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Priority Research Direction Key challenges General Evaluation of current algorithms Evaluation of use of algorithms in Applications Application of “standard” approaches Rethink approaches (high risk/high payoff) Scalability Fault tolerance/resilience Conforming to architectural requirements New areas/uses of algorithms See Frameworks and Libraries How will this impact the range of applications that may benefit from exascale systems? Some applications will require breakthroughs in algorithms. Others will be far less efficient or reliable without new algorithms What’s the timescale in which that impact may be felt? Algorithms must be realized efficiently in libraries, frameworks, and application codes Depends critically on availability of tools to develop, test, and tune codes Summary of research direction Potential impact on software component Potential impact on usability, capability, and breadth of community

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Key Challenges Scalability – Concurrency Finding enough independent tasks – Latency hiding or Communication/computation Overlap Creating “split” operations Fault tolerance/resilience – Algorithm role in detecting faults – Algorithm role in providing alternative strategies to repairing faults (particularly transient faults) Conforming to architectural requirements – Power – Heterogeneity of processing elements – Memory Limitations, particularly smaller memory per core New areas/uses of algorithms – E.g., UQ.

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Key Challenges: Scalability Concurrency – Exascale systems expected to have 10 8 to 10 9 threads – 1000 3 mesh has one point per thread; low computation/communication ratio typically inefficient Latency Hiding – Even current systems have 10 3 -10 4 cycle hardware latency to remote access – Algorithms need to permit computation/communication overlap of at least 10 4 cycles – Many current algorithms have synchronization points (such as dot products/allreduce) that limit opportunities for latency hiding (this includes Krylov methods for solving sparse linear systems) Load balancing – Static load balancing rarely provides an exact load balance; experience with current terascale and near petascale systems suggests that this is already/will become a major scalability problem for many algorithms.

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Key Challenges: Fault Tolerance Detecting faults – Experience shows applications may not detect faults; see “Assessing Fault Sensitivity in MPI Applications” – Need to evaluate role of algorithms in detecting faults (tradeoff wrt hardware detection) Detecting faults in hardware requires additional power, memory, etc. Repairing faults – Regardless of who detects fault, need to repair – General solution (e.g., checkpoint/restart) is already demanding on high-end platforms (e.g., requiring significant I/O bandwidth) – Need to evaluate role of algorithms in repairing faults, particularly transient (e.g., memory upset) faults

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Key Challenges: Architectural Constraints Power – Power is a major constraint; to date, few algorithms have been developed (or evaluated with respect to) minimize power – May be combined with other constraints E.g., data motion consumes energy Heterogeneity – Many proposals for Exascale systems (and power-efficient petascale systems) exploit heterogeneous processors – Current experience with GPGPU systems, while promising for some algorithms, has not shown benefits with others – Heterogeneous systems also require different strategies for use of memory and functional units Memory Ratios (speeds and size) – Exascale systems are likely to have orders of magnitude less memory per core than current systems (though still large amounts of memory) – Power constraints may reduce the amount of fast memory available; adding to need for latency hiding – Algorithms needs to use memory more efficiently (more accuracy per byte; fewer data moves per result)

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Key Challenges: New Application Areas Each generation of supercomputer has seemed to reduce the number of applications that can make use HPC Exascale systems are likely to be different than simple extrapolations of petascale systems Some application areas may become suitable again; others (because of the extreme scale and degree of concurrency) may become possible for the first time – This needs to be evaluate wrt possible architectures and performance models

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Summary of Research Directions (Discuss role of terascale/petascale systems in developing/testing algorithmic developments) Concern: Much of this depends on discovering new algorithms. – This cannot be scheduled – we can devote effort to searching for such algorithms, but we cannot predict the development of new mathematics – One possibility for a roadmap would be to have decision points in case the hoped-for breakthroughs do not occur – "Genius doesn't work on an assembly line basis. You can't simply say, 'Today I will be brilliant.'" -- Kirk, The Ultimate Computer, Ep 53/4729.4

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Summary of Research Directions General Evaluation – What is the suitability of current algorithms to likely Exascale systems (gap analysis) Must distinguish between current implementations and fundamental limits – For each class of algorithms, there are some strategies that may be used to improve for exascale Evolutionary approach – For each problem area, rethink approach Need a model architecture against which ideas can be evaluated

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Summary of Research Directions Scalability – Alternative mathematical models Create concurrency by rethinking approximations Re-evaluate existing methods; e.g., use of Monte Carlo; tradeoffs between implicit/explicit methods; replace FFT with other approaches (to avoid all-to-all) – Non-blocking Algorithms Fault Tolerance – Use or creation of redundant information (in algorithm or mathematical model) Architectural Requirements – Incl. higher-order methods (more memory space and locality efficient) – Enhanced models to evaluate algorithms (include memory hierarchy and locality, power, etc.) New Areas – Incl. strong scaling (application areas that haven’t scaled to date)

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Potential Impact on Software Components (What capabilities will result?) (What new methods and components will be developed?) See Frameworks and Libraries Latency hiding requires program model support – Split and nonblocking operations introduce programming hazards Need tools to write, debug, and analyze correctness

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Potential impact on usability, capability, and breadth of community How will this impact the range of applications that may benefit from exascale systems? – Some applications will require breakthroughs in algorithms. Others will be far less efficient or reliable without new algorithms – To date, there is little quantified evaluation of the needs What’s the timescale in which that impact may be felt? – Algorithms must be realized efficiently in libraries, frameworks, and application codes – Depends critically on availability of tools to develop, test, and tune codes

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4.3.2 Application Element: Algorithms Availability of Efficient Exascale Algorithms Gap Analysis Application needs Evaluation Better Scaling in Node Count; Better scaling within node Prototype algorithms for Heterogeneous Systems Fault Resilience Efficient Implementation 2010201120122013201420152016201720182019 Exascale Suitability

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4.3.2 Application Element: Algorithms Location of box indicates when results are available; the expectation is that further refinement takes place 1.Gap analysis. Needs to be completed early to guide the rest of the effort 2.Application needs evaluation. Needs to be initiated early and completed early to guide allocation of effort and to identify areas where apps need to rethink approach (cross-cutting issue). Needs to develop and use more realistic models of computation (quantify need) 3.Better scaling in node count and within nodes can be performed using petascale systems in this time frame (so it makes sense to deliver a first pass in this time frame) 4.Heterogeneous systems are available now but require both programming model and algorithmic innovation; while some work has already been done, others may require more time. At the time of this bullet, view this as “a significant fraction of algorithms required for applications expected to run at Exascale have effective algorithms for heterogeneous processor systems” 5.Fault resilience is a very hard problem; this assumes that work starts now but will take this long to meet the same definition as for heterogeneous systems – “a significant fraction of algorithms have fault resilience” 6.Efficient implementation includes the realization in exascale programming models and tuning for real systems, which may involve algorithm modifications (since the real architecture will most likely be different from the models used in earlier developments). In addition, the choice of data structures may also change, depending on the abilities of compilers and runtimes to provide efficient execution of the algorithms.

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4.3.2 Application Element: Algorithms Technology drivers – Concurrency; Latency; Low Memory; Probability of transient and permanent faults Alternative R&D strategies – Refine existing algorithms to expose more concurrency, adapt to heterogeneous architectures, manage faults – New algorithms (high risk/high payoff) Recommended research agenda – Follow both strategies (Evolutionary + Re-evaluate solution method) – Gap analysis needed ASAP – Must re-evaluate application needs (change model/approximation to allow use of Exascale-appropriate algorithms) Crosscutting considerations – Realize more complex algorithms (execution and programming models, debugging and tuning tools) – Hardware architectural features – Application’s mathematical models

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Updates What specific requirements? What are the capabilities that are needed? – For the up and to the right graph Another way of looking at it: – Scalability/perf needed now; will be increasingly serious – Fault resilience likely needed as we approach exascale (thus needed about 2017 to give 3 years to realize, test, and provide enough time for a second round of developments – Connect requirements to applications Show why is something needed Problem: Analysis to date has often focused on anecdotal or simple extrapolation from current systems.

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LLNL-PRES-653431 This work was performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under contract DE-AC52-07NA27344.

LLNL-PRES-653431 This work was performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under contract DE-AC52-07NA27344.

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