Use of computational intelligence for the prediction of vacancy migration energies in atomistic kinetic monte carlo simulations

In this work, we try to build a regression tool to partially replace the use of CPU-time consuming atomic-level procedures for the calculation of point-defect migration energies in Atomistic Kinetic Monte Carlo (AKMC) simulations, as functions of the Local Atomic Configuration (LAC). Two approaches are considered: the Cluster Expansion (CE) and the Artificial Neural Network (ANN). The first is found to be unpromising because of its high computational complexity. On the contrary, the second provides very encouraging results and is found to be very well behaved.

[1]  Lorenzo Malerba,et al.  Simulation of radiation damage in Fe alloys: an object kinetic Monte Carlo approach , 2004 .

[2]  G. Henkelman,et al.  Methods for Finding Saddle Points and Minimum Energy Paths , 2002 .

[3]  David E. Goldberg,et al.  Genetic Algorithms in Search Optimization and Machine Learning , 1988 .

[4]  D. Dubois,et al.  Unfair coins and necessity measures: Towards a possibilistic interpretation of histograms , 1983 .

[5]  W M Young,et al.  Monte Carlo studies of vacancy migration in binary ordered alloys: I , 1966 .

[6]  L. Trefethen,et al.  Numerical linear algebra , 1997 .

[7]  Martin A. Riedmiller,et al.  A direct adaptive method for faster backpropagation learning: the RPROP algorithm , 1993, IEEE International Conference on Neural Networks.

[8]  K. Murty,et al.  Materials issues in light water reactors , 2001 .

[9]  L. Zadeh.  Fuzzy sets as a basis for a theory of possibility , 1999 .

[10]  Simon Haykin,et al.  Neural Networks: A Comprehensive Foundation , 1998 .

[11]  Kurt Hornik,et al.  Multilayer feedforward networks are universal approximators , 1989, Neural Networks.

[12]  Jonathan M. Hyde,et al.  Microstructural evolution in medium copper low alloy steels irradiated in a pressurized water reactor and a material test reactor , 2003 .

[13]  Siegfried Schmauder,et al.  Experimental and numerical investigations of two material states of the material 15 NiCuMoNb5 (WB 36) , 2002 .

[14]  Christian Lebiere,et al.  The Cascade-Correlation Learning Architecture , 1989, NIPS.

[15]  Gerbrand Ceder,et al.  Vacancies in ordered and disordered binary alloys treated with the cluster expansion , 2005 .

[16]  Roberto P. Domingos,et al.  Artificial intelligence applied to atomistic kinetic Monte Carlo simulations in Fe–Cu alloys , 2007 .

[17]  S. Dumbill,et al.  Irradiation-induced microstructural changes, and hardening mechanisms, in model PWR reactor pressure vessel steels , 1995 .

[18]  Yasuyoshi Nagai,et al.  Irradiation-induced Cu aggregations in Fe: An origin of embrittlement of reactor pressure vessel steels , 2001 .

[19]  Scott E. Fahlman,et al.  An empirical study of learning speed in back-propagation networks , 1988 .

[20]  P. Gill,et al.  Algorithms for the Solution of the Nonlinear Least-Squares Problem , 1978 .

[21]  Christopher M. Bishop,et al.  Neural networks for pattern recognition , 1995 .

[22]  C. J. Ortiz,et al.  He diffusion in irradiated α-Fe : An ab-initio-based rate theory model , 2007 .

[23]  C. J. Ortiz,et al.  Simulation of defect evolution in irradiated materials: Role of intracascade clustering and correlated recombination , 2007 .

[24]  Charlotte Becquart,et al.  Atomic kinetic Monte Carlo model based on ab initio data: Simulation of microstructural evolution under irradiation of dilute Fe–CuNiMnSi alloys , 2007 .

[25]  C. Domain,et al.  Precipitation of the FeCu system: A critical review of atomic kinetic Monte Carlo simulations , 2008 .

[26]  G. E. Lucas,et al.  Embrittlement of nuclear reactor pressure vessels , 2001 .

[27]  Gus L. W. Hart,et al.  Evolutionary approach for determining first-principles hamiltonians , 2005, Nature materials.

[28]  Gerard T. Barkema,et al.  Monte Carlo Methods in Statistical Physics , 1999 .

[29]  Frédéric Soisson,et al.  Kinetic pathways from embedded-atom-method potentials: Influence of the activation barriers , 2002 .

[30]  G. R. Odette,et al.  Kinetic Lattice Monte Carlo Simulations of Cascade Aging in Iron and Dilute Iron-Copper Alloys , 1998 .

[31]  Charlotte Becquart,et al.  Solute interaction with point defects in α Fe during thermal ageing: A combined ab initio and atomic kinetic Monte Carlo approach , 2006 .