A Posteriori Error Analysis of Stochastic Differential Equations Using Polynomial Chaos Approximations
Abstract not provided.
Publications
Statistical surrogate models for prediction of high-consequence climate change
In safety engineering, performance metrics are defined using probabilistic risk assessments focused on the low-probability, high-consequence tail of the distribution of possible events, as opposed to best estimates based on central tendencies. We frame the climate change problem and its associated risks in a similar manner. To properly explore the tails of the distribution requires extensive sampling, which is not possible with existing coupled atmospheric models due to the high computational cost of each simulation. We therefore propose the use of specialized statistical surrogate models (SSMs) for the purpose of exploring the probability law of various climate variables of interest. A SSM is different than a deterministic surrogate model in that it represents each climate variable of interest as a space/time random field. The SSM can be calibrated to available spatial and temporal data from existing climate databases, e.g., the Program for Climate Model Diagnosis and Intercomparison (PCMDI), or to a collection of outputs from a General Circulation Model (GCM), e.g., the Community Earth System Model (CESM) and its predecessors. Because of its reduced size and complexity, the realization of a large number of independent model outputs from a SSM becomes computationally straightforward, so that quantifying the risk associated with low-probability, high-consequence climate events becomes feasible. A Bayesian framework is developed to provide quantitative measures of confidence, via Bayesian credible intervals, in the use of the proposed approach to assess these risks.
Tall and skinny QR factorizations in MapReduce architectures
MapReduce'11 - Proceedings of the 2nd International Workshop on MapReduce and Its Applications
The QR factorization is one of the most important and useful matrix factorizations in scientific computing. A recent communication-avoiding version of the QR factorization trades flops for messages and is ideal for MapReduce, where computationally intensive processes operate locally on subsets of the data. We present an implementation of the tall and skinny QR (TSQR) factorization in the MapReduce framework, and we provide computational results for nearly terabyte-sized datasets. These tasks run in just a few minutes under a variety of parameter choices. © 2011 ACM.
A Stieltjes-Lanczos procedure for parameterized matrix problems
Abstract not provided.
A posteriori error analysis of parameterized linear systems using spectral methods
SIAM Journal on Matrix Analysis and Applications
Abstract not provided.
CO2 Inversion using Ensemble Kalman Filtersand Reduced Order Models
Abstract not provided.
Computational methods for parameterized matrix equations
Abstract not provided.
7 Results