PAUL CONSTANTINE Ben L. Fryrear Assistant Professor Applied Mathematics & Statistics Colorado School of Mines activesubspaces.org! @DrPaulynomial! DISCLAIMER: These slides are meant to complement the oral presentation. Use out of context at your own risk.
Wang Aeronautics and Astronautics Youssef Marzouk Aeronautics and Astronautics Reed Maxwell Hyrdological Science & Engineering Michael Wakin Electrical Engineering Stephen Pankavich Applied Mathematics Tan Bui-Thanh Aerospace Engineering David Gleich Computer Science Michael Eldred Optimization & Uncertainty Quantification John Shadid Computational Mathematics
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)
B. Zaharatos, M. Campanelli) Sensitivity analysis in HIV modeling (with T. Loudon, S. Pankavich) Sensitivity analysis in Ebola transmission models (with P. Diaz, S. Pankavich) Calibration of an atmospheric reentry vehicle model (with P. Congedo, T. Magin)
10 points per dimension) Time for parameter study (at 1 second per run) 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) REDUCED-ORDER MODELS BETTER DESIGNS DIMENSION REDUCTION
x )T ⇢( x ) d x = W ⇤W T The dominant eigenspace of a matrix derived from the model’s gradient gradient of the model output averaged over the input space eigenvalue decomposition
of pressures at the channel exit? P. Constantine, M. Emory, J. Larsson, and G. Iaccarino Exploiting active subspaces to quantify uncertainty in the numerical simulation of the HyShot II scramjet Journal of Computational Physics (2015)
of models does this work on? How new is all this? PAUL CONSTANTINE Ben L. Fryrear Assistant Professor Applied Mathematics & Statistics Colorado School of Mines activesubspaces.org! @DrPaulynomial! QUESTIONS?