Taming Waves: A Physically-Interpretable Machine Learning Framework for Realizable Control of Wave Dynamics
This work addresses the challenge of realizable control in wave dynamics for acoustics and metamaterial design, representing an incremental advance in applying interpretable ML to PDE-based systems.
The authors tackled the problem of controlling acoustic wave dynamics under physical constraints by developing a physically-interpretable machine learning framework that learns from samples and incorporates a trainable perfectly matched layer to model dissipation, achieving results in minimizing total scattered energy with generalization to long time horizons.
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.