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Overcoming the Curse of Dimension: Methods Based on Sparse Representation and Adaptive Sampling
Final rept. 15 Aug 2008-30 Nov 2010
PRINCETON UNIV NJ DEPT OF MATHEMATICS
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A major issue in modeling and computation is how to handle high dimensional problems. We can divide these high dimensional problems into two classes Moderately high dimensional problems or very high dimensional problems. In the former class, we have problems such as the Boltzmann equation, whose dimensionality is high but they are still amendable to grid-based methods. In the latter class we have problems such as exploration of the configuration space of a large molecule. These problems often involve hundreds of thousands of dimensions, and methods based on fixed grids are far from being adequate. We have explored various ways of handling these problems using the sparse representation or the adaptive sampling.
APPROVED FOR PUBLIC RELEASE