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HPC Technology Track: Foundations of Computational Science Lecture 1

Dr. Greg Wettstein, Ph.D. Research Support Group Leader Division of Information Technology Adjunct Professor Department of Computer Science North Dakota State University. HPC Technology Track: Foundations of Computational Science Lecture 1. What is Computational Science?.

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HPC Technology Track: Foundations of Computational Science Lecture 1

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  1. Dr. Greg Wettstein, Ph.D. Research Support Group Leader Division of Information Technology Adjunct Professor Department of Computer Science North Dakota State University HPC Technology Track:Foundations of Computational ScienceLecture 1

  2. What is Computational Science? • Application of computational methods to fundamental problems in science and engineering. • Concerned with application of computational methods to one of three objectives. • Modeling • Simulation • Prediction

  3. Modeling • Involves development of a mathematical model capable of predicting physical phenomenon. • weather prediction • molecular energy and force fields • properties of materials • Typically involves solving systems of differential equations expressed in linear form.

  4. Challenges in Modeling • Currently only order 0 systems can be solved directly. • Computational approaches are frequently implemented with methods involving truncated series. • Garbage In/Garbage out (GIGO) • Limitations constantly demand attention to model parameterization and viability. • The field considers better differential equation solvers to be essential.

  5. Emerging Opportunities in Modeling • Model parameter evaluation. • Considered important by the national laboratories • Involves computation of first and second derivatives of the model with respect to finalized model parameters • Important focus is to determine quality or stability of model. ** Model evaluation is critical.

  6. Multi-Scale Studies • Defn: Calculation of system behavior or properties on one level using information from subordinate levels. • Continuum of levels (physical systems): • quantum mechanical • molecular dynamics • meso or nanoscale levels • level of continuum • level of device

  7. Simulation • Focuses on simulating the behavior of physical systems. • Usually involves Monte Carlo methods to solve stochastic systems. • Most commonly employed in computational physics.

  8. Simulation – con't. • Central to the 'birth' of computational science. • Metropolis, Rosenbluth, Rosenbluth, Teller and Teller • “Equation of State Calculations by Fast Computing Machines” • Goal is to develop 'ensembles' or collections of parameters. • Typically implemented as 'coarse grained' parallelism.

  9. Prediction • The analysis or 'mining' of large sets of data for the purpose of predicting future phenomenon. • Centrally important to marketing and e-commerce. • Represents a type of computational problem referred to as 'embarassingly' parallel. • Most famous example is NetFlix competition.

  10. Challenges in Prediction • Data locality • More processors does not equal more speed. • NetFlix competition demonstrated inadequacy of improperly 'balanced' computational architectures. • Primary concern of national labs involved in security based computation. • Current HPC architectures exacerbate data locality problems.

  11. 'The Wettstein Rule of Computational Reality' “If filling a cache line is too slow you will be really unhappy doing a cross-node lookup to a machine 200 racks away.”

  12. RoadRunner Configuration • 1.72 petaflops peak / 1.456 petaflops demonstrated • 296 racks covering 6,000 square feet • Massively parallel – hybrid architecture • 6,480 Opteron (x86) processors • 12,960 IBM PowerXCell processors • 122,400 cores • 103.6 terrabytes of memory But when is it fast?

  13. A Tradeoff • Compelling speeds when each node can work on a discrete element of the problem. • Strictly orthogonal decomposition • Embarrassingly parallel problems. • MIMD • Less efficient when. • Boundary condition dependent problem. • Access to entire memory space is required.

  14. LatencyThe Enemy of Prediction • Latency definition: • The amount of time required to retrieve the next relevant item of data required in a computational or predictive sequence. • 'Achilles Heel' of modern massively parallel systems such as RoadRunner. • Common problem since the design of the Cray-1. • Wiring optimized to place time critical connections on the inner portion of the computer.

  15. Reducing Latencies through PTree's • Current area of research interest. • Addition of second order PTree's to optimize data selection decisions. • Minimizes: • cache line flushing • cross-node data lookups

  16. Exercise • Log into cluster1.chpc.ndsu.nodak.edu. • Use sinfo command to locate an available node. • e.g. node64-49 • Use ping command to measure message latency over standard TCP/IP network. • ping -c 5 node64-49 • Use ping command to measure message latency over Myrinet: • ping -c 5 node64M-49

  17. Exercise – con't. • Bottom of ping command details min, average and maximum communication latencies. • Compute expected performance change if a computation is constrained by the length of time required to pass a message from one node to another.

  18. goto technology_lecture1_2;

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