On the Compressive Spectral Method

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Deep Hidden Physics Models: Deep Learning of Nonlinear Partial Differential Equations (2018, methodology): “More recently, sparsity (Tibshirani, 1996) has been used to determine the governing dynamical system (Brunton et al., 2016; Mangan et al., 2016; Wang et al., 2011; Schaeffer et al., 2013; Ozoliņš et al., 2013; Mackey et al., 2014; Brunton et al., 2014; Proctor et al., 2014; Bai et al., 2014; Tran an”
Discovering governing equations from data by sparse identification of nonlinear dynamical systems (2015, background): “The trend to exploit sparsity in dynamical systems is recent but growing [38, 33, 25, 6, 35, 1].”
Sparse Identification of Nonlinear Dynamics with Control (SINDYc) (2016, methodology): “There are many other interesting methods recently developed to incorporate sparsity and nonlinear dynamics (Schaeffer et al., 2013; Ozoliņš et al., 2013; Mackey et al., 2014).”
Chaos as an intermittently forced linear system (2016, background): “This work is part of a growing literature that is exploring the use of sparsity in dynamics [72, 84, 64] and dynamical systems [8, 78, 14].”
Koopman Invariant Subspaces and Finite Linear Representations of Nonlinear Dynamical Systems for Control (2015, background): “This follows a growing trend to exploit sparsity in dynamics [35, 36, 37] and dynamical systems [38, 39, 40].”