Data-Driven Spatially Dependent PDE Identification
Ruixian Liu, Michael J. Bianco, Peter Gerstoft, Bhaskar D. Rao
Abstract
We propose a data-driven partial differential equation (PDE) identification scheme based on ℓ <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</inf> -norm minimization which can identify spatially-dependent PDEs from measurements. Spatially-dependent PDEs refers to that the terms in the PDEs vary across space. In reality a physical system is often governed by spatially-dependent PDEs because the properties of the medium can be various across space, and the proposed method is the first data-driven spatially-dependent PDEs identification scheme. In addition, our method is efficient owing to its non-iterative nature and efficient implementation by coordinate descent. <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sup>
BibTeX
@inproceedings{icassp2022_datadrivenspatia,
title = {Data-Driven Spatially Dependent PDE Identification},
author = {Ruixian Liu and Michael J. Bianco and Peter Gerstoft and Bhaskar D. Rao},
booktitle = {ICASSP 2022},
year = {2022}
}