Taming Waves: A Physically-Interpretable Machine Learning Framework for
  Realizable Control of Wave Dynamics
Tristan Shah Feruza Amirkulova Stas Tiomkin
Controlling systems governed by partial differential equations is an
inherently hard problem. Specifically, control of wave dynamics is challenging
due to additional physical constraints and intrinsic properties of wave
phenomena such as dissipation, attenuation, reflection, and scattering. In this
work, we introduce an environment designed for the study of the control of
acoustic waves by actuated metamaterial designs. We utilize this environment
for the development of a novel machine-learning method, based on deep neural
networks, for efficiently learning the dynamics of an acoustic PDE from
samples. Our model is fully interpretable and maps physical constraints and
intrinsic properties of the real acoustic environment into its latent
representation of information. Within our model we use a trainable perfectly
matched layer to explicitly learn the property of acoustic energy dissipation.
Our model can be used to predict and control scattered wave energy. The
capabilities of our model are demonstrated on an important problem in
acoustics, which is the minimization of total scattered energy. Furthermore, we
show that the prediction of scattered energy by our model generalizes in time
and can be extended to long time horizons. We make our code repository publicly
available.