DATA-DRIVEN SPATIALLY DEPENDENT PDE IDENTIFICATION

被引：3

作者：

Liu, Ruixian ^{[1
]}

Bianco, Michael J. ^{[1
]}

Gerstoft, Peter ^{[1
]}

Rao, Bhaskar D. ^{[1
]}

机构：

[1] Univ Calif San Diego, La Jolla, CA 92093 USA

来源：

2022 IEEE INTERNATIONAL CONFERENCE ON ACOUSTICS, SPEECH AND SIGNAL PROCESSING (ICASSP) | 2022年

关键词：

data-driven; l(1-)norm minimization; lasso; spatially-dependent PDEs; efficient identification; EQUATIONS;

D O I：

10.1109/ICASSP43922.2022.9747392

中图分类号：

O42 [声学];

学科分类号：

070206 ; 082403 ;

摘要：

We propose a data-driven partial differential equation (PDE) identification scheme based on l(1)-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.(1)

引用

页码：3383 / 3387

页数：5

共 21 条

[1] Ames W.F., 2014, NUMER METH PART D E
[2] Brunton SL., 2019, DATA DRIVEN SCI ENG, DOI [10.1017/9781108380690, DOI 10.1017/9781108380690]
[3] Discovering governing equations from data by sparse identification of nonlinear dynamical systems
Brunton, Steven L.
Proctor, Joshua L.
Kutz, J. Nathan
[J]. PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA, 2016, 113 (15) : 3932 - 3937
[4] On the transient solutions of three acoustic wave equations: van Wijngaarden's equation, Stokes' equation and the time-dependent diffusion equation
Buckingham, Michael J.
[J]. JOURNAL OF THE ACOUSTICAL SOCIETY OF AMERICA, 2008, 124 (04) : 1909 - 1920
[5] Optimally sparse representation in general (nonorthogonal) dictionaries via l1 minimization
Donoho, DL
Elad, M
[J]. PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA, 2003, 100 (05) : 2197 - 2202
[6] Regularization Paths for Generalized Linear Models via Coordinate Descent
Friedman, Jerome
Hastie, Trevor
Tibshirani, Rob
[J]. JOURNAL OF STATISTICAL SOFTWARE, 2010, 33 (01): : 1 - 22
[7] Multiple and single snapshot compressive beamforming
Gerstoft, Peter
Xenaki, Angeliki
Mecklenbraeuker, Christoph F.
[J]. JOURNAL OF THE ACOUSTICAL SOCIETY OF AMERICA, 2015, 138 (04) : 2003 - 2014
[8] Spatially dependent parameter estimation and nonlinear data assimilation by autosynchronization of a system of partial differential equations
Kramer, Sean
Bollt, Erik M.
[J]. CHAOS, 2013, 23 (03)
[9] Automated partial differential equation identification
Liu, Ruixian
Bianco, Michael J.
Gerstoft, Peter
[J]. JOURNAL OF THE ACOUSTICAL SOCIETY OF AMERICA, 2021, 150 (04) : 2364 - 2374
[10] Liu RX, 2019, CONF REC ASILOMAR C, P2160, DOI [10.1109/IEEECONF44664.2019.9048953, 10.1109/ieeeconf44664.2019.9048953]

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