Quantum energies which are used in applications are usually composed of repulsive and attractive terms. The objective of this study is to use an accurate and efficient fitting of the repulsive energy instead of using ...Quantum energies which are used in applications are usually composed of repulsive and attractive terms. The objective of this study is to use an accurate and efficient fitting of the repulsive energy instead of using standard parametrizations. The investigation is based on Density Functional Theory and Tight Binding simulations. Our objective is not only to capture the values of the repulsive terms but also to efficiently reproduce the elastic properties and the forces. The elasticity values determine the rigidity of a material when some traction or load is applied on it. The pair-potential is based on an exponential term corrected by B-spline terms. In order to accelerate the computations, one uses a hierarchical optimization for the B-splines on different levels. Carbon graphenes constitute the configurations used in the simulations. We report on some results to show the efficiency of the B-splines on different levels.展开更多
The original online version of this article (Randrianarivony, M. (June 2014) On DFT Molecular Simulation for Non-Adaptive Kernel Approximation. Advances in Materials Physics and Chemistry, Vol. 4 No. 6, 105-115. http:...The original online version of this article (Randrianarivony, M. (June 2014) On DFT Molecular Simulation for Non-Adaptive Kernel Approximation. Advances in Materials Physics and Chemistry, Vol. 4 No. 6, 105-115. http://dx.doi.org/10.4236/ampc.2014.46013) did not contain any acknowledgment. The author wishes to add the following acknowledgements: Acknowledgements: This work was partially supported by Eurostars Project E!6935 funded by German Federal Ministry of Education and Research.展开更多
Quantum energies which are used in applications are usually composed of repulsive and attractive terms. The objective of this study is to use an accurate and efficient fitting of the repulsive energy instead of using ...Quantum energies which are used in applications are usually composed of repulsive and attractive terms. The objective of this study is to use an accurate and efficient fitting of the repulsive energy instead of using standard parametrizations. The investigation is based on Density Functional Theory and Tight Binding simulations. Our objective is not only to capture the values of the repulsive terms but also to efficiently reproduce the elastic properties and the forces. The elasticity values determine the rigidity of a material when some traction or load is applied on it. The pair-potential is based on an exponential term corrected by B-spline terms. In order to accelerate the computations, one uses a hierarchical optimization for the B-splines on different levels. Carbon graphenes constitute the configurations used in the simulations. We report on some results to show the efficiency of the B-splines on different levels.展开更多
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 p...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.展开更多
文摘Quantum energies which are used in applications are usually composed of repulsive and attractive terms. The objective of this study is to use an accurate and efficient fitting of the repulsive energy instead of using standard parametrizations. The investigation is based on Density Functional Theory and Tight Binding simulations. Our objective is not only to capture the values of the repulsive terms but also to efficiently reproduce the elastic properties and the forces. The elasticity values determine the rigidity of a material when some traction or load is applied on it. The pair-potential is based on an exponential term corrected by B-spline terms. In order to accelerate the computations, one uses a hierarchical optimization for the B-splines on different levels. Carbon graphenes constitute the configurations used in the simulations. We report on some results to show the efficiency of the B-splines on different levels.
文摘The original online version of this article (Randrianarivony, M. (June 2014) On DFT Molecular Simulation for Non-Adaptive Kernel Approximation. Advances in Materials Physics and Chemistry, Vol. 4 No. 6, 105-115. http://dx.doi.org/10.4236/ampc.2014.46013) did not contain any acknowledgment. The author wishes to add the following acknowledgements: Acknowledgements: This work was partially supported by Eurostars Project E!6935 funded by German Federal Ministry of Education and Research.
文摘Quantum energies which are used in applications are usually composed of repulsive and attractive terms. The objective of this study is to use an accurate and efficient fitting of the repulsive energy instead of using standard parametrizations. The investigation is based on Density Functional Theory and Tight Binding simulations. Our objective is not only to capture the values of the repulsive terms but also to efficiently reproduce the elastic properties and the forces. The elasticity values determine the rigidity of a material when some traction or load is applied on it. The pair-potential is based on an exponential term corrected by B-spline terms. In order to accelerate the computations, one uses a hierarchical optimization for the B-splines on different levels. Carbon graphenes constitute the configurations used in the simulations. We report on some results to show the efficiency of the B-splines on different levels.
文摘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.
