Grand Challenges in Computational Mathematics: Numerical, Symbolic and Algebraic Computing An NSF...
-
date post
18-Dec-2015 -
Category
Documents
-
view
216 -
download
1
Transcript of Grand Challenges in Computational Mathematics: Numerical, Symbolic and Algebraic Computing An NSF...
Grand Challenges in Computational Mathematics:
Numerical, Symbolic and Algebraic Computing
An NSF ViewLenore M. MullinProgram Director
CISE CCFTheoretical Foundations Cluster
National Science Foundation
2Mullin, 26 April, 2007 ACAT 2007 Amsterdam
Outline• NSF Overview
– CISE and CCF– Theoretical Foundations
• Numeric, Symbolic, and Algebraic Computing and Optimizations
• Grand Challenges in the Theoretical Foundations of Computational Mathematics
4Mullin, 26 April, 2007 ACAT 2007 Amsterdam
CCFComputing and
CommunicationsFoundations
CNSComputer and
NetworkSystems
IISInformation and
IntelligentSystems
Office of theAssistant Director
for CISE
OCIOffice of
Cyberinfra-structure
(formerly SCI, now an NSF-wide mission, reporting to Director of NSF
since 2006)
Office of the Director
Clusters ClustersClusters
Crosscutting CISE Emphasis Areas
• EMT• CPA• TF
• NeTS• CSR• CRI
• HCC• III• RI
CISE Organization
5Mullin, 26 April, 2007 ACAT 2007 Amsterdam
Computing andCommunication Foundations
Division (CCF)• Emerging Models and Technologies for Computation (EMT)– computational algorithms and simulation techniques for nanoscale systems;
design and architecture of systems based on molecular scale devices; quantum algorithms for computation, communication, and coding; realization of quantum computing; algorithms and computational modeling of biological processes; computing models and systems for future technologies.
• Computing Processes and Artifacts (CPA)– software design methodologies; tools for software testing, analysis, and
verification; semantics, design, and implementation of programming languages; micro-architectures; memory and I/O subsystems; application-specific architectures; performance metrics; VLSI electronic design; analysis, synthesis and simulation algorithms; system-on-a-chip; architecture and design for mixed or future media (e.g., nanotechnology).
• Theoretical Foundations (TF)– models of computation; computational complexity; parallel and distributed
computation; random and approximate algorithms; algorithmic algebra, geometry, topology, and logic; computational optimization; computational algorithms for high-end scientific and engineering applications; techniques for representing, coding and transmitting information; mobile communication; optical communication; signal processing systems; analysis of images, video, and multimedia information.
6Mullin, 26 April, 2007 ACAT 2007 Amsterdam
NewPhysics, Biology, Chemistry, Economics, Geosciences, Statistics…
Computational Discovery
Data
Core Concept ExperimentTheory
Visualization, simulation, Computational Science
Interpretation
InsightsDomains of inquiry
ManufacturingProcesses
Statistical learning
DNA Transcription
Current
Computational Computational DiscoveryDiscovery
7Mullin, 26 April, 2007 ACAT 2007 Amsterdam
Underlying Themes
• Exploring and modeling nature’s interactions, connections, complex relations, and interdependencies, scaling from sub-particles to galactic, from cellular to societal, in microns to light years, in order to understand them, mimic them, synthesize them, and exploit them (examples include science of design, theory of networked computing, plant genomics, control systems, management sciences, prediction, risk assessment, decision making, distributed data driven application systems, sustainability engineering, social, behavioral sciences, economics, politics…)
• Coupling of the physical world with the cyber world, integrating natural sciences with social, and computing sciences and engineering (examples include logistical systems, supply chains, power networks, all sensor related applications, signal processing, quantum computing, molecular computing, bioinformatics, communications systems, cognitive sciences, learning, artificial intelligence, biomedical engineering applications, human computer interface, virtual or smart environments, health systems, interactive games…)
8Mullin, 26 April, 2007 ACAT 2007 Amsterdam
Moore’s Law: Data Density Doubles every 18 Months
EXCEPT Notice flattening of slope due to Compilers
1850 1950 20001900 2050
10-6
103
1
10-3
106
109
Babbage Engine
CMOS ICs
TX-2
ENIAC
Differential Analyzer
GeneralArchitecture
Lattice-GasArchitecture
Quantum Dots
Liquid NMR
Conve
ntio
nal C
ompu
ter R
oadm
ap
QC
Roa
dmap
MIPS
Year
9Mullin, 26 April, 2007 ACAT 2007 Amsterdam
Proebsting’s Law:Compiler Advances Double Computing Power Every 18 Years
This means that while hardware computing horsepower increases at roughly 60%/year, compiler optimizations contribute only 4%.
1850 1950 20001900 2050
10-6
103
1
10-3
106
109
Babbage Engine
CMOS ICs
TX-2
ENIAC
Differential Analyzer
GeneralArchitecture
Lattice-GasArchitecture
Quantum Dots
Liquid NMR
Conve
ntio
nal C
ompu
ter R
oadm
ap
QC
Roa
dmap
MIPS
Year
10Mullin, 26 April, 2007 ACAT 2007 Amsterdam
Why do we need Grand Challenges?
• Moore’s Law slope flattens out• Moore’s Law slope eventually declines• Software can not keep up with hardware
advances• How can we put a stop to these declines?• How can we verify correctness of
– Semantics– Performance
• Time, Space, Power, Heat, etc.
11Mullin, 26 April, 2007 ACAT 2007 Amsterdam
Grand Challenge Motivating Questions
• What have we learned (to date) about Computational Mathematics? – Are programming languages closed under an
algebra?• For numerical computing• For symbolic computing• For algebraic computing• For optimizations in all the above
– Can we verify programs?• Semantically?• Operationally?
12Mullin, 26 April, 2007 ACAT 2007 Amsterdam
Grand Challenge Motivating Questions
– Are there data structures with deterministic characteristics?
• For Layout and storage• That are pervasive across scientific disciplines
– DSP– Computational Quantum Mechanics– …
• That are Closed under one algebra– Can we describe decomposition and
mappings of such data structures to processor/memory hierarchies using the same algebra?
• For Block, cyclic, block-cyclic, etc decompositions• Over Cache, Main, Shared, Distributed, Grid, etc.
memories
13Mullin, 26 April, 2007 ACAT 2007 Amsterdam
Grand Challenge Motivating Questions
– Can we abstract computing architectures using the same algebra?
• For RASCs?• Quantum Computers?• Combined RASC/Quantum/… Computers• For FPGA and ASICS?• …
– Can we create tools that can theoretically predict performance attributes prior to execution?
• That Interface to compilers or translators?• That are Domain specific?
– Experimental Methods?• Can we create Reproducible computational experiments?
– In time, space, power, etc.• Provide Numerical stability when there are enormous numbers of
processors and communications networks working on one problem?
14Mullin, 26 April, 2007 ACAT 2007 Amsterdam
Grand Challenge Motivating Questions
Can we build software to keep up with Moore’s Law?
15Mullin, 26 April, 2007 ACAT 2007 Amsterdam
Where is the Research Needed?
• What disciplines?– How do they work together?
• What theories? New?
• What curriculums?– BS, MS, PhD– Within existing university department
structures?– K-12?
16Mullin, 26 April, 2007 ACAT 2007 Amsterdam
What is Computational Science and Engineering?
Mathematics
Physical Sciences and Biological Sciences
Computer Science and Engineering
X
X = The Intersection of Domain Sciences, Mathematics andComputer Science and Engineering
17Mullin, 26 April, 2007 ACAT 2007 Amsterdam
Theoretical Grand Challengesfor Computational Mathematics:
Numerical, Symbolic, and Algebraic Computing
• The Theory of Computing– Mathematical Models of Computation
• Is the Turing Model sufficient for complex parallel and distributed multilevel-memory architectures and grids?
• Is the Turing Model sufficient for Quantum Computers?
• What are the data structures, algorithms, and algebras pervasive in science worthy of domain specific languages, tools, and architectures/networks such that a deterministic analysis is possible?
– Could we then theorize about performance? Predictable reproducible performance? On any machine/network? Verify semantics as well as operational costs? …
18Mullin, 26 April, 2007 ACAT 2007 Amsterdam
NSF and the Research Community
• Need the Research community to address questions posed
• Need the Research community to cross disciplinary lines
• Need the Academic community to cross disciplinary lines
• Develop Academic and Research Programs to address initiatives
19Mullin, 26 April, 2007 ACAT 2007 Amsterdam
NSF and the International Community
• OISE– Small research initiation with funding organizations in other
countries• Promote collaborations, teams
– Example: This week at NSF Title: How to Cooperate with European Commission Research Programs What are the European Union research programs? What is Framework Programme VII (FP7)? What is the new European Research Council (ERC)?Come and find out at panel discussion featuring:
Lou Brown, GEO Carmen Huber, DMR/ MPS Jeanne Hudson, OISE/O/D Suzi Iacono, CNS/CISE
Where: Room 375 When: Monday, April 23 Time: 10:30 a.m.
20Mullin, 26 April, 2007 ACAT 2007 Amsterdam
NSF and the International Community
• Add-ons to individual reseach grants– Student/faculty exchanges– Conferences and Workshops– Jointly with EC, e.g. initial workshop in
Europe.• Fund researchers from US to Europe
– Foster connections with researchers in European Research Agencies
» EC. …
21Mullin, 26 April, 2007 ACAT 2007 Amsterdam
Contact Information
Lenore M. Mullin
CISE/CCF
Theoretical Foundations
(703) [email protected]