Lenore M. Mullin Program Director CISE CCF Theoretical Foundations Cluster

1. Grand Challenges in Computational Mathematics: Numerical, Symbolic and Algebraic ComputingAn NSF View Lenore M. Mullin Program Director CISE CCF Theoretical Foundations Cluster National Science Foundation

2. NSF Overview CISE and CCF Theoretical Foundations Numeric, Symbolic, and Algebraic Computing and Optimizations Grand Challenges in the Theoretical Foundations of Computational Mathematics Outline ACAT 2007 Amsterdam

3. National Science Foundation ACAT 2007 Amsterdam

4. CISE Organization Office of the Director Office of the Assistant Director for CISE CCF Computing and Communications Foundations CNS Computer and Network Systems IIS Information and Intelligent Systems OCI Office of Cyberinfra- structure (formerly SCI, now an NSF-wide mission, reporting to Director of NSF since 2006) Clusters Clusters Clusters • NeTS • CSR • CRI • HCC • III • RI • EMT • CPA • TF Crosscutting CISE Emphasis Areas ACAT 2007 Amsterdam

5. 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. Computing andCommunication Foundations Division (CCF) ACAT 2007 Amsterdam

6. Computational Discovery DNA Transcription Manufacturing Processes Computational Discovery Statistical learning Insights Domains of inquiry Physics, Biology, Chemistry, Economics, Geosciences, Statistics… Theory Core Concept Experiment Interpretation Data Visualization, simulation, Computational Science Current New ACAT 2007 Amsterdam

7. 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…) Underlying Themes ACAT 2007 Amsterdam

8. Moore’s Law:Data Density Doubles every 18 MonthsEXCEPT Notice flattening of slope due to Compilers CMOS ICs General Architecture 109 106 TX-2 Lattice-Gas Architecture 103 QC Roadmap MIPS 1 ENIAC Quantum Dots 10-3 Conventional Computer Roadmap 10-6 Differential Analyzer Year 1850 1900 2000 1950 2050 ACAT 2007 Amsterdam Liquid NMR Babbage Engine

9. Proebsting’s Law:Compiler Advances Double Computing Power Every 18 YearsThis means that while hardware computing horsepower increases at roughly 60%/year, compiler optimizations contribute only 4%. General Architecture 109 CMOS ICs 106 Lattice-Gas Architecture TX-2 103 QC Roadmap MIPS 1 ENIAC Quantum Dots 10-3 Conventional Computer Roadmap 10-6 Differential Analyzer Year 1850 1900 2000 1950 2050 ACAT 2007 Amsterdam Liquid NMR Babbage Engine

10. 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. Why do we need Grand Challenges? ACAT 2007 Amsterdam

11. 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? Grand Challenge Motivating Questions ACAT 2007 Amsterdam

12. 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 Grand Challenge Motivating Questions ACAT 2007 Amsterdam

13. 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? Grand Challenge Motivating Questions ACAT 2007 Amsterdam

14. Can we build software to keep up with Moore’s Law? Grand Challenge Motivating Questions ACAT 2007 Amsterdam

15. What disciplines? How do they work together? What theories? New? What curriculums? BS, MS, PhD Within existing university department structures? K-12? Where is the Research Needed? ACAT 2007 Amsterdam

16. What is Computational Science and Engineering? Computer Science and Engineering Physical Sciences and Biological Sciences X Mathematics X = TheIntersectionofDomain Sciences, Mathematicsand Computer Science and Engineering ACAT 2007 Amsterdam

17. 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? … Theoretical Grand Challengesfor Computational Mathematics:Numerical, Symbolic, and Algebraic Computing ACAT 2007 Amsterdam

18. 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 NSF and the Research Community ACAT 2007 Amsterdam

19. 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. NSF and the International Community ACAT 2007 Amsterdam

20. 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. … NSF and the International Community ACAT 2007 Amsterdam

21. Lenore M. Mullin CISE/CCF Theoretical Foundations (703) 292-8910 lmullin@nsf.gov Contact Information ACAT 2007 Amsterdam