Liu Ruixian, Bianco Michael J, Gerstoft Peter
Department of Electrical and Computer Engineering, University of California, San Diego, California 92161, USA.
Scripps Institution of Oceanography, University of California San Diego, La Jolla, California 92037, USA.
J Acoust Soc Am. 2021 Oct;150(4):2364. doi: 10.1121/10.0006444.
Inspired by recent developments in data-driven methods for partial differential equation (PDE) estimation, we use sparse modeling techniques to automatically estimate PDEs from data. A dictionary consisting of hypothetical PDE terms is constructed using numerical differentiation. Given data, PDE terms are selected assuming a parsimonious representation, which is enforced using a sparsity constraint. Unlike previous PDE identification schemes, we make no assumptions about which PDE terms are responsible for a given field. The approach is demonstrated on synthetic and real video data, with physical phenomena governed by wave, Burgers, and Helmholtz equations. Codes are available at https://github.com/NoiseLab-RLiu/Automate-PDE-identification.
受偏微分方程（PDE）估计中数据驱动方法的最新进展启发，我们使用稀疏建模技术从数据中自动估计偏微分方程。通过数值微分构建一个由假设的偏微分方程项组成的字典。给定数据后，假设采用简洁表示来选择偏微分方程项，并使用稀疏约束来强化这种表示。与以前的偏微分方程识别方案不同，我们不对哪些偏微分方程项导致给定的场做任何假设。该方法在合成和真实视频数据上得到了验证，其中物理现象由波动方程、伯格斯方程和亥姆霍兹方程控制。代码可在https://github.com/NoiseLab-RLiu/Automate-PDE-identification获取。
