Physics Simulation · polymathic-ai
active_matter
High-fidelity simulations of biological active matter for benchmarking neural PDE solvers and collective dynamics.
What active_matter is
The active_matter dataset provides numerical simulations of biological active matter, capturing the continuum dynamics of self-propelled, rod-like active particles suspended in a Stokes fluid. Published by Polymathic AI and developed in collaboration with Suryanarayana Maddu at the Flatiron Institute's Center for Computational Biology, the data models how energy transfers across scales and how fluid vorticity couples to particle orientation.
A central challenge in active fluid mechanics is capturing emergent collective behaviour, such as the transition from an isotropic state (where particles have no preferred alignment) to a nematic state (where particles align along a shared director). This benchmark provides standardized simulation trajectories designed to evaluate machine learning approaches and learned partial differential equation (PDE) solvers against multi-scale physical dynamics.
How it was made
Simulations are governed by continuum kinetic theory equations describing active particles in a two-dimensional domain with dimensions Lx = 10 and Ly = 10 under periodic boundary conditions. The concentration scalar field is initialised to a uniform value, while the orientation tensor is initialised with plane-wave perturbations around the isotropic state. The numerical solver steps forward in time with an internal step of 3.90625 × 10⁻⁴ seconds using double precision on NVIDIA A100 GPUs.
The dataset spans 225 total simulation runs across varying physical parameters: dipole strength (α), activity parameter (β = 0.8), and alignment parameter (ζ). Each parameter combination comprises five trajectories with different initial state field configurations. States are recorded at intervals of 0.25 seconds across a 0 to 20 second window, yielding 81 time steps per trajectory discretized on a 256 × 256 uniform Cartesian grid.
Key facts
- Publisher
- polymathic-ai
- Domain expert
- Suryanarayana Maddu
- Dataset size
- 51.3 GB
- Total simulations
- 225 trajectories
- Trajectories per parameter set
- 5
- Spatial resolution
- 256 × 256 uniform grid
- Temporal resolution
- 81 time-steps per trajectory (0.25 s interval)
- Simulation time range
- 0 to 20 seconds
- Available fields
- Concentration, velocity, orientation tensor, strain-rate tensor
- Boundary conditions
- Periodic
What you can use it for
- Benchmarking learned PDE surrogates
- Test and compare deep learning architectures, such as Fourier Neural Operators and U-Nets, on their ability to predict multi-scale fluid-particle evolution over time.
- Studying isotropic-to-nematic phase transitions
- Evaluate whether models can identify critical transition thresholds driven by changes in alignment parameter ζ and dipole strength α.
- Analyzing active fluid energy transfer
- Examine power spectra and vorticity-orientation coupling to model cross-scale turbulent energy transfer in active suspensions.
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
- Provides complete physical field representations including scalar concentration, vector velocity, and orientation and strain-rate tensors.
- Systematically sweeps across non-dimensional alignment and dipole parameters across 225 simulations.
- Generated using high-precision double-precision solver runs on NVIDIA A100 hardware.
Watch out for
- Restricted to two-dimensional spatial domains with periodic boundary conditions.
- Evaluates a single fixed activity coefficient value (β = 0.8).
- Contains five trajectories per parameter combination, which may limit statistical diversity per specific parameter set.
Questions
Can I look inside active_matter without downloading it?
Not here: it is not available in a queryable form. Its description and statistics are still shown.
What licence is active_matter under?
Its authors declare cc-by-4.0. Read the terms on the original page before reusing the data.
What quantities are included in the simulation fields?
The dataset contains concentration as a scalar field, fluid velocity as a vector field, the particle orientation tensor, and the fluid strain-rate tensor.
How are neural operators benchmarked on this dataset?
Models are evaluated using Volume Root Mean Squared Error (VRMSE) on test trajectories, scaled such that predicting the mean target field yields a score of 1. Baselines include FNO, TFNO, Unet, and CNextU-net.
How is the dataset loaded in Python?
The data is accessed using the WellDataModule from the pip package the_well via the repository path polymathic-ai/active_matter_cloud_optimized.
How to cite it
Maddu, Suryanarayana, Scott Weady, and Michael J. Shelley. 'Learning fast, accurate, and stable closures of a kinetic theory of an active fluid.' Journal of Computational Physics 504 (2024): 112869.
Written from active_matter'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.