Scheduling Many-Body Short Range MD Simulations on a Cluster of Workstations and Custom VLSI Hardware

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Scheduling Many-Body Short Range MD Simulations
on a Cluster of Workstations and Custom VLSI
Hardware

• Sumanth J.V, David R. Swanson and Hong Jiang
• University of Nebraska-Lincoln

We thank ONR, RCF and SDI(NSF 0091900) for
funding this research and Dr. Kenji Yasuoka and
Dr. Takahiro Koishi for the many useful talks we
had.
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Introduction

• MD is very computationally intensive.
• Luckily, MD is parallelizable hence can be
  efficiently implemented on a cluster.
• Custom VLSI solutions like the MD-GRAPE 2 are
  another approach, but is more limited to kinds of
  potential functions that can be evaluated.
• We combine the above two techniques to combine
  the advantages of both.

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Computational Aspects of MD

• Perform time integration of following equation

• Forces are computed as

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Potential Function

• We restrict ourselves to 2-body and 3-body
  potentials.
• The MD-GRAPE 2 is designed to compute only 2-body
  potentials.
• The cluster can however be programmed to evaluate
  any kind of potential.
• We use a combination of the cluster and the
  MD-GRAPE 2 board to evaluate a 3-body potential.

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Lennard-Jones(LJ) Potential

• Is a very simple empirical 2-body potential

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Reactive Bond Order (REBO) Potential
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Simple MD Algorithm

• Can improve execution time by using cut-off
  radius, neighbor lists, link cell or combination
  of these.
• Cut-off radius introduces discontinuities. Can be
  overcome by smoothing the potential function.
• Velocity-Verlet Integration.

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Boundary Conditions
Minimum Image Convention
Periodic Boundary Conditions
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Neighbor Lists
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Link Cell Method
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Parallel MD Atom Decomposition

• Involves dividing up the N atoms into sets of N/P
  atoms and assigning each set to one of the P
  processors.
• At every time-step, two global communication
  operations are required (one for updating
  positions and the other for updating forces).
• Runs in time proportional to the square of the
  number of atoms N.
• Very good efficiency but long running times.
• Is a suitable technique if the system is dense.

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Parallel MD Spatial Decomposition

• Involves dividing up the simulation box into
  domains and assigning domains to processors.
• Communication is local.
• Efficiency is worse, but has lower running time.
• Works better when the system is not very dense.
• Load balancing can be performed by dynamically
  varying the volume of the domains.
• When the system is not very dense, the running
  time is nearly linear.

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Efficiency of Atom and Spatial Decomposition
Atom Decomposition
Spatial Decomposition
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MD-GRAPE 2 for MD simulations

• Parallel pipelined special purpose hardware for
  computing non-bonded forces.
• Bonded forces and time integrations are performed
  on the host machine.
• Can compute forces either in the all-pairs method
  or link-cell method.
• If there are more than half a million atoms in
  the system, they must be split into batches of at
  most half a million before being sent to the
  MD-GRAPE 2.
• Peak Performance of 64Gflops.

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MD-GRAPE 2 Calculations

• The forces and potentials are computed using the
  following two equations.

• The function G(x) is evaluated using a segmented
  fourth order polynomial interpolation.

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MD-GRAPE 2 Architecture
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Link Cell Method on MD-GRAPE 2
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Number of Processors vs. Execution Time for
MD-GRAPE 2 link cell method and domain
decomposition method.
Relative Error in Computing Total Energy with
MD-GRAPE2
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Scheduling MD on a cluster and MD-GRAPE 2
simultaneously

• The REBO is a three-body potential.
• It comprises of three two-body components VR, VA
  and VvdW and a three-body component Bij.
• The MD-GRAPE 2 is not capable of computing
  three-body potentials due to its architecture.
• The custom function evaluation table does not
  allow for conditional statements to be placed in
  the function, but this feature is required to
  evaluate VR and VA.
• This allows us to compute the VvdW on the
  MD-GRAPE 2 and all the other components on the
  cluster.

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Scheduling MD on a cluster and MD-GRAPE 2
simultaneously contd.

• The motivation for doing so is that the Vvdw has
  a cut-off that is roughly twice that of the other
  components.
• This can however be efficiently computed on the
  MD-GRAPE 2 while the other components are being
  evaluated on the cluster simultaneously.
• To aid in communication between the cluster and
  the machine hosting the MD-GRAPE 2, we implement
  a server.

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Scheduling MD on a cluster and MD-GRAPE 2
simultaneously contd.

• The server accepts a position vector and outputs
  a partial forces vector and a partial potential
  vector.
• They are called partial since they only contain
  contributions due to the Vvdw component.
• This has to be added to the other contributions
  that are computed on the cluster.

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Scheduling MD on a cluster and MD-GRAPE 2
simultaneously contd.

• At every time step, before the parallel code
  begins its computations, it sends a copy of the
  position vector to the MD-GRAPE 2.
• Now the cluster and the MD-GRAPE 2 compute
  partial forces/potentials simultaneously.
• When the MD-GRAPE 2 completes its computations,
  it returns the partial forces/potentials to the
  host and the host sums them to give the actual
  forces and total potential energy.
• The cut-off for the computations on the cluster
  is now 2.5 instead of 5.5 which is required if
  all the components of the REBO potential were
  computed on it.

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Scheduling MD on a cluster and MD-GRAPE 2
simultaneously contd.

• The execution time of an MD simulation using the
  atom-decomposition method can be well
  approximated by a second degree polynomial tc(N).
• The execution time on the MD-GRAPE 2 can also be
  approximated by a second degree polynomial tg(N).
• The total time it takes to run such a simulation
  on the cluster and the MD-GRAPE 2 simultaneously
  is given by

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Scheduling MD on a cluster and MD-GRAPE 2
simultaneously contd.

• The optimum number of processors to use can be
  determined by

• Experimentally, we have determined an optimal p
  to be 35 for our setup.
• With this setup, we found the speedup to
  gradually approach 1.4 and nearly remain constant
  after that.
• We used the atom-decomposition method since the
  system being simulated is very dense.

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Plot of speedup when using a cluster and MD-GRAPE
2 simultaneously vs. using a cluster alone
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Conclusion

• At the time of writing, cost per processor
  including network was 1500 USD.
• Cost of MD-GRAPE 2 was 15000 USD.
• For long range potentials it is more cost
  effective to use MD-GRAPE 2 since it takes 61
  cluster CPUs to equal its performance.
• For short range potentials, it is more effective
  to use a cluster since it takes only 12 cluster
  CPUs to match performance.
• However, using a combination of a cluster and
  MD-GRAPE 2 to solve more complex potentials can
  yield a significant gain.

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Future Work

• Incorporate multiple MD-GRAPE 2 boards into the
  current setup.
• Schedule MD simulations on larger scale systems
  with Globus.
• Custom FPGA solutions to solve more than just
  pair potentials.
• Using GPUs to perform MD.
• Hand optimizing energy calculations to use
  SSE/SSE2/SSE3 instructions for optimal
  performance.