Seminar 2: Efficient Algorithms for Molecular Dynamics Simulations and Other Dynamic Spatial Join Queries

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Seminar 2Efficient Algorithms for Molecular
Dynamics Simulations and Other Dynamic Spatial
Join Queries

• Andrew Noske

Thesis code is available at gtgt
http//manning.it.jcu.edu.au/jc130551/thesis/ ltlt
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About the Project

• Build an engine layer for particle simulations
  part of TOMSK (Towards Molecular Structure
  Kinetics) Project
• Molecular Dynamics (MD) integrates equations of
  motion of atoms each timestep.
• Cannot predict precisely what will happen
  generates statistical prediction

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Definitions
Single Range Query

• Range Query Find all points (neighbour atoms)
  within cutoff radius of each other
• Self-spatial join query Execute range query for
  all points (to determine complete list of
  neighbour atoms)

Ignore
Cutoff radius (Rc)
Spatial join query
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Methods Used in Testing

• Lennard-JonesPotential Pair
• I have used this to simulateatoms in a stable
  liquid.
• NOTE Final code allows you to extend system
  class implement any interaction model
  statistical analysis functions you choose.

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Methods Used in Testing

• To simulate bulk liquidHave used Periodic
  Bounding Condition ? (boundaries wrap around)

Surface particle have less neighbours
Range search on box with PBC
Microscopic droplet (finite particles)
PBC on 2D box
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Spatial Data Structure Fixed Grid

• Fixed grid
• Most effective for uniform particle distribution.
• Time to build (placeall pointsinto index)
  O(N)

Fixed grid
NOTE cells per side (CPS)5
boxLen
Cutoff radius (rc)
Original cell list technique
cellLen
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Simulation Steps

• Set-up
• 1) Setup grid structure
• 2) Setup atoms in offset lattice
• 3) Assign random velocities.
• Iterate
• 1) Build grid (assign all atoms to cells).
• 2) Build neighbor list (for each atom in each
  cell find neighbors). ? take up to 95 of time
• 3) Calculate force and move atoms ? implements
  interaction model (can change).
• 4) Wrap atoms back into cell boundaries.
• 5) Increment timestep.

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Scientific Process

• Used MS Visual C console application.
• Testing process
• Run a series of simulations in batch
• Output results to CSV including
• grid parameters,
• clock tics elapsed, ? main focus
• distance calculates,
• more
• Analyze/graph CSV using Excel.
• Was time consuming! ?

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Atom List vs. Cell List
Cell list approach Predetermine which cells are
within rc of each cell
Atom list approach For each atom check which
cells are within rc of atom
Original (cubic) cell list
Minimum cell list
Cubic atom list

• NOTE Volume sphere 52 of its bounding cube

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Loaded vs. Unloaded Cell List
(?3 min)
(?2 mins)
(?1 min)
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Half-Range Search Technique
Normal approach Search sphere
Faster approach Search upper hemi-sphere
i
HALF minimum cell list
minimum cell list
j
Range search
i
HALF-range search
j
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Size of Various Cell Lists
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Size of Various Cell Lists
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Half-Range Search Technique
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Half-Range Search Technique
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Atom List vs. Cell Lists
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Improving Cache Hits through Spatial Locality

• Spatial locality principle objects close to
  referred ones are more likely to be requested in
  the future.
• Unsorted atoms ? many cache misses.
• Space-filling curve A line passing through every
  point in grid, in some order.

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5
2
3
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Z-ordering
Row-wise
Hilbert curve
Gray curve
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Improving Spatial Locality with Space-Filling
Curve

• Improvements for small number of atoms were crap.
• However improvements for 200,000 atoms were
  significant ? virtual paging

Less than 3 performance improvements ?
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Finding Optimal Cells Per Side
for a cell list
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Finding Optimal Cells Per Side
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Finding Optimal Cells Per Side
EXTRA SLIDE
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Verlet Neighbour List Technique

• Choose a verlet radius greater than rc.
• Build the verlet neighbor list using verlet
  radius (use the fixed grid)
• Next few iterations update list by recalculating
  distances flag neighbour pairs inside rc.

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Verlet Neighbour List
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Verlet Neighbour List
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Finding Optimal Verlet Radius
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Selective Checking of Verlet List Using Atom
Displacement

• Dont update distances between verlet neighbours
  outside cut-off radius each iteration calculate
  safeDistance for these neighbours decrement
  that by the displacement of both atoms each
  iteration.

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Selective Checking of Verlet List Using Atom
Displacement
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Summary of Results Contribution

• Results for proposed techniques
• Minimum cell list ? better than traditional cell
  list (?)
• Half-range search ? great results! (????)
• Using MBRs in cells ? not effective for evenly
  spread particles, but has potential for skewed
  data sets
• Sub-grid cell list template guide ? refines of
  cells in loaded cell list you must check for each
  atom results successful, but only when avg.
  of atoms per cell were high.
• Early elimination of non-neighbours ? good idea,
  yet made performance worse (?).
• Selective checking of verlet list using atom
  displacement ? makes verlet list cheaper to
  update (especially if verlet radius big) (???)

Interesting ideas results, but insufficient
time to cover here
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Summary of Results Contribution

• Other findings
• Space-filling curves ? if simulation fits in
  memory gives negligible improvement, if not curve
  can up-to double performance! Hilbert curve
  best curve. (?)
• Argued half-cubic atom list best choice (most
  dynamic)
• Investigated optimal of cells per side verlet
  radius
• Proposed algorithms to find optimal values above
  worked quite well (??)
• Investigated performance vs. accuracy
  relationship for MD simulation
• Thesis code is guideline to implementing/optimiz
  ing spatial join simulations

Interesting results, but insufficient time to
cover
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Future Work

• Much opportunity to further investigate
  optimization techniques including those proposed.
• Some suggestions
• Test techniques for much larger simulations
  (cant in memory).
• Investigate other optimal value finding
  algorithms find optimal verlet radius cells
  per side simultaneously!
• Try different compilers/languages platforms.
• Test techniques for skewed data sets.
• and many more little technical suggestions
  more intelligent ways to decide which cells to
  check.
• Work may be carried out by future TOMSK students.

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DEMONSTRATION OF CODE
gtgt http//manning.it.jcu.edu.au/jc130551/thesis/
ltlt
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QUESTION TIME
gtgt http//manning.it.jcu.edu.au/jc130551/thesis/
ltlt
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QUESTION TIME
Dont tell anyone, but I fell asleep after the
first slide
QUESTION TIME OVER
Thank you for listening,and thanks again to
those who helped with my thesis. ?
gtgt http//manning.it.jcu.edu.au/jc130551/thesis/
ltlt
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THESIS first half

• Im not going to the next slide until everyone
  has finished reading up to here

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OTHER TECHNIQUES
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Sub-Grid Cell List Template Guide

• Sub-grid break each cell into (imaginary)
  sub-grid.
• When considering an atom, check with sub-cell it
  belongs to, that sub-cell will refine which cells
  in the cell list to search.

Minimum cell list representation
(-1,1), (0,1), (1,1), (-1,0), (0,0), (1,0),
Corresponding cell list template guide (for this
sub-cell only)
(false), (false), (false), (true), (true),
(false)
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Sub-Grid Cell List Template Guide
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Sub-Grid Cell List Template Guide
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Sub-Grid Cell List Template Guide
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Use of MBRs in Cells

• For each cell, maintain a Minimum Bounding
  Rectangle (MBR) around its atoms.
• For any cell JUST tipped by rc, check atom is
  inside rc of MBR before considering atoms
  exhaustively.

This cell is just tipped, but MBR is out of range
MBR
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Use of MBRs in Cells
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Early Elimination Technique
EXTRA SLIDE

• Early elimination if distancebetween atoms along
  anydimension gt cutoffRadius.
• Dont calculate sqrt
• Lennard-Jones can be doneusing dist2
• NOTE if (dist2 lt cutoffRadius2)
  ? is in range
• Determine optimal of cells per size.
• Is cell length cutoff radius optimal?

j
i
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Early Elimination Technique
EXTRA SLIDE
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ADDITIONAL RESULTS
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Linear Growth
EXTRA SLIDE
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Linear Growth
EXTRA SLIDE

• O(N) ? where N is number of neighbors

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Performance vs. Accuracy

• Some techniques that will improve performance,
  but decrease accuracy
• Increasing timestep
• Decreasing cutoff radius
• I collected results for these by comparing all
  simulations with control simulations

small timestep
larger timestep
large rc
smaller rc
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Optimal choice of cell length
EXTRA SLIDE
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Average Atoms per Cell
EXTRA SLIDE
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Performance Breakdown
EXTRA SLIDE
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Adjacency List Savings
EXTRA SLIDE
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Chosen Solution
Single Range Query

• Chosen approach chose cutoff radius, and ignore
  particles beyond this.
• Involves moving self-spatial join query (many
  range queries) ? has numerous applications
• GIS, Computer graphics, etc.

Ignore
Cutoff radius (Rc)
Spatial join query
Symmetrical attractive/ repulsive forces
O--
NOTEDirection forces!

H

H
Permanent dipole
Argon atom (inert)
Water molecule




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Improving Cache Hits through Spatial Locality

• Spatial locality principle objects close to
  referred ones will probably be requested again in
  the future.
• Unsorted atoms ? means many cache misses.

4
5
2
3
6
1
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Space Filling Curves

• Space-filling curve A line passing through every
  point in a space, in some order (according to
  some algorithm).
• Resort atom periodically (group by cells order
  using curve).
• Improves CPU performance gt50 in 2D moving point
  query ? worth trying.

Z-ordering
Row-wise
Hilbert curve
Gray curve