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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

Conferences

Preprints

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