Accession Number ADA564054
Title Overcoming the Curse of Dimension: Methods Based on Sparse Representation and Adaptive Sampling.
Publication Date Feb 2011
Media Count 5p
Personal Author E. Weinan
Abstract 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.
Keywords Adaptive systems
Boltzmann equation
Configurations
Curse of dimension
Effective sampling methods
Grids
Rare events
Sparse grids

 
Source Agency Non Paid ADAS
NTIS Subject Category 46 - Physics
Corporate Author Princeton Univ., NJ. Dept. of Mathematics.
Document Type Technical report
Title Note Final rept. 15 Aug 2008-30 Nov 2010.
NTIS Issue Number 1302
Contract Number FA9550-08-1-0433

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