Nonlinear Laplacian spectral analysis for time series with intermittency and low-frequency variability

By Dimitrios Giannakis, Andrew J. Majda. 2012

228 citations recorded by the source corpus.

Subfields: Economics and Econometrics, Global and Planetary Change, Statistical and Nonlinear Physics

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Citations in the corpus

Deep Hidden Physics Models: Deep Learning of Nonlinear Partial Differential Equations (2018, background): “, 2009), nonlinear Laplacian spectral analysis (Giannakis and Majda, 2012), modeling emergent behavior (Roberts, 2014), Koopman analysis (Mezić, 2005; Budǐsić et al.”
Data-driven discovery of partial differential equations (2016, background): “Methods for data-driven discovery of dynamical systems (1) include equation-free modeling (2), artificial neural networks (3), nonlinear regression (4), empirical dynamic modeling (5, 6), normal form identification (7), nonlinear Laplacian spectral analysis (8), modeling emergent behavior (9), and a”
Hidden physics models: Machine learning of nonlinear partial differential equations (2017, background): “The literature on data-driven discovery of dynamical systems [3] is vast and encompasses equation-free modeling [4], artificial neural networks [5], nonlinear regression [6], empirical dynamic modeling [7,8], modeling emergent behavior [9], automated inference of dynamics [10–12], normal form identi”
Machine Learning Control – Taming Nonlinear Dynamics and Turbulence (2016, background): “Recently SSA has been extended in the nonlinear Laplacian spectral analysis (NLSA) [117], which includes kernel methods from machine learning.”
Ensemble-SINDy: Robust sparse model discovery in the low-data, high-noise limit, with active learning and control (2021, methodology): “…model discovery methods exist, including equation-free modeling [1], normal form identiﬁcation [2–4], nonlinear Laplacian spectral analysis [5], Koop-man analysis [6, 7] and dynamic mode decomposition (DMD) [8–10], symbolic regression [11–15], sparse regression [16, 17], Gaussian processes…”
Chaos as an intermittently forced linear system (2016, methodology): “The motion of planets [76], weather and climate [63, 65, 66, 38, 83, 67], population dynamics [9, 94, 102], epidemiology [93], financial markets, earthquakes, solar flares, and turbulence [53, 51, 52, 95, 12], all provide compelling examples of chaos.”
Learning Parameters and Constitutive Relationships with Physics Informed Deep Neural Networks (2018, methodology): “These methods include NARMAX [7], equation-free methods [12], Laplacian spectral analysis [9], and neural networks [11].”
SINDy-PI: a robust algorithm for parallel implicit sparse identification of nonlinear dynamics (2020, background): “…Koopman theory [6–9], nonlinear autoregressive models [10, 11], neural networks [12–20], Gaussian process regression [21, 22], nonlinear Laplacian spectral analysis [23], diffusion maps [24], genetic programming [25–27], and sparse regression [28, 29], to highlight some of the recent developments.”
Embeddings of Riemannian Manifolds with Heat Kernels and Eigenfunctions (2013, background): “in machine learning (see, for instance, [32]) and to pattern recognition in experiments [23].”
Data Driven Governing Equations Approximation Using Deep Neural Networks (2018, methodology): “…regression ([5, 43]), equation-free modeling [24], heterogeneous multi-scale method (HMM) ([15]), artiﬁcial neural networks ([19]), nonlinear regression ([50]), empirical dynamic modeling ([46, 53]), nonlinear Laplacian spectral analysis ([18]), automated inference of dynamics ([44, 12, 13]), etc.”