metadata

language:
  - en
license: cc-by-4.0
tags:
  - physics
task_categories:
  - time-series-forecasting
  - other
task_ids:
  - multivariate-time-series-forecasting

This Dataset is part of The Well Collection.

How To Load from HuggingFace Hub

Be sure to have the_well installed (pip install the_well)
Use the WellDataModule to retrieve data as follows:

from the_well.benchmark.data import WellDataModule

# The following line may take a couple of minutes to instantiate the datamodule
datamodule = WellDataModule(
    "hf://datasets/polymathic-ai/",
    "acoustic_scattering_discontinuous",
)
train_dataloader = datamodule.train_dataloader()

for batch in dataloader:
    # Process training batch
    ...

Acoustic Scattering - Single Discontinuity

One line description of the data: Simple acoustic wave propogation over a domain split into two continuously varying sub-domains with a single discountinuous interface.

Longer description of the data: These variable-coefficient acoustic equations describe the propogation of an acoustic pressure wave through domains consisting of multiple materials with different scattering properties. This problem emerges in source optimization and it's inverse - that of identifying the material properties from the scattering of the wave - is a vital problem in geology and radar design. This is the simplest of three scenarios. In this case, we have a variable number of initial point sources and single discontinuity separating two sub-domains. Within each subdomain, the density of the underlying material varies smoothly.

Domain expert: Michael McCabe, Polymathic AI.

Code or software used to generate the data: Clawpack, adapted from this example.

Equation:

$\begin{align} \frac{ \partial p}{\partial t} + K(x, y) \left( \frac{\partial u}{\partial x} + \frac{\partial v}{\partial y} \right) &= 0 \\ \frac{ \partial u }{\partial t} + \frac{1}{\rho(x, y)} \frac{\partial p}{\partial x} &= 0 \\ \frac{ \partial v }{\partial t} + \frac{1}{\rho(x, y)} \frac{\partial p}{\partial v} &= 0 \end{align}$

with $\rho$ the material density, $u, v$ the velocity in the $x, y$ directions respectively, $p$ the pressure, and $K$ the bulk modulus.

Example material densities can be seen below:

About the data

Dimension of discretized data: 101 steps of 256 $\times$ 256 images.

Fields available in the data: pressure (scalar field), material density (constant scalar field), material speed of sound (constant scalar field), velocity field (vector field).

Number of trajectories: 2000.

Estimated size of the ensemble of all simulations: 157.7 GB.

Grid type: uniform, cartesian coordinates.

Initial conditions: Flat pressure static field with 1-4 high pressure rings randomly placed in domain. The rings are defined with variable intensity $\sim \mathcal U(.5, 2)$ and radius $\sim \mathcal U(.06, .15)$ .

Boundary conditions: Open domain in $y$ , reflective walls in $x$ .

Simulation time-step: Variable based on CFL with safety factor .25.

Data are stored separated by ( $\Delta t$ ): 2/101.

Total time range ( $t_{min}$ to $t_{max}$ ): [0, 2]

Spatial domain size ( $L_{x}$ , $L_{y}$ ): [-1, 1] x [-1, 1]

Set of coefficients or non-dimensional parameters evaluated:

$K$ is fixed at 4.0.
$\rho$ is the primary coefficient here. Each side is generated with one of the following distributions:
- Gaussian Bump - Peak density samples from $\sim\mathcal U(1, 7)$ and $\sigma \sim\mathcal U(.1, 5)$ with the center of the bump uniformly sampled from the extent of the subdomain.
- Linear gradient - Four corners sampled with $\rho \sim \mathcal U(1, 7)$ . Inner density is bilinearly interpolated.
- Constant - Constant $\rho \sim\mathcal U(1, 7)$ .
- Smoothed Gaussian Noise - Constant background sampled $\rho \sim\mathcal U(1, 7)$ with IID standard normal noise applied. This is then smoothed by a Gaussian filter of varying sigma $\sigma \sim\mathcal U(5, 10)$ .

Approximate time to generate the data: ~15 minutes per simulation.

Hardware used to generate the data and precision used for generating the data: 64 Intel Icelake cores per simulation. Generated in double precision.

What is interesting and challenging about the data:

Wave propogation through discontinuous media. Most existing machine learning datasets for computational physics are highly smooth and the acoustic challenges presented here offer challenging discontinuous scenarios that approximate complicated geometry through the variable density.

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

@article{mandli2016clawpack,
  title={Clawpack: building an open source ecosystem for solving hyperbolic PDEs},
  author={Mandli, Kyle T and Ahmadia, Aron J and Berger, Marsha and Calhoun, Donna and George, David L and Hadjimichael, Yiannis and Ketcheson, David I and Lemoine, Grady I and LeVeque, Randall J},
  journal={PeerJ Computer Science},
  volume={2},
  pages={e68},
  year={2016},
  publisher={PeerJ Inc.}
}