Dynamic Active Subspaces

Doc 27-09-2017, 10-58 PM

Masters Thesis work at the University of Colorado, Boulder.

PRESENTATIONS
-Aguiar, I. (2018, April). “Visualizing dynamic global sensitivities in time-dependent systems with active subspaces.” Poster presentation at the SIAM Conference on Uncertainty Quantification. Orange County, CA.
-Aguiar, I. (2018, April). “Active Subspaces in Parameterized Dynamical Systems”. Contributed presentation at the SIAM Conference on Uncertainty Quantification. Orange County, CA.
-Aguiar, I. (2018, March). “Active Subspaces in Parameterized Dynamical Systems”. Poster presentation at the DOE Conference on Data Analysis. Santa Fe, NM.
-Aguiar, I. (2018, Feb). “Dynamic Active Subspaces”. Complex and Dynamical Systems Seminar. Boulder, CO.
-Aguiar, I. (2018, Feb). “Dynamic Active Subspaces”. Auckland Conference for Numerical ODEs. Auckland, NZ
-Aguiar, I. (2018, Jan). “Active Subspaces in Parameterized Dynamical Systems”. Presentation at Joint Mathematics Meetings session on Dynamic and Ergodic Theory. San Diego, CA.
-Aguiar, I. (2018, Jan). “Active Subspaces in Parameterized Dynamical Systems”. Ignite talk and poster presentation at 2018 US Dynamics Days Conference. Denver, CO.
-Aguiar, I. (2017, July). “Dynamic Active Subspaces”. Poster presentation at the SIAM Workshop on Parameter Space Dimension Reduction. Pittsburgh, PA.
-Aguiar, I. (2017, July). “Dynamic Active Subspaces”. Poster presentation at the SIAM Annual Meeting (AN17). Pittsburgh, PA.
(SIAM AN17 Poster)(Mini-Book)

For an introduction to my research, check out these (Informational Slides)

This research explores the concepts of parameter space dimension reduction for dynamical systems using active subspaces. Analysis, dynamic mode decomposition (DMD), sparse identification for nonlinear dynamic systems (SINDy), and other methods are implemented to discover and reconstruct active subspaces for time-dependent systems. Such methods allow us to build dynamical systems that model parameter sensitivity over time for a specific state of the original system.

REFERENCES

[1] Constantine, P. G. Active Subspaces: Emerging Ideas for Dimension Reduction in Parameter Studies. SIAM, Philadelphia (2015).

[2] Keener, J. and Sneyd, J. Mathematical Physiology I: Cellular Physiology. Interdisciplinary Applied Mathematics. Springer, New York, 2nd Edition (2009).

[3] Louden, T. and Pankavich, S. Mathematical Analysis and Dynamic Active Subspaces for a Long term model of HIV (2016).

[4] Kutz, J. N., Brunton, S., Brunton, B., and Proctor, J. Dynamic Mode Decomposition: Data-Driven Modeling of Complex Systems. SIAM, Philadelphia (2016).

[5] Brunton, S., Proctor, J., and Kutz, J. N. Discovering governing equations from data by sparse identification of nonlinear dynamical systems. PNAS (2016).