EAM potential fitting using parallel simulated annealing algorithm

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EAM potential fitting using parallel simulated
annealing algorithm
Tao Xu Midterm Report 03/16/05 School of
Materials Science and Engineering Georgia
Institute of Technology
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Outline

• The force-matching method
• The Embedded atom method
• Simulated annealing algorithm
• Parallel version of the algorithm

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The force-matching method
Background The force-matching method is
proposed by F. Ercolessi and J.B. Adams to
extract numerically optimal interatomic potential
from large amounts of data produced by
first-principle calculations. Reference
Interatomic potentials from first-principle
calculation the force-matching
method Europhysics Letters, 26(8), 583-588, 1994
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The EAM potential
The lattice constant is given by the equilibrium
condition where,
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Elastic constants of FCC metals
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Sublimation Energy, Vacancy-formation energy and
force calcuation
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The object (cost) function
The key of force-matching method is to minimize
the object function Z(a) ZF(a) ZC(a) where,
M of sets of atomic configurations(e.g.
structures). Nk of atoms in configuration
k. Fki(a) is the force on the ith atom in set k
obtained with parameter set a. Fki0 is the
reference force from first principle. ZC
contains contribution from Nc additional
constraints. Ar(a) are physical quantities as
calculated from potentials.
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Minimization using Simulated Annealing

• The computational engine of force-matching method
  is a minimization procedure for the object
  function.
• Simulated annealing is a technique suitable for
  optimization problem of large scale.
• SA was first formally introduced by S.
  Kirkpatrick, et al in 1983. In this technique,
  one or more artificial temperatures are
  introduced and gradually cooled, in complete
  analogy with the well-known annealing technique
  frequently used in Metallurgy for making a molten
  metal reach its crystalline state ( global
  minimum of the thermodynamics energy).
• Generalized simulated annealing is introduced by
  C. Tsallis and D.A. Stariolo, which is a new
  stochastic algorithm turns out to be faster than
  the classical simulated annealing algorithm.

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Simulated Annealing Algorithm
Initial configuration a
Random number generator
Create new random configuration a
Evaluate the cost function
Acceptance probability
No
Yes
Accept new config
Terminate Search?
Adjust Temperature
END
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Four key elements in SA

• Random number generator generate a random change
  in the parameter space based on the current
  temperature
• Object function Z(a) ZF(a) ZC(a)
• Acceptance probability
• Annealing schedule the cooling rate

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Parallel version of the Simulated Annealing
Algorithm
Initial configuration a
Random number generator
Create new random configuration a
Evaluate the cost function
Parallel phase
Acceptance probability
No
Yes
Accept new config
Terminate Search?
Adjust Temperature
END