My research interests fall in the category of uncertainty quantification (UQ), which attempts to formulate and compute measures of confidence for physics and engineering simulations---analogous to confidence measures from physical experiments. In this context, I work on methods for dimension reduction and reduced-order modeling that find cheap and accurate approximations to costly simulations.
I wrote a book on active subspaces for parameter space dimension reduction. Purchase the book for $39 (SIAM member price $27) from the SIAM bookstore.
Here's a review at Amazon UK by Mark Girolami.
Active subspaces: Theory
- Constantine, Kent, and Bui-Thanh. Accelerating Markov chain Monte Carlo with active subspaces. SIAM Journal on Scientific Computing (2016)
- Constantine, Eftekhari, and Ward. A near-stationary subspace for ridge approximation. arXiv:1606.01929 (2016)
- Constantine, del Rosario, and Iaccarino. Many physical laws are ridge functions. arXiv:1605.07974 (2016)
- Stinson, Gleich, and Constantine. A randomized algorithm for enumerating zonotope vertices. arXiv:1602.06620 (2016)
- Constantine and Diaz. Global sensitivity metrics from active subspaces. arXiv:1510.04361v2 (2015)
- Constantine and Gleich. Computing active subspaces with Monte Carlo. arXiv:1408.0545v2 (2015)
- Constantine, Eftekhari, and Wakin. Computing active subspaces efficiently with gradient sketching. IEEE CAMSAP (2015)
- Constantine, Dow, and Wang. Active subspace methods in theory and practice: Applications to kriging surfaces. SIAM Journal on Scientific Computing (2014) Erratum
Active subspaces: Applications
- Constantine and Doostan. Time-dependent global sensitivity analysis with active subspaces for a lithium ion battery model. arXiv:1606.08770 (2016)
- Glaws, Constantine, Shadid, and Wildey. Dimension reduction in MHD power generation models: dimensional analysis and active subspaces. arXiv:1609.01255 (2016)
- Gilbert, Jefferson, Constantine, and Maxwell. Global spatial sensitivity of runoff to subsurface permeability using the active subspace method. Advances in Water Resources (2016)
- Bauerheim, Ndiaye, Constantine, Moreau, and Nicoud. Symmetry breaking of azimuthal thermoacoustic modes: The UQ perspective. Journal of Fluid Mechanics (2016)
- Constantine, Emory, Larsson, and Iaccarino. Exploiting active subspaces to quantify uncertainty in the numerical simulation of the HyShot II scramjet. Journal of Computational Physics (2015)
- Jefferson, Gilbert, Constantine, and Maxwell. Active subspaces for sensitivity analysis and dimension reduction of an integrated hydrologic model. Computers & Geosciences (2015)
- Constantine, Zaharatos, and Campanelli. Discovering an active subspace in a single-diode solar cell model. Statistical Analysis and Data Mining: The ASA Data Science Journal (2015)
- Lukaczyk, Palacios, Alonso, and Constantine. Active subspaces for shape optimization. AIAA SciTech (2014)
- Constantine, Gleich, Hou, and Templeton. Model reduction with MapReduce-enabled tall and skinny singular value decomposition. SIAM Journal on Scientific Computing (2014)
- Constantine and Iaccarino. Reduced order models for conservations laws with shock reconstruction . Center for Turbulence Research Annual Brief (2012)
- Constantine and Wang, Residual minimizing model reduction for parameterized nonlinear dynamical systems. SIAM Journal on Scientific Computing (2012)
- Constantine and Gleich. Tall and skinny QR factorizations in MapReduce architectures. MAPREDUCE 2011: The Second International Workshop on MapReduce and its Applications
Polynomial approximation methods in UQ
- Constantine, Phipps, and Wildey. Efficient uncertainty propagation for network multiphysics systems. International Journal for Numerical Methods in Engineering (2014)
- Constantine, Eldred, and Phipps. Sparse pseudospectral approximation method. Computer Methods in Applied Mechanics and Engineering (2012)
- Constantine and Phipps. A Lanczos method for approximating composite functions. Applied Mathematics and Computation (2012)
- Butler, Constantine, and Wildey. A posteriori error analysis of parameterized linear systems using spectral methods. SIAM Journal on Matrix Analysis and Applications (2012)
- Constantine, Gleich, and Iaccarino. A factorization of the spectral Galerkin system for parameterized matrix equations: Derivation and applications. SIAM Journal on Scientific Computing (2011)
- Constantine, Gleich, and Iaccarino. Spectral methods for parameterized matrix equations. SIAM Journal on Matrix Analysis and Applications (2010)
- Constantine, Doostan, and Iaccarino. A hybrid collocation/Galerkin scheme for convective heat transfer problems with stochastic boundary conditions. International Journal for Numerical Methods in Engineering (2009)
- Constantine. Spectral methods for parameterized matrix equations. Stanford Ph.D. Thesis (2009)
- Constantine. A primer on stochastic Galerkin methods. Stanford UQ Technical Report (2007)
I give a lot of talks. I use SpeakerDeck and Prezi to make some of my presentations available. SpeakerDeck takes PDF files, and I usually use Powerpoint for slides. Converting Powerpoint to PDF removes any animations or movies.
Here are some places where I make code available. Links to my respective community profiles in the images.