Active matter simulations

One line description of the data: Modeling and simulation of biological active matter.

Longer description of the data: Simulation of a continuum theory describing the dynamics of \(N\) rod-like active particles immersed in a Stokes fluid having linear dimension \(L\) and colume \(L^2\).

Associated paper: Paper.

Domain expert: Suryanarayana Maddu, Center for Computaional Biology, Flatiron Institute.

Code or software used to generate the data: Github repository.

Equations: Equations (1) to (5) of the associated paper.

Dataset	FNO	TFNO	Unet	CNextU-net
active_matter	0.3691	0.3598	0.2489	\(\mathbf{0.1034}\)

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

Dimension of discretized data: 81 time-steps of 256 \(\times\) 256 images per trajectory.

Fields available in the data: concentration (scalar field), velocity (vector field), orientation tensor (tensor field), strain-rate tensor (tensor field).

Number of trajectories: \(5\) trajectories per parameter-set, each trajectory being generated with a different initialization of the state field {\(c,D,U\)}.

Size of the ensemble of all simulations: 51.3 GB.

Grid type: Uniform grid, cartesian coordinates.

Initial conditions: The concentration is set to constant value \(c(x,t)=1\) and the orientation tensor is initialized as plane-wave perturbation about the isotropic state.

Boundary conditions: Periodic boundary conditions.

Simulation time-step: \(3.90625\times 10^{-4}\) seconds.

Data are stored separated by ( \(\Delta t\) ): 0.25 seconds.

Total time range ( \(t_{min}\) to \(t_{max}\) ): \(0\) to \(20\) seconds.

Spatial domain size ( \(L_x\), \(L_y\) ): \(L_x=10\) and \(L_y=10\).

Set of coefficients or non-dimensional parameters evaluated: \(\alpha =\) {-1,-2,-3,-4,-5}; \(\beta =\) {0.8}; \(\zeta =\) {1,3,5,7,9,11,13,15,17}.

Approximate time and hardware to generate the data: 20 minutes per simulation on an A100 GPU in double precision. There is a total of 225 simulations, which is approximately 75 hours.

What is interesting and challenging about the data:

What phenomena of physical interest are catpured in the data: How is energy being transferred between scales? How is vorticity coupled to the orientation field? Where does the transition from isotropic state to nematic state occur with the change in alignment ( \(\zeta\) ) or dipole strength (\(\alpha\))?

How to evaluate a new simulator operating in this space: Reproducing some summary statistics like power spectra and average scalar order parameters. Additionally, being able to accurately capture the phase transition from isotropic to nematic state.

Please cite the associated paper if you use this data in your research:

@article{maddu2024learning,
  title={Learning fast, accurate, and stable closures of a kinetic theory of an active fluid},
  author={Maddu, Suryanarayana and Weady, Scott and Shelley, Michael J},
  journal={Journal of Computational Physics},
  volume={504},
  pages={112869},
  year={2024},
  publisher={Elsevier}
}