Presentation in the Future of Fluids session of AIAA Aviation Meeting 2018

1. Data-driven discovery of governing
physical laws and their parametric
dependencies in the engineering
and physical sciences
J. Nathan Kutz
Department of Applied Mathematics
University of Washington
Seattle, WA 98195-3925
Email: kutz@uw.edu
June 28, 2018 – AIAA 2018
Steven Brunton
Mechanical Engineering
University of Washington

2. Ax=b

3. Governing Dynamical Systems
Generic
nonlinear
,
time-­‐dependent,
parametric
system
Measurements
(assimilation)

4. What Could the Right Side Be?
Limited
by
your
imagination
2nd degree
polynomials

5. Sparse Identification of Nonlinear Dynamics (SINDy)

6. Discovering PDEs
Sam Rudy, Brunton, Proctor & Kutz, Sci Adv (2017)
Sam Rudy

7. Lagrangian Measurements

8. Disambiguation

10. Parametric Burgers

11. Group Sparsity

12. Parametric Discovery
Group
LASSO
vs
Sequential
Group
Threshold
Regression
(SGTR)
Our
innovation:
SGTR
(works
amazingly
well!)

13. Parametric Dependence

14. Spatial Dependence

15. What is this?

16. Limits of Model Discovery
Champion, Brunton, & Kutz, arxiv (2018)

17. Multiscale Physics Discovery

18. Experiments

19. Arduino Magic
Taren Gorman

20. Pendulum Discovery

21. Conclusions
Model
Selection
&
Sparse
Regression
Matter
- Principled approach to determining dynamics
- (i) classification, (ii) reconstruction, (iii) future state prediction
- Sensors should be maximally informative