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

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

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.

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.

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.

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

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

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.

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.

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.

'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.”

RoadRunner Configuration 1.72 petaflops peak / 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 terrabytes of memory But when is it fast?

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.

Latency The 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.

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

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

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.

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