Multi-Frequency Far-Field Wave Scattering Data

This is a dataset designed to train and evaluate deep learning methods for forward and inverse multi-frequency far-field wave scattering problems. In this dataset, we have pairs of 2D scattering potentials q and scattered wave field measurements d_k, measured at several incident wave frequencies k. We define a distribution of scattering potentials that have piecewise constant geometric shapes with an unknown low-frequency background. With this dataset, one can train machine learning models to solve the forward problem q -> d_k, or the inverse problem d_k-> q. 

Please see our article for a formal definition of the forward and inverse scattering problems: 

Melia, O., Tsang, O., Charisopoulos, V., Khoo, Y., Hoskins, J., Willett, R., 2025. Multi-frequency progressive refinement for learned inverse scattering. Journal of Computational Physics 527, 113809. https://doi.org/10.1016/j.jcp.2025.113809

Also see our code repository which was used to generate the data and train neural networks to solve the multi-frequency inverse problem: https://github.com/meliao/MFISNets

Once decompressed, our dataset has the following file structure.

data/
└── dataset/
├── train_measurements_nu_*/ # We have directories for nu={1,2,4,8,16}, equivalently k={2pi,4pi,8pi,16pi,32pi}
│ └── measurements_*.h5 # each measurements_i.h5 has 500 scattering potentials.
├── val_measurements_nu_*/
│ └── measurements_*.h5
└── test_measurements_nu_*/
└── measurements_*.h5

The measurement files are saved in hdf5 format, with the following fields:

q_cart: the scattering potentials sampled on a Cartesian grid.

q_polar: the scattering potentials sampled on a polar grid.

x_vals: 1d coordinates of the regular Cartesian grid for the scattering domain

rho_vals: radius values of the regular polar grid for the scattering domain

theta_vals: angular values of the regular polar grid for the scattering domain. Also used as the source/receiver directions when generating measurements.

seed: the RNG seed used when generating this file.

contrast: the maximum contrast setting.

background_max_freq: the maximum frequency parameter used when defining the random background part of the scattering potentials.

background_max_radius: the radius of the disk occupied by the background field.

num_shapes: how many piecewise-constant shapes were generated.

gaussian_lpf_param: parameter used to build Gaussian lowpass filter that slightly smooths the scattering potentials.

nu_sf: non-angular wavenumber (in space).

omega_sf: angular frequency (in time).

q_cart_lpf: scattering objects transformed by a Gaussian LPF, sampled on the Cartesian grid.

q_polar_lpf: scattering objects transformed by a Gaussian LPF, sampled on the polar grid.

d_rs: Measurements of the scattered wave field, in the original (receiver, source) coordinates.

d_mh: Measurements of the scattered wave field, in the (m, h) coordinates suggested by Fan and Ying, 2022.

m_vals: Coordinates of the (m, h) transformed data.

h_vals: Coordinates of the (m, h) transformed data.

sample_completion: array of booleans indicating whether individual samples were generated.

file_completion: single boolean set to True when the entire generation script is completed.