Exploiting sparsity and equation-free architectures in complex systems

By Joshua L. Proctor, Steven L. Brunton, Bingni W. Brunton, J. Nathan Kutz. 2014

68 citations recorded by the source corpus.

Subfields: Cognitive Neuroscience, Statistical and Nonlinear Physics, Numerical Methods & Scientific Computing, AI for Physical Sciences

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Cognitive Neuroscience

1. Maizar Raissi
2. Steven L. Brunton
3. J. Nathan Kutz
4. Rachel A. Ward
5. Giang Tran
6. Joshua L. Proctor

In Statistical and Nonlinear Physics

1. Steven L. Brunton
2. J. Nathan Kutz
3. Maizar Raissi
4. Bingni W. Brunton
5. Joshua L. Proctor
6. G. Em Karniadakis
7. Benjamin Peherstorfer
8. Karen E. Willcox

In Numerical Methods & Scientific Computing

1. Maizar Raissi
2. Steven L. Brunton
3. J. Nathan Kutz
4. G. Em Karniadakis
5. Rachel A. Ward
6. Giang Tran
7. Bingni W. Brunton
8. Karen E. Willcox

In AI for Physical Sciences

1. Maizar Raissi
2. Steven L. Brunton
3. J. Nathan Kutz
4. G. Em Karniadakis
5. Bingni W. Brunton
6. Joshua L. Proctor
7. Paris Perdikaris
8. Karen E. Willcox

Citations in the corpus

• 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”
• 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].”
• Exact Recovery of Chaotic Systems from Highly Corrupted Data (2016, methodology): “Recently, sparse-inducing methods used in image processing and compressed sensing have been applied to partial differential equations, dynamical systems and physical sciences [WSWK12, SCHO13, CHZ13, BLK13, OLCO13, OLCO14, PBBK14, MSO14, BTBK14, COST15, TSFO15, BPK16].”
• Projection-based model reduction: Formulations for physics-based machine learning (2019, methodology): “larization to select reduced-model components from a library [41, 45].”
• Multiresolution Dynamic Mode Decomposition (2015, background): “In the dynamical applications considered here, one might exploit these patterns, or DMD modes, by building libraries of low-rank dynamical modes, much like is done with POD modes [25, 26, 27].”