis forces, and compound diurnal and annual seasonal forcings.
- Demonstrates stable long-term dynamics, making it well-suited for evaluating multi-year autoregressive stability.
- Conveniently integrated into The Well collection via a standardised PyTorch data loader module.
Watch out for
- Approximates atmospheric motion as a single-layer, two-dimensional depth-integrated fluid rather than full 3D atmospheric physics.
- Requires models that can handle equiangular polar coordinate singularities and spherical geometry.
- High storage requirement, totalling 185.8 GB across the 40 simulation runs.
Questions
Can I look inside planetswe without downloading it?
Not here: it is not available in a queryable form. Its description and statistics are still shown.
What licence is planetswe 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 snapshot?
Each snapshot contains a scalar field for the pressure surface height deviation and a vector field representing two-dimensional flow velocity across a 256 by 512 grid.
How are initial conditions generated?
Initial states are extracted from the 500 hPa pressure level of the ERA5 reanalysis dataset, filtered to ensure stable initialization, and run through a burn-in phase of half a simulation year before data recording begins.
What machine learning models have been evaluated on this dataset?
Baseline evaluations reported in the benchmark include Fourier Neural Operators (FNO), Tensorized Fourier Neural Operators (TFNO), U-Net, and ConvNeXt U-Net (CNextU-net), with TFNO achieving the lowest VRMSE score of 0.0853.
How are time units defined in the simulation?
A model day is defined as 24 timesteps and a model year comprises 1,008 timesteps, with recorded snapshots saved at intervals of one simulation hour.
How to cite it
McCabe, Michael, Peter Harrington, Shashank Subramanian, and Jed Brown. "Towards stability of autoregressive neural operators." arXiv preprint arXiv:2306.10619 (2023).
Written from planetswe'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.