Overcoming the Curse of Dimension: Methods Based on Sparse Representation and Adaptive Sampling
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.
Document Details
- Document Type
- Technical Report
- Publication Date
- Feb 28, 2011
- Accession Number
- ADA564054
Entities
People
- E. Weinan
Organizations
- Princeton University