Latency Tolerance Through Parallelization of Time in Scientific Applications

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Latency Tolerance Through Parallelization of Time
in Scientific Applications

• Ashok Srinivasan
• Computer Science
• Florida State University

Namas Chandra Mechanical Engineering Florida
State University
Aim Long time scales on small physical
systems Solution features Time parallelization
to avoid fine granularity
www.cs.fsu.edu/asriniva
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Outline

• Application
• Time parallelization
• Prediction of a Carbon nanotube state
• Experimental results
• Conclusions and future work

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Applications

• Small physical systems for long time scales
• Class of applications considered
• State(Ti) F(StateTi-1)
• Inherently sequential
• Example
• Molecular dynamics simulations of Carbon
  nanotubes
• Time step size 10-15 second
• After a million steps, we are still only in the
  nanosecond range
• Even that requires about a day of sequential
  computing time for around 3000 atoms
• Spatial parallelization will lead to too fine a
  granularity

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CNT application

• Pull the CNT at a constant velocity
• Performed to determine material property
• Material response can be used by an FEM
  simulation in a multiscale model

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Time parallelization

• Based on a predict-verify approach
• Use results of old simulations to speed up the
  current simulation
• Relationship between different problem parameters
  often occurs in engineering
• Example Temperature and time, stress and time
• Find a relationship and use it to predict the
  state at different times
• The relationship is determined automatically, and
  updated dynamically

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Guided simulations

• Notation
• r Exact time/ Parallel overhead
• P of Procs
• a Progress rate
• Speedup
• P a /(11/r)
• P a
• If prediction and communication overheads are
  relatively small
• P Time steps
• a ? 1/P,1
• Requires all-reduce and broadcast

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Fault tolerance too

• In case of node failure, another processor fills
  in the missing time interval
• Other computations need not be discarded
• Efficiency close to 1
• For large P
• Excluding loss in efficiency from errors
• If communication cost is negligible
• A master-worker design me be useful sometimes

Master
t1
t3
t4
t2
P3
P1
P2
P4
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Fault tolerance

• In case of node failure, another processor fills
  in the missing time interval
• Other computations need not be discarded
• Efficiency close to 1
• For large P
• Excluding loss in efficiency from errors
• If communication cost is negligible
• A master-worker design me be useful sometimes

Master
t2
t5
t6
P3
P1
P2
P4
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Requirements for this approach

• Method for predicting a state
• Criterion for determining whether two states
  (predicted and actual) are similar
• Choice of suitable base (old) simulation

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Prediction of a Carbon nanotube state

• Definition of equivalence of two states
• Atoms vibrate around their mean position
• Consider states equivalent if difference in
  position, potential energy, and temperature are
  within the normal range of fluctuations

• Max displacement 0.211
• Mean displacement 0.0789
• Potential energy fluctuation 0.35
• Temperature fluctuation 12.5 K

Displacement (from mean)
Mean position
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Prediction

• Predictor
• Independently predict change in each coordinate
• Normalize coordinates to be in 0,1
• x tDt x t x tDt Dt
• x tDt is the rate of change of x in this time
  interval
• It is unknown and needs to be estimated

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Predict change in coordinates

• Express x in terms of basis functions
• Example
• x tDt a0, tDt a1, tDt x t
• a0, tDt, a1, tDt are unknown
• Express changes, y, for the base (old) simulation
  similarly, in terms of coefficients b and perform
  least squares fit
• Predict ai, tDt as bi, tDt R tDt
• R tDt (1-b) R tDt b(ai, t- bi, t)
• Intuitively, the difference between the base
  coefficient and the current coefficient is
  predicted as a weighted combination of previous
  weights
• We use b 0.5
• Gives more weight to latest results
• Does not let random fluctuations affect the
  predictor too much
• Velocity estimated as latest accurate results
  known

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Experimental results

• Experimental parameters
• Carbon nanotube with 1000 atoms
• Around 200 atoms in the beginning fixed
• Around 200 atoms at the end moved
  deterministically
• Time step size 0.5 femto seconds
• Time interval per processor 1000 time steps
• Tersoff-Brenner potential for MD
• 300 K temperature current 10 K base
• b 0.5
• Base simulation v 0.05A/1000 time steps
• Actual simulation v 0.0625A/1000 time steps
• A parallel run was simulated

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Errors on 50 processors
Threshold for accepting the results
Difference between predictor and verifier
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Errors on 50 processors
Threshold for accepting the results
Difference between predictor and verifier
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Errors on 50 processors
Threshold for accepting the results
Error
Energy
Difference between predictor and verifier
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Errors on 50 processors
Temperature
Threshold for accepting the results
Error
Difference between predictor and verifier
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Speedup
Expected based on progress rate
Observed in simulations

• Computation time for one time interval 10 s
• Prediction time 10-3 s
• Broadcast on 100 processors of IBM SP3 0.005 s
• Allreduce on 100 processors of IBM SP3 0.0005 s

Overhead/computation is ratio negligible, and
speedup is determined only by errors
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Limitations of the experiments

• They are simulations of a parallel implementation
• But large difference between computation and
  communication time suggests efficient
  implementation

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Conclusions and future work

• Conclusions
• Promises significant improvement in speedup and
  efficiency for long-time simulations, through
  latency and fault-tolerance
• Future work
• Implementation on a parallel machine
• Base simulations with a smaller time scale
• Better predictors
• Basis functions corresponding to physical
  phenomena likely to be experienced
• Use clustering techniques to determine phenomena
  experienced by different regions
• Automatically and dynamically determine a
  suitable base to use from a large set of
  existing results