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arXiv · 1306.4690

Model Reduction with MapReduce-enabled Tall-and-Skinny Singular Value Decomposition

Paul G. Constantine·David F. Gleich·Yangyang Hou·Jeremy Templeton
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Abstract

We present a method for computing reduced-order models of parameterized partial differential equation solutions. The key analytical tool is the singular value expansion of the parameterized solution, which we approximate with a singular value decomposition of a parameter snapshot matrix. To evaluate the reduced-order model at a new parameter, we interpolate a subset of the right singular vectors to generate the reduced-order model's coefficients. We employ a novel method to select this subset that uses the parameter gradient of the right singular vectors to split the terms in the expansion yielding a mean prediction and a prediction covariance---similar to a Gaussian process approximation. The covariance serves as a confidence measure for the reduce order model. We demonstrate the efficacy of the reduced-order model using a parameter study of heat transfer in random media. The high-fidelity simulations produce more than 4TB of data; we compute the singular value decomposition and evaluate the reduced-order model using scalable MapReduce/Hadoop implementations. We compare the accuracy of our method with a scalar response surface on a set of temperature profile measurements and find that our model better captures sharp, local features in the parameter space.

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Paul G. Constantine, David F. Gleich, Yangyang Hou, Jeremy Templeton. 2013-10-10. Model Reduction with MapReduce-enabled Tall-and-Skinny Singular Value Decomposition. https://doi.org/10.1137/130925219

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