  Disentangling and recovering physical attributes, such as shape and material,
from a few waveform examples is a challenging inverse problem in audio signal
processing, with numerous applications in musical acoustics as well as
structural engineering. We propose to address this problem via a combination of
time--frequency analysis and supervised machine learning. We start by
synthesizing a dataset of sounds using the functional transformation method.
Then, we represent each percussive sound in terms of its time-invariant
scattering transform coefficients and formulate the parametric estimation of
the resonator as multidimensional regression with a deep convolutional neural
network. We interpolate scattering coefficients over the surface of the drum as
a surrogate for potentially missing data, and study the response of the neural
network to interpolated samples. Lastly, we resynthesize drum sounds from
scattering coefficients, therefore paving the way towards a deep generative
model of drum sounds whose latent variables are physically interpretable.
