On DFT Molecular Simulation for Non-Adaptive Kernel Approximation
Author(s)
Maharavo Randrianarivony
ABSTRACT
Using accurate quantum energy computations in nanotechnologic applications is usually very computationally intensive. That makes it difficult to apply in subsequent quantum simulation. In this paper, we present some preliminary results pertaining to stochastic methods for alleviating the numerical expense of quantum estimations. The initial information about the quantum energy originates from the Density Functional Theory. The determination of the parameters is performed by using methods stemming from machine learning. We survey the covariance method using marginal likelihood for the statistical simulation. More emphasis is put at the position of equilibrium where the total atomic energy attains its minimum. The originally intensive data can be reproduced efficiently without losing accuracy. A significant acceleration gain is perceived by using the proposed method.
Using accurate quantum energy computations in nanotechnologic applications is usually very computationally intensive. That makes it difficult to apply in subsequent quantum simulation. In this paper, we present some preliminary results pertaining to stochastic methods for alleviating the numerical expense of quantum estimations. The initial information about the quantum energy originates from the Density Functional Theory. The determination of the parameters is performed by using methods stemming from machine learning. We survey the covariance method using marginal likelihood for the statistical simulation. More emphasis is put at the position of equilibrium where the total atomic energy attains its minimum. The originally intensive data can be reproduced efficiently without losing accuracy. A significant acceleration gain is perceived by using the proposed method.
Cite this paper
Randrianarivony, M. (2014) On DFT Molecular Simulation for Non-Adaptive Kernel Approximation. Advances in Materials Physics and Chemistry, 4, 105-115. doi: 10.4236/ampc.2014.46013.
Randrianarivony, M. (2014) On DFT Molecular Simulation for Non-Adaptive Kernel Approximation. Advances in Materials Physics and Chemistry, 4, 105-115. doi: 10.4236/ampc.2014.46013.
References
[1] Hill, J., Subramanian, L. and Maiti, A. (2005) Molecular Modeling Techniques in Material Sciences. Taylor & Francis Group, Boca Raton. [2] Harbrecht, H. and Randrianarivony, M. (2011) Wavelet BEM on Molecular Surfaces: Solvent Excluded Surfaces. Computing, 92, 335-364.
http://dx.doi.org/10.1007/s00607-011-0147-y [3] Randrianarivony, M. (2013) On Space Enrichment Estimator for Nonlinear Poisson-Boltzmann. American Institute of Physics, 1558, 2365-2369. [4] Randrianarivony, M. (2013) Parallel Processing of Analytical Poisson-Boltzmann Using Higher Order FEM. In: Klement, E.P., Borutzky, W., Fahringer, T., Hamza, M.H. and Uskov, V., Eds., Proceeding of Conference “Parallel and Distributed Computing and Networks”, ACTA Press, 455434, 1-6. [5] Kohn, W. and Sham, L. (1965) Self-Consistent Equations Including Exchange and Correlation Effects. Physical Review, 140, 1133-11388.
http://dx.doi.org/10.1103/PhysRev.140.A1133 [6] Perdew, J. and Wang, Y. (1992) Accurate and Simple Analytic Representation of the Electron-Gas Correlation Energy. Physical Review B, 45, 13244.
http://dx.doi.org/10.1103/PhysRevB.45.13244 [7] Suryanarayana, P., Gavini, V., Blesgen, T., Bhattacharya, K. and Ortiz, M. (2010) Non-Periodic Finite-Element Formulation of Kohn-Sham Density Functional Theory. Journal of the Mechanics and Physics of Solids, 58, 256-280.
http://dx.doi.org/10.1016/j.jmps.2009.10.002 [8] Rasmussen, C. and Williams, C. (2006) Gaussian Processes for Machine Learning. The MIT Press, Massachusetts. [9] Johnson, S. (2010) The NLopt Nonlinear Optimization Package.
http://ab-initio.mit.edu/nlopt [10] Atomistix ToolKit Version 13.8.0, QuantumWise A/S.
www.quantumwise.com [11] Brandbyge, M., Mozos, J., Ordejon, P., Taylor, J. and Stokbro, K. (2002) Density-Functional Method for Nonequilibrium Electron Transport. Physical Review B, 65, 165401.
http://dx.doi.org/10.1103/PhysRevB.65.165401 [12] American Mineralogist Crystal Structure Database.
http://rruff.geo.arizona.edu/AMS/
[1] Hill, J., Subramanian, L. and Maiti, A. (2005) Molecular Modeling Techniques in Material Sciences. Taylor & Francis Group, Boca Raton. [2] Harbrecht, H. and Randrianarivony, M. (2011) Wavelet BEM on Molecular Surfaces: Solvent Excluded Surfaces. Computing, 92, 335-364.
http://dx.doi.org/10.1007/s00607-011-0147-y [3] Randrianarivony, M. (2013) On Space Enrichment Estimator for Nonlinear Poisson-Boltzmann. American Institute of Physics, 1558, 2365-2369. [4] Randrianarivony, M. (2013) Parallel Processing of Analytical Poisson-Boltzmann Using Higher Order FEM. In: Klement, E.P., Borutzky, W., Fahringer, T., Hamza, M.H. and Uskov, V., Eds., Proceeding of Conference “Parallel and Distributed Computing and Networks”, ACTA Press, 455434, 1-6. [5] Kohn, W. and Sham, L. (1965) Self-Consistent Equations Including Exchange and Correlation Effects. Physical Review, 140, 1133-11388.
http://dx.doi.org/10.1103/PhysRev.140.A1133 [6] Perdew, J. and Wang, Y. (1992) Accurate and Simple Analytic Representation of the Electron-Gas Correlation Energy. Physical Review B, 45, 13244.
http://dx.doi.org/10.1103/PhysRevB.45.13244 [7] Suryanarayana, P., Gavini, V., Blesgen, T., Bhattacharya, K. and Ortiz, M. (2010) Non-Periodic Finite-Element Formulation of Kohn-Sham Density Functional Theory. Journal of the Mechanics and Physics of Solids, 58, 256-280.
http://dx.doi.org/10.1016/j.jmps.2009.10.002 [8] Rasmussen, C. and Williams, C. (2006) Gaussian Processes for Machine Learning. The MIT Press, Massachusetts. [9] Johnson, S. (2010) The NLopt Nonlinear Optimization Package.
http://ab-initio.mit.edu/nlopt [10] Atomistix ToolKit Version 13.8.0, QuantumWise A/S.
www.quantumwise.com [11] Brandbyge, M., Mozos, J., Ordejon, P., Taylor, J. and Stokbro, K. (2002) Density-Functional Method for Nonequilibrium Electron Transport. Physical Review B, 65, 165401.
http://dx.doi.org/10.1103/PhysRevB.65.165401 [12] American Mineralogist Crystal Structure Database.
http://rruff.geo.arizona.edu/AMS/