Focus Group: Computational Applied Mathematics
 
Multigrid/Multilevel Methods Wavelets Fast Multipole Methods (FMM) Randomized fast algorithms for approximation of Singular Value Decomposition (SVD) of a huge matrix (e.g., 20 seconds to compute a rank-10 approximation of a matrix of size 1,000,000 x 1,000,000 on a highend laptop). Compressive Sensing
By: Lambert
10 months 19 days ago
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Presentation Transcript
Focus Group: Computational Applied Mathematics : Focus Group: Computational Applied Mathematics CSE Retreat University of California January 22, 2007
Introduction : Introduction What we do: Analysis and development of fast, robust, and accurate numerical algorithms and their applications to a variety of problems Key point 1: Data are taking up huge volumes, becoming high dimensional, unorganized, and irregularly distributed Key point 2: Objects (models, data, and operators) are structured → dimension reduction; efficient representations Key point 3: Continuous vs Discrete Key point 4: Deterministic vs Stochastic Key point 5: Multiscale Key point 6: Optimization of increasingly complex models Applications: data mining; feature extraction; data analysis; circuit simulation; wireless communication; imaging science; inverse problems; computational statistics; financial modeling; biological systems; CFD; ...
Introduction…Examples : Introduction…Examples Multigrid/Multilevel Methods Wavelets Fast Multipole Methods (FMM) Randomized fast algorithms for approximation of Singular Value Decomposition (SVD) of a huge matrix (e.g., 20 seconds to compute a rank-10 approximation of a matrix of size 1,000,000 x 1,000,000 on a highend laptop). Compressive Sensing ...
Introduction... : Introduction... Member’s names: Most of GGAM members; some people in other departments Campus community: GGAM Anesthesiology Applied Science Biomedical Engineering Chemical Engineering and Material Science Chemistry Civil and Environmental Engineering Computer Science Electrical and Computer Engineering Environmental Science and Policy Evolution and Ecology Geology Land, Air and Water Resources Mathematics Mechanical and Aeronautical Engineering Physics Radiology Statistics … Existing funding: NSF; DOE; DOD; NIH; other foundations, etc.
Opportunities : Opportunities Larger grants ↔ Attracting good students ↔ High quality research Future Funding: NSF MSPA-MCS (Mathematical Sciences: Innovations at the Interface with Computer Sciences) NSF CPATH (CISE: Pathways to Revitalized Undergraduate Computing Education) DOD/DOE/NIH/NSA … More relationship with industry Opportunities for Interdisciplinary Research & Education: Funding agencies love interdisciplinary research Funding agencies love novel approach to education
Intellectual Overlap : Intellectual Overlap With other focus groups: Computational Applied Mathematics is fundamental to all the focus groups With other campus groups: GGAM, Statistics, CS, ECE, Applied Science, ... With other programs: Computational Applied Mathematics is fundamental to any program that uses computation
What we need… : What we need… A vehicle to attract top students! In the context of a CSE Research Center: Annual workshops (one or two) by inviting top people in some targeted fields Occasional forums to interact, discuss, and present current research projects among participants Research seminar series by inviting top people Interdisciplinary reading seminars/journal clubs In the context of CSE Education: Structure of offering graduate (and possibly undergraudate) degrees and courses Programming courses Cross-listing appropriate courses A mechanism of reward/encouragement for activities!!