TY - JOUR
T1 - Inadequacy of Linear Methods for Minimal Sensor Placement and Feature Selection in Nonlinear Systems
T2 - A New Approach Using Secants
AU - Otto, Samuel E.
AU - Rowley, Clarence W.
N1 - Funding Information:
This research was supported by the Army Research Office under grant number W911NF-17-1-0512. S.E.O. was supported by a National Science Foundation Graduate Research Fellowship Program under Grant No. DGE-2039656. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the National Science Foundation.
Publisher Copyright:
© 2022, The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature.
PY - 2022/10
Y1 - 2022/10
N2 - Sensor placement and feature selection are critical steps in engineering, modeling, and data science that share a common mathematical theme: the selected measurements should enable solution of an inverse problem. Most real-world systems of interest are nonlinear, yet the majority of available techniques for feature selection and sensor placement rely on assumptions of linearity or simple statistical models. We show that when these assumptions are violated, standard techniques can lead to costly over-sensing without guaranteeing that the desired information can be recovered from the measurements. In order to remedy these problems, we introduce a novel data-driven approach for sensor placement and feature selection for a general type of nonlinear inverse problem based on the information contained in secant vectors between data points. Using the secant-based approach, we develop three efficient greedy algorithms that each provide different types of robust, near-minimal reconstruction guarantees. We demonstrate them on two problems where linear techniques consistently fail: sensor placement to reconstruct a fluid flow formed by a complicated shock–mixing layer interaction and selecting fundamental manifold learning coordinates on a torus.
AB - Sensor placement and feature selection are critical steps in engineering, modeling, and data science that share a common mathematical theme: the selected measurements should enable solution of an inverse problem. Most real-world systems of interest are nonlinear, yet the majority of available techniques for feature selection and sensor placement rely on assumptions of linearity or simple statistical models. We show that when these assumptions are violated, standard techniques can lead to costly over-sensing without guaranteeing that the desired information can be recovered from the measurements. In order to remedy these problems, we introduce a novel data-driven approach for sensor placement and feature selection for a general type of nonlinear inverse problem based on the information contained in secant vectors between data points. Using the secant-based approach, we develop three efficient greedy algorithms that each provide different types of robust, near-minimal reconstruction guarantees. We demonstrate them on two problems where linear techniques consistently fail: sensor placement to reconstruct a fluid flow formed by a complicated shock–mixing layer interaction and selecting fundamental manifold learning coordinates on a torus.
KW - Feature selection
KW - Greedy algorithms
KW - Manifold learning
KW - Nonlinear inverse problems
KW - Reduced-order modeling
KW - Shock–turbulence interaction
KW - State estimation
KW - Submodular optimization
UR - http://www.scopus.com/inward/record.url?scp=85135636852&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85135636852&partnerID=8YFLogxK
U2 - 10.1007/s00332-022-09806-9
DO - 10.1007/s00332-022-09806-9
M3 - Article
AN - SCOPUS:85135636852
SN - 0938-8974
VL - 32
JO - Journal of Nonlinear Science
JF - Journal of Nonlinear Science
IS - 5
M1 - 69
ER -