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Data-driven approaches to dynamical networks: Integrating equation-free methods, machine learning and sparsity J. Nathan Kutz Department of Applied Mathematics.

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Presentation on theme: "Data-driven approaches to dynamical networks: Integrating equation-free methods, machine learning and sparsity J. Nathan Kutz Department of Applied Mathematics."— Presentation transcript:

1 Data-driven approaches to dynamical networks: Integrating equation-free methods, machine learning and sparsity J. Nathan Kutz Department of Applied Mathematics University of Washington Seattle, WA

2 Mathematical Foundations Dimensionality Reductions
+ Machine Learning - Goal is production of 2D light bullet Phase velocity in z direction Field confined to waveguides with Bragg Grating Contact layer pumps 0th waveguide

3 Dynamical Systems + PDEs
i. Generic nonlinear , time-dependent system ii. Measurements (assimilation) - Goal is production of 2D light bullet Phase velocity in z direction Field confined to waveguides with Bragg Grating Contact layer pumps 0th waveguide iii. My commitment – low-dimensional subspaces x

4 Encoding Dynamics

5 Sparsity + Sensors - Goal is production of 2D light bullet
Phase velocity in z direction Field confined to waveguides with Bragg Grating Contact layer pumps 0th waveguide

6 Compressive Sensing: A Cartoon
- Goal is production of 2D light bullet Phase velocity in z direction Field confined to waveguides with Bragg Grating Contact layer pumps 0th waveguide

7 Compressive Sensing for Fluids
- Goal is production of 2D light bullet Phase velocity in z direction Field confined to waveguides with Bragg Grating Contact layer pumps 0th waveguide

8 Flow Around a Cylinder

9 Compressive Sensing Reconstruction
1000 Re What about sensor placement?

10 Dynamic Mode Decomposition
Equation-Free Dynamic Mode Decomposition & Koopman Operators - Goal is production of 2D light bullet Phase velocity in z direction Field confined to waveguides with Bragg Grating Contact layer pumps 0th waveguide

11 Dynamic Mode Decomposition
- Goal is production of 2D light bullet Phase velocity in z direction Field confined to waveguides with Bragg Grating Contact layer pumps 0th waveguide

12 Regression to Dynamical Systems
Linear dynamics (equation-free) Eigenfunction expansion - Goal is production of 2D light bullet Phase velocity in z direction Field confined to waveguides with Bragg Grating Contact layer pumps 0th waveguide Least-square fit

13 Multi-Scale Physics - Goal is production of 2D light bullet
Phase velocity in z direction Field confined to waveguides with Bragg Grating Contact layer pumps 0th waveguide

14 El Nino data (1990s-2010+) - Goal is production of 2D light bullet
Phase velocity in z direction Field confined to waveguides with Bragg Grating Contact layer pumps 0th waveguide

15 Compressive DMD & Control
- Goal is production of 2D light bullet Phase velocity in z direction Field confined to waveguides with Bragg Grating Contact layer pumps 0th waveguide

16 With Yu Hu, Eric Shea-Brown, Steve Brunton, Nick Cain & Stefan Mihalas
Dynamic Networks & Functionality With Yu Hu, Eric Shea-Brown, Steve Brunton, Nick Cain & Stefan Mihalas - Goal is production of 2D light bullet Phase velocity in z direction Field confined to waveguides with Bragg Grating Contact layer pumps 0th waveguide

17 Network Motifs - Goal is production of 2D light bullet
Phase velocity in z direction Field confined to waveguides with Bragg Grating Contact layer pumps 0th waveguide

18 Engineering Second Order Motifs
- Goal is production of 2D light bullet Phase velocity in z direction Field confined to waveguides with Bragg Grating Contact layer pumps 0th waveguide Yu Hu, Brunton …. Kutz, Shea-Brown, arxiv 2015 (soon)

19 Bringing It All Together
- Goal is production of 2D light bullet Phase velocity in z direction Field confined to waveguides with Bragg Grating Contact layer pumps 0th waveguide

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