Fault tolerant parallelization of time in molecular dynamics simulations

1
Fault tolerant parallelization of time in
molecular dynamics simulations

• Ashok Srinivasan
• Computer Science
• Florida State University

Namas Chandra Mechanical Engineering Florida
State University
Aim Long time scales on small physical systems,
on massively parallel machines Solution features
Latency and fault tolerance are related, through
independence of tasks
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Outline

• Application
• Background Parareal scheme
• Time parallelization with guided simulations
• Parallelization of a model problem
• Parallelization of molecular dynamics simulations
  on a Carbon nanotube
• Conclusions and future work

3
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

4
Background

• Parareal scheme Baffico et. al.
• Based on an approximate-verify-correct sequence

• Notation
• r Exact time/ Approx. time
• P of Procs
• k iterations to convergence
• Speedup
• (1/k) Pr/(Pr)
• Ignoring communication cost

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Limitations of the parareal approach

• Speedups obtained (ignoring communication)
• Toy MD problem with r 1000
• Different time step size for approximation
• Speedup 130, efficiency 1.3
• Value of r is also not realistic adaptive
  sequential computation may be as effective
• Toy MD problem with different model for
  approximation
• Speedup 8, efficiency 25
• Quantum control
• Speedup 14, efficiency 1.5
• Limiting factors
• Sequential component
• Methods for approximation unlikely to bring major
  improvements

6
Time parallelization with guided simulations

• 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 Latency tolerance

• Notation
• s Exact time/ Prediction time
• P of Procs
• l Error rate
• Speedup
• (1/l) Ps/(1s)
• Ignoring communication cost
• P/l
• If prediction cost is relatively small
• Note l lt k

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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

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

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

• Method for predicting a state
• Criterion for determining whether two states
  (predicted and actual) are similar
• A means of informing the master about node failure

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Parallelization of a model problem

• x x0 (x0/L0)a L0 v t
• x current position, L0 initial length, v
  velocity, t time, x0 position at time 0, a a
  material property
• Experimental parameters
• L0 1, Dt 0.01, 600 points
• Base a 1.5, v 0.05
• Actual a 2.0 , v 0.0625
• xpred xold (Dxold/DBold)DB

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Parallelization without node failure

• P 100, simulated results

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Speedup without node failure

• Speedup 99.9
• Efficiency 0.999
• Justification for ignoring prediction time and
  communication costs
• A similar MD computation would take 10 s/time
  interval (15 s on IBM SP3)
• A reduction on IBM SP3 takes 0.0005s on 100
  processors
• Prediction is at least three orders of magnitude
  smaller than MD computation

• P 100, simulated results

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Speedup with node failure
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Parallelization of molecular dynamics simulations
on a Carbon nanotube

• Definition of equivalence of two states
• Atoms vibrate around their mean position
• So consider positions equivalent if the
  difference is within the range of motion for the
  temperature at which the simulation is being
  performed

• Max displacement 0.211
• Mean displacement 0.0789
• s 0.0426

Displacement (from mean)
Mean position
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Prediction

• Predictor
• Use predictor of a form similar to the model
  problem
• But the changes are computed in spherical
  coordinates
• Instead of using xpred xold (Dxold/DBold)DB
• Use xpred xold RDB
• where R b (Dxold/DBold) (1-b) Rold
• This prevents R from becoming large due to a
  single small value of DBold caused by random
  motion

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Experimental parameters

• Carbon nanotube with 1000 atoms
• Subjected to a pull out test
• 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
• f 0.2
• Base simulation v 0.05A/1000 time steps
• Actual simulation v 0.0625A/1000 time steps

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Error and speedup without faults
0.1641 A

• Speedup on 10 processors 9.5
• Good speedup on larger number of processors too

Loss in efficiency only due to first few sets of
iterations
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Maximum error
0.422 A
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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
• Positions alone do not define the state
• Velocities and Energy too are needed
• Velocities can be handled through standard
  techniques
• Pre-computed MD results were used to initialize
  the states
• Other types of experiments too should be
  performed
• Use of higher temperature smaller time as base

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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
• Better predictor
• First predict mean positions, and perturb based
  on a probability distribution
• Reduce information needed for prediction
• Better definition of the equivalence of states
• Include velocity and energy
• Actual implementation on a parallel machine
• Etc ...