What Does Paul Constantine Do?

A nontechnical overview presentation to the applied math and statistics grad students (and whoever else stops by) on my work. Presented Oct 7, 2015.

Transcript

1. PAUL CONSTANTINE Ben L. Fryrear Assistant Professor Applied Mathematics and Statistics WHAT DOES PAUL CONSTANTINE DO? AMS Grad Student Presentation SLIDES: DISCLAIMER: These slides are meant to complement the oral presentation. Use out of context at your own risk. WEB PRESENCE inside.mines.edu/~pconstan activesubsapces.org tinyurl.com/paul-gscholar twitter.com/DrPaulynomial facebook.com/paul.g.constantine youtube.com/c/paulcon feedly.com/paulconstantine
3. Ben L. Fryrear Assistant Professorship $250k / 4 years, 2 students DOE Office of Science Advanced Scientific Computing Research With UT Austin and MIT, $1.1M / 3 years Lead PI, $300k DARPA EQUiPS With Stanford, Michigan, and Sandia, $4.5M / 3 years Mines PI, $450k NSF DMREF Lead PI Geoff Brennecka, $1.5M / 5 years $33k / 5 years
4. 2015 Constantine, Eftekhari, Wakin. Computing active subspaces efficiently with gradient sketching. CAMSAP ‘15 Constantine, Emory, Larsson, Iaccarino. Exploiting active subspaces to quantify uncertainty in the numerical simulation of the HyShot II scramjet. J of Computational Physics Jefferson, Gilbert, Constantine, Maxwell. Active subspaces for sensitivity analysis and dimension reduction of an integrated hydrologic model. Computers and Geosciences Constantine, Zaharatos, Campanelli. Discovering an active subspace in a single- diode solar cell model. Statistical Analysis and Data Mining 2014 Constantine, Dow, Wang. Active subspace methods in theory and practice: Applications to kriging surfaces. SIAM J of Scientific Computing Constantine, Phipps, Wildey. Efficient uncertainty propagation for network multiphysics systems. International J of Numerical Methods in Engineering Constantine, Gleich, Hou, Templeton. Model reduction with MapReduce-enabled tall and skinny singular value decomposition. SIAM J of Scientific Computing
5. $27 VISIT THE SIAM BOOKSTORE! Coupon code: BKSL15
6. Paul Diaz MS 2016 DOE funded Zach Grey PhD 2019 Fryrear Fellow Kerrek Stinson BS 2016 DOE funded Andrew Glaws PhD 2018 Fryrear Fellow
7. THE POSTDOC?
8. Brian Zahartos PhD 2015 Lecturer at CU Boulder Applied Math Constantine, Zaharatos, Campanelli. Discovering an active subspace in a single-diode solar cell model (2015) Carson Kent BS 2015 DOE CSGF Stanford ICME for grad school Constantine, Kent, Bui-Thanh. Accelerating MCMC with active subspaces (In review 2015)
9. Trent Lukaczyk PhD 2015 Stanford Aero-Astro “Startup” Pranay Seshadri PhD 2015 Cambridge ME Postdoc at Vanderbilt Lukaczyk, Palacios, Alonso, and Constantine. Active subspaces for shape optimization. AIAA SciTech (2014) Seshadri, Constantine, Iaccarino, Parks. A density-matching approach for optimization under uncertainty (In review 2015)
12. Structure for an applied mathematician.
13. Structure for an engineer.
14. + numerical analysis + coding skillz Structure for a computational scientist.
15. www.youtube.com/watch?v=OAKSQgPGkCg
16. f( x )
17. f( x ) Uncertainty quantification for hypersonic scramjets (with G. Iaccarino, J. Larsson, M. Emory) Sensitivity analysis in hydrological models (with R. Maxwell, J. Jefferson, J. Gilbert) Shape optimization in aerospace vehicles (with J. Alonso, T. Lukaczyk)
18. APPROXIMATION OPTIMIZATION INTEGRATION ˜ f( x ) ⇡ f( x ) Z f( x ) ⇢ d x minimize x f( x )
19. How many dimensions is high dimensions?
20. Dimension 10 points / dimension 1 second / evaluation 1 10 10 sec 2 100 ~ 1.6 min 3 1,000 ~ 16 min 4 10,000 ~ 2.7 hours 5 100,000 ~ 1.1 days 6 1,000,000 ~ 1.6 weeks … … … 20 1e20 3 trillion years (240x age of the universe) DIMENSION REDUCTION BETTER DESIGNS REDUCED-ORDER MODELS
21. METHOD STRUCTURE
22. www.youtube.com/watch?v=mJvKzjT6lmY
23. f( x ) ⇡ g ⇣ ˆ W T 1 x ⌘ How do you construct g? What is the approximation error? How do you choose these weights? Active subspaces help answer …
24. IMPACT
25. Paul discovers and exploits low-dimensional structure in complex simulations with lots of parameters to help scientists and engineers learn about their models. WHAT DOES PAUL CONSTANTINE DO? IN BUZZWORDS… •  active subspaces •  reduced-order models •  dimension reduction •  applied approximation theory •  uncertainty quantification •  computational science IN MATH… f( x ) ⇡ g ⇣ ˆ W T 1 x ⌘
26. •  You hardly mentioned uncertainty quantification. •  Where does statistics fit in? •  What kind of math do you use? •  How often do you find active subspaces? •  Tell me about an open problem in your research. •  How new is all this? QUESTIONS?