# Taming Waves: A Physically-Interpretable Machine Learning Framework for Realizable Control of Wave Dynamics

arXiv: https://arxiv.org/abs/2312.09460 · HTML: https://mlsanity.com/paper/2312.09460/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 9 of its 18 references that are in the map.
- First posted on arXiv 27 Nov 2023.

## Builds on (most cited first, 9 of 9)

- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [Recurrent Neural Network Regularization](https://mlsanity.com/paper/1409.2329/) (2014)
- [Fashionable Modelling with Flux](https://mlsanity.com/paper/1811.01457/) (2018)
- [Learning to Accelerate Partial Differential Equations via Latent Global Evolution](https://mlsanity.com/paper/2206.07681/) (2022)
- [Reinforcement Learning with Function-Valued Action Spaces for Partial Differential Equation Control](https://mlsanity.com/paper/1806.06931/) (2018)
- [Learning a model is paramount for sample efficiency in reinforcement learning control of PDEs](https://mlsanity.com/paper/2302.07160/) (2023)
- [Notes on Perfectly Matched Layers (PMLs)](https://mlsanity.com/paper/2108.05348/) (2021)
- [Design of arbitrarily shaped acoustic cloaks through PDE-constrained optimization satisfying sonic-metamaterial design requirements](https://mlsanity.com/paper/2109.11713/) (2021)
- [Interpretable Additive Recurrent Neural Networks For Multivariate Clinical Time Series](https://mlsanity.com/paper/2109.07602/) (2021)

## Abstract (arXiv)

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.