JavaGenes Evolving Molecules and Molecular Force Fields

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JavaGenesEvolving Molecules and Molecular Force
Fields

• Al Globus
• Deepak Srivastava
• Sandy Johan
• A Work In Progress

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Molecules to Evolve
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Graph Crossover Problem

• Any edge may be a member of one or more cycles.
• Graph fragments produced by division may have
  more than one crossover point ("broken edges")
• When two fragments are combined they may have
  different numbers of  broken edges to be merged.
• Our crossover operator
• Operate on any connected graph.
• Divides graphs at randomly generated cut sets.
• Can evolve arbitrary cyclic structures given at
  least some cycles in the initial population.
• Always produces connected undirected graphs.
• Almost always produces connected directed graphs.

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Crossover
Graphs
Strings
Trees
abcd wxyz
abcd wxyz
abyz wxcd
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Graph Crossover
Combine into a Child
Rip Two Parents Apart
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Molecule Division

• Choose an initial random bond
• Repeat
• Find the shortest path between the initial bond's
  atoms.
• Remove and remember a random bond from this path.
  These bonds are called "broken edges.
• Until a cut set is found, i.e., no path exists
  between the initial bond's vertices.

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Fragment Recombination

• Repeat
• Select a random broken edge. Determine which
  fragment it is associated with.
• If at least one broken edge in other fragment
  exists
• choose one at random
• merge the broken edges into one bond respecting
  valence by reducing the order of the bond if
  necessary
• Else flip coin
• heads -- attach the broken edge to a random atom
  in other fragment (respecting valence)
• tails -- discard the broken edge
• Until each broken edge has been processed exactly
  once

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Molecule Fitness Function

• All-pairs-shortest-path distance
• Assign extended types to each atom
• Extended type (element, single bonds, double
  bonds, triple bonds)
• Find shortest bond path between each pair of
  atoms
• Create bag one item per atom pair
• item (type1, type2, path length)
• bag set with repeated items
• distance 1 - intersection / union

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Finding Small Molecules
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Finding Larger Molecules
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JavaGenes in Action
Finding
with all-pairs-shortest-path and Tanimoto index
fitness function (0 is perfect)
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Molecular Dynamics and Mechanics

• Newtons laws of motion in a potential field
• Discover common conformations during dynamics
• Discover minimum energy conformations (e.g.,
  protein folding problem)
• Began in 1960s with two body potentials for inert
  gas modeling
• 1980s extended to metals and bonded systems
  (upper-right corner of periodic table)
• Our studies focus on the evolving potentials for
  reactive systems (bonds break and form)

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Molecular Potentials

• Energy sum 2-body terms sum 3-body terms
• Stillinger-Weber SiF potential function
• 2-body(r)
• A(Br-p - r-q) cutoff
• Cutoff exp(C/(r-a)) r lt a, 0 otherwise
• 3-body(rij,rjk,theta)
• (alpha lambda (cos(theta) - cos(theta0))2))
  cutoff
• Cutoff exp(gamma(1/(rij- a1) 1/(rjk- a1))
• FFF additional term
• delta(rijrjk)-m cutoff
• Cutoff exp(beta(1/(rij - a2) 1/(rjk- a2)))
• Discovering parameters can require months or years

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Evolving Molecular Force Fields

• Chromosome
• 2D ragged array of floating point numbers
• SiSi, SiF, FF, SiSiSi, SiSiF, SiFSi, FSiF, FFSi,
  FFF
• 5-63 parameters
• Transmission operators
• Interval crossover
• Mutation
• Fitness Function
• RMS difference between individuals and correct
  energies for n molecules
• Correct energies
• Currently energies generated with the force
  field with published parameters
• Next step energies generated by higher quality
  quantum codes

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Interval Crossover

• For each allele

Construct an interval from parental values
1.
Lower Parental Value (1.1)
Higher Parental Value (2.1)
Construct larger interval (100 larger)
2.
(.6)
(2.6)
Choose a random number
3.
(1.3)
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Si potential results

• population 1000
• generations 3000
• fitness function 100 random 5-body Si tetrahedra
• 31 runs. Best run results
• A 7.151346144801161 (7.049556277)
• B 0.6007865398735448 (0.6022245584)
• p 3.9825158463763977 (4)
• q 0.014970062068368135 (0)
• a 1.797123919332413 (1.8)
• alpha 0.1442970771852687 (0)
• lambda 27.783092740584205 (21)
• gamma 1.328091763076223 (1.2)
• a1 1.8173559091012945 (1.8)

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Future Plans

• Hill climbing
• Use experimental data for new fitness functions
• Feed results from easy to hard evolution

SiF (6)
SiSi (5)
FF (6)
SiFSi (10)
FSiF (10)
SiSiF (10)
FFSi (10)
SiSiSi (9)
FFF (14)
Full SiF (63)
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Condor

• Cycle-scavenging batch system for single
  workstation jobs
• Desktop machines, nights, weekends, etc.
• University of Wisconsin
• In production since 1986
• Unix workstations
• 250 SGI and 50 Sun workstations at code IN
• Good for
• parameter studies
• stochastic algorithms (e.g., GA)
• One JavaGenes job per Condor job