Department of Electrical and Computer Engineering, University of California, San Diego, California 92161, USA.
Scripps Institution of Oceanography, University of California, San Diego, California 92037, USA.
J Acoust Soc Am. 2023 Jun 1;153(6):3169. doi: 10.1121/10.0019592.
Observable dynamics, such as waves propagating on a surface, are generally governed by partial differential equations (PDEs), which are determined by the physical properties of the propagation media. The spatial variations of these properties lead to spatially dependent PDEs. It is useful in many fields to recover the variations from the observations of dynamical behaviors on the material. A method is proposed to form a map of the physical properties' spatial variations for a material via data-driven spatially dependent PDE identification and applied to recover acoustical properties (viscosity, attenuation, and phase speeds) for propagating waves. The proposed data-driven PDE identification scheme is based on ℓ1-norm minimization. It does not require any PDE term that is assumed active from the prior knowledge and is the first approach that is capable of identifying spatially dependent PDEs from measurements of phenomena. In addition, the method is efficient as a result of its non-iterative nature and can be robust against noise if used with an integration transformation technique. It is demonstrated in multiple experimental settings, including real laser measurements of a vibrating aluminum plate. Codes and data are available online at https://tinyurl.com/4wza8vxs.
可观测动力学，如在表面上传播的波，通常由偏微分方程（PDE）控制，这些方程由传播介质的物理性质决定。这些性质的空间变化导致了空间依赖的 PDE。从材料上动态行为的观测中恢复这些变化在许多领域都很有用。提出了一种通过数据驱动的空间依赖 PDE 识别来形成材料物理性质空间变化图的方法，并应用于恢复传播波的声特性（粘度、衰减和相速度）。所提出的数据驱动 PDE 识别方案基于ℓ1范数最小化。它不需要任何从先验知识中假设的活跃 PDE 项，是第一个能够从现象的测量中识别空间依赖 PDE 的方法。此外，该方法由于其非迭代性质而非常高效，如果与积分变换技术一起使用，它可以具有抗噪性。在多个实验设置中进行了演示，包括对振动铝板的实际激光测量。代码和数据可在 https://tinyurl.com/4wza8vxs 上获得。
