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.