## Research Projects

Most of my current research activities focus on the practical challenges associated with characterizing the uncertainties in the predictions from physical simulations. These tend to fall under the large umbrella of*uncertainty quantification*(UQ). Here are a few of my current projects.

### Simulation Informatics

As computing power for simulation-based analysis approaches the exascale, the need will arise for practical, efficient, and robust exascale data management and analysis. Modern physical simulations produce prodigious amounts of data that must be compared to experiments, theory, and other simulations. Moreover, simulation results contain uncertainties that typically require an ensemble of runs to characterize. We are exploring the application of scalable informatics and machine learning methods to the outputs of physical simulations, where theoretical insights from the physical models inform the choice of learning methods.

I am particularly interested in model reduction methods. Given a database of simulation outputs at select points in the input space, can we efficiently approximate the outputs at other points in the input space without running the simulation code? This question leads to many explorations in reduced order models, surrogate models, and interpolation methods.

Joint with David Gleich, Qiqi Wang, and Jeremy Templeton (Sandia). Funded by Sandia National Labs' Computer Science Applied Research program.

### Uncertainty Quantification for Coupled Multi-physics Models

Two persistent challenges in uncertainty quantification are (i) the high computational cost of repeated runs of a physical simulation and (ii) the exponential increase in the work required by UQ methods as the dimension of the input space increases. These challenges meet in multi-physics models, where each component model has its own independent sources of uncertainty; the effects of these sources are coupled together through the physical model. The full system can be treated as a single physical model with a set of inputs. Alternatively, we may be able to take advantage of the coupling interface to apply methods on an input space of reduced dimension. Toward this goal, we are exploring dimension reduction techniques and alternative methods for quadrature that take advantage of the structure of the multi-physics model.

Joint with Eric Phipps, Tim Wildey, and John Red-Horse (Sandia). Funded by DOE Office of Science's Applied Mathematics program.

## Papers

Here's a list of my papers; I'll do my best to keep this updated. You can also see all the things Google Scholar finds with my name it here!### Journals

- Constantine and Wang.
*Residual Minimizing Model Reduction for Parameterized Nonlinear Dynamical Systems*. SIAM Journal on Scientific Computing, 34 (2012), pp. A2118–A2144 - Field Jr., Constantine, and Boslough.
*Statistical Surrogate Models for Prediction of High-Consequence Climate Change*. International Journal for Uncertainty Quantification, 2012. Accepted for publication - Constantine, Eldred, and Phipps.
*Sparse Pseudospectral Approximation Method*. Computer Methods in Applied Mechanics and Engineering, 229-232 (2012), pp. 1–12 - Constantine and Phipps.
*A Lanczos Method for Approximating Composite Functions*. Applied Mathematics and Computation, 218 (2012), pp. 11751 – 11762 - Butler, Constantine, and Wildey.
*A Posteriori Error Analysis of Parameterized Linear Systems Using Spectral Methods*. SIAM Journal on Matrix Analysis and Applications, 33 (2012), pp. 195–209 - Constantine, Gleich, and Iaccarino.
*A Factorization of The Spectral Galerkin System for Parameterized Matrix Equations: Derivation and Applications*. SIAM Journal on Scientific Computing, 33 (2011), pp. 2995–3009. (Special Section: 2010 Copper Mountain Conference) - Constantine, Gleich, and Iaccarino.
*Spectral Methods for Parameterized Matrix Equations*. SIAM Journal on Matrix Analysis and Applications, 31 (2010), pp. 2681–2699 - Constantine and Gleich.
*Random Alpha PageRank*. Internet Mathematics, Vol. 6, Number 2, 2010. 198 -- 236 - Constantine, Doostan, and Iaccarino.
*A Hybrid Collocation/Galerkin Scheme for Convective Heat Transfer Problems with Stochastic Boundary Conditions*. IJNME, Vol. 80, November 2009. 868 -- 880

### Conferences

- Constantine and Gleich.
*Distinguising signal from noise in an SVD of simulation data*. IEEE Confrence on Acoustics, Speech, and Signal Processing, 2012 - Constantine and Gleich.
*Tall and Skinny QR factorizations in MapReduce Architectures*. MAPREDUCE, '11 - Constantine, Wang, Doostan, and Iaccarino.
*A Surrogate-Accelerated Bayesian Inverse Analysis of the HyShot II Flight Data*. AIAA-2011-2037 - Chen, Wang, Hu, and Constantine.
*Conditional Sampling and Experiment Design for Quantifying Manufacturing Error of Transonic Airfoil*. AIAA-2011-658 - Gleich, Constantine, Flaxman, and Gunawardana.
*Tracking The Random Surfer: Empirically Measured Teleportation Parameters in PageRank*. WWW2010. Raleigh, NC. April, 2010 - Iaccarino and Constantine.
*Large Eddy Simulations of Flow Around a Cylinder with Uncertain Wall Heating*AIAA-2009-0975 - Eldred, Webster, and Constantine.
*Evaluation of Non-intrusive Approaches for Wiener-Askey Generalized Polynomial Chaos*. AIAA-2008-1892 - Constantine and Gleich.
*Using Polynomial Chaos to Compute the Influence of Multiple Random Surfers in the PageRank Model*. The 5th Workshop On Algorithms And Models For The Web-Graph. San Diego, CA. Dececember 2007

### Preprints

- Constantine, Dow, and Wang.
*Active subspace methods in theory and practice: Applications to kriging surfaces*. arXiv:1304.2070 - Constantine and Iaccarino.
*Reduced order models for conservations laws with shock reconstruction*. Center for Turbulence Research Annual Brief, 2012 - Constantine, Wang, and Iaccarino.
*A method for spatial sensitivity analysis*. Center for Turbulence Research Annual Brief, 2012

### Thesis

## Software

I support the call for reproducible research in computational science.- Parameterized Matrix Package: A MATLAB toolbox for approximation of parameterized matrix equations with multivariate polynomial spectral methods. Available on Mathworks File Exchange.
- Random Field Simulation: A MATLAB toolbox for generating conditional random fields. Available on Mathworks File Exchange.

Last modified Monday, 08-Apr-2013 21:13:12 PDT