Work Description

Date: 18 January, 2025

Dataset Title: Self-oscillating gel simulation snapshots

Dataset Creators: D. Aksoy, D. Kim

Dataset Contact: Doruk Aksoy [email protected]

Funding: Michigan Institute for Computational Discovery and Engineering Catalyst Grant, DARPA AIRA program grant HR0011199002

Use and Access:
This data set is made available under a Attribution 4.0 International (CC BY 4.0) license.

To Cite Data:
Aksoy, D. , Kim, D., Self Oscillating Gel Snapshot Dataset [Data set]. University of Michigan - Deep Blue.

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Welcome! Thank you for downloading the self-oscillating gel simulation snapshot dataset.

This dataset contains snapshots from simulations of a hexagonal self oscillating gel sheet defined via a triangular lattice. The lattice has stretching springs between neighboring vertices and bending springs with energy proportional to the square of the angle between neighboring traingular faces.

The motion of the lattice is driven by time- and space-varying distributions of the rest lengths of the stretching springs. In the motivating experiments on thin gel sheets, there are chemical waves, radial or spiral in form, that induce local swelling of the sheets. As a simple model, this dataset considers radial or planar (unidirectional) traveling waves in the simulations.

The sheet is modeled as a flat hexagon of radius 1 with an equilateral triangular triangle lattice mesh, with initially uniform mesh spacing of 1/33, resulting in 3367 mesh points. A small out-of-plane perturbation is applied and the motion evolves over the sheet over time. The sheet is modeled to have damped dynamics. However for large enough wave amplitudes, the sheet rapidly buckles into shapes with time-varying distributions of curvature, large in magnitude.

For more information on the simulation that generated the data, please refer to "Semi-implicit methods for the dynamics of elastic sheets,” at Journal of Computational Physics by Alben et al.

For an example SciML application that considers this dataset, please refer to "Inverse design of self-oscillatory gels through deep learning." Neural Computing and Applications by Aksoy et al.
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Created Publications:

- Aksoy, Doruk, et al. "Inverse design of self-oscillatory gels through deep learning." Neural Computing and Applications 34.9 (2022): 6879-6905.
- Aksoy, Doruk, et al. "An incremental tensor train decomposition algorithm." SIAM Journal on Scientific Computing 46.2 (2024): A1047-A1075.
- Aksoy, Doruk, and Alex A. Gorodetsky. "Incremental Hierarchical Tucker Decomposition." arXiv preprint arXiv:2412.16544 (2024).
- Alben, Silas, et al. "Semi-implicit methods for the dynamics of elastic sheets." Journal of Computational Physics 399 (2019): 108952.

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Inputs:

There are 3 continuous and 1 discrete parameters to the input simulation. The input parameters (and their feasible ranges) are:

- Continuous:
1 - Wavenumber: [0.1, 10]
2 - Stiffness (Ks): Nondimensionalized stretching stiffness constant [1e-3, 1e-4]
3 - KCap: Amplitude of the perturbation ([0.01-0.27] for radial waves, [0.01, 0.21] for planar waves)
- Discrete:
1 - Motion type (1 for radial, 2 for planar waves)

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Outputs:

The simulation outputs the following quantities:
1 - Mesh points: x, y, and z positions of the 3367 mesh points (has shape (3367,3,10))
2 - Bending forces: 2-norm of the forces on mesh points (has shape (100,))
3 - Stretching forces: (has shape (100,))

The motion is simulated for t=[0,20] seconds but the initial 5s is left out as it corresponds to the transient portion of the motion. The mesh points are recorded with 0.1s intervals, whereas the force terms are recorded with 0.01s intervals.
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Dataset structure:

The dataset is split into distinct training and test parts for effective (and isolated) implementations for SciML pipelines. The training set is constructed by discretizing the feasible space into equidistant points (20x20x20=8000 combinations for radial waves, 20x20x16=6400 combinations for planar waves). The test set is constructed by uniformly sampling 30,000 points from the respective feasible parameter spaces of each motion type.

To provide a breadth of combinations for downstream SciML tasks, we provide snapshots from the following timeframes:

- Training set:
- 6-7s
- 7-8s
- Test set:
- 7-8s
- 8-9s
- 14-15s

At the end of this file you can find the tree structure of the dataset folders. The dataset is composed of compressed (as .tar.gz) .npy files for each simulation. You can decompress the archive folders using the "tar -xzvf" command. When extracted, each archive file will output files with the following pattern:

catgel_[pts/fbend/fstretch]_[time interval]s_Kcap_[Kcap value]_Ks_[Ks value]_Wv_[wavenumber]_Ty_[motion type].npy

Note that the [Kcap value], [Ks value], and [wavenumber] are given as float values and are separated by underscores to allow parsing directly from file name.

You can use the reconstruct_mesh.py script as a baseline in case you want to visualise the hexagonal sheet for your desired purpose.

Doruk Aksoy - 2025

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Folder structure:

./
├── reconstruct_mesh.py
├── README.txt
├── test
│ ├── 1
│ │ ├── 14_15s
│ │ │ ├── fbend
│ │ │ │ ├── fbend_part_001.tar.gz
│ │ │ │ ├── ...
│ │ │ │ └── fbend_part_031.tar.gz
│ │ │ ├── fstretch
│ │ │ │ ├── fstretch_part_001.tar.gz
│ │ │ │ ├── ...
│ │ │ │ └── fstretch_part_031.tar.gz
│ │ │ └── pts
│ │ │ ├── pts_part_001.tar.gz
│ │ │ ├── ...
│ │ │ └── pts_part_031.tar.gz
│ │ ├── 7_8s
│ │ │ ├── fbend
│ │ │ │ ├── fbend_part_001.tar.gz
│ │ │ │ ├── ...
│ │ │ │ └── fbend_part_031.tar.gz
│ │ │ ├── fstretch
│ │ │ │ ├── fstretch_part_001.tar.gz
│ │ │ │ ├── ...
│ │ │ │ └── fstretch_part_031.tar.gz
│ │ │ └── pts
│ │ │ ├── pts_part_001.tar.gz
│ │ │ ├── ...
│ │ │ └── pts_part_031.tar.gz
│ │ └── 8_9s
│ │ ├── fbend
│ │ │ ├── fbend_part_001.tar.gz
│ │ │ ├── ...
│ │ │ └── fbend_part_031.tar.gz
│ │ ├── fstretch
│ │ │ ├── fstretch_part_001.tar.gz
│ │ │ ├── ...
│ │ │ └── fstretch_part_031.tar.gz
│ │ └── pts
│ │ ├── pts_part_001.tar.gz
│ │ ├── ...
│ │ └── pts_part_031.tar.gz
│ └── 2
│ ├── 14_15s
│ │ ├── fbend
│ │ │ ├── fbend_part_001.tar.gz
│ │ │ ├── ...
│ │ │ └── fbend_part_031.tar.gz
│ │ ├── fstretch
│ │ │ ├── fstretch_part_001.tar.gz
│ │ │ ├── ...
│ │ │ └── fstretch_part_031.tar.gz
│ │ └── pts
│ │ ├── pts_part_001.tar.gz
│ │ ├── ...
│ │ └── pts_part_031.tar.gz
│ ├── 7_8s
│ │ ├── fbend
│ │ │ ├── fbend_part_001.tar.gz
│ │ │ ├── ...
│ │ │ └── fbend_part_031.tar.gz
│ │ ├── fstretch
│ │ │ ├── fstretch_part_001.tar.gz
│ │ │ ├── ...
│ │ │ └── fstretch_part_031.tar.gz
│ │ └── pts
│ │ ├── pts_part_001.tar.gz
│ │ ├── ...
│ │ └── pts_part_031.tar.gz
│ └── 8_9s
│ ├── fbend
│ │ ├── fbend_part_001.tar.gz
│ │ ├── ...
│ │ └── fbend_part_031.tar.gz
│ ├── fstretch
│ │ ├── fstretch_part_001.tar.gz
│ │ ├── ...
│ │ └── fstretch_part_031.tar.gz
│ └── pts
│ ├── pts_part_001.tar.gz
│ ├── ...
│ └── pts_part_031.tar.gz
└── train
├── 1
│ ├── 6_7s
│ │ ├── fbend
│ │ │ ├── fbend_part_001.tar.gz
│ │ │ ├── ...
│ │ │ └── fbend_part_009.tar.gz
│ │ ├── fstretch
│ │ │ ├── fstretch_part_001.tar.gz
│ │ │ ├── ...
│ │ │ └── fstretch_part_009.tar.gz
│ │ └── pts
│ │ ├── pts_part_001.tar.gz
│ │ ├── ...
│ │ └── pts_part_009.tar.gz
│ └── 7_8s
│ ├── fbend
│ │ ├── fbend_part_001.tar.gz
│ │ ├── ...
│ │ └── fbend_part_009.tar.gz
│ ├── fstretch
│ │ ├── fstretch_part_001.tar.gz
│ │ ├── ...
│ │ └── fstretch_part_009.tar.gz
│ └── pts
│ ├── pts_part_001.tar.gz
│ ├── ...
│ └── pts_part_009.tar.gz
└── 2
├── 6_7s
│ ├── fbend
│ │ ├── fbend_part_001.tar.gz
│ │ ├── ...
│ │ └── fbend_part_007.tar.gz
│ ├── fstretch
│ │ ├── fstretch_part_001.tar.gz
│ │ ├── ...
│ │ └── fstretch_part_007.tar.gz
│ └── pts
│ ├── pts_part_001.tar.gz
│ ├── ...
│ └── pts_part_007.tar.gz
└── 7_8s
├── fbend
│ ├── fbend_part_001.tar.gz
│ ├── ...
│ └── fbend_part_007.tar.gz
├── fstretch
│ ├── fstretch_part_001.tar.gz
│ ├── ...
│ └── fstretch_part_007.tar.gz
└── pts
├── pts_part_001.tar.gz
├── ...
└── pts_part_007.tar.gz