多尺度介面與吸收性邊界條件應用於非平衡態分子動力學模擬：半解析法與機器學習

許育銓

doi:10.6342/NTU201801340

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多尺度介面與吸收性邊界條件應用於非平衡態分子動力學模擬：半解析法與機器學習

Multiscale Interface and Absorbing Boundary Condition for Non-Equilibrium Molecular Dynamics Simulation: Semi-Analytical Formulation and Machine Learning

許育銓 , Masters　　Advisor：陳俊杉　　

繁體中文 DOI： 10.6342/NTU201801340

非平衡態分子動力學；失真性波反射；多尺度介面；吸收性邊界條件；無反射；尺寸效應；機器學習； non-equilibrium molecular dynamics ； spurious wave reflection ； multiscale interface ； absorbing boundary condition ； non-reflection ； size effect ； machine learning

Abstract │ Reference (31) │ Altmetrics

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Molecular dynamics (MD) simulation has been widely applied in studying materials behavior in the past decades. However, owning to its great demands on the modeling fidelity, MD is often limited by the length scale it can handle. Although it is much desired to develop multiscale modeling to overcome this limitation, the development of dynamic multiscale modeling is limited by the spurious wave-reflection problems on the interface between atoms and continuum.
This study has developed a multiscale semi-analytical formulation for arbitrary lattices in MD. This method decomposes MD system into a coupled-domain of real and virtual domains, dissembles the contribution from the virtual domain in frequency, and derives the time-history kernel function (THKF) accounting for the interaction of virtual domain implicitly. The virtual atoms on the interface can further be controlled by this numerical method after pairing of degree-of-freedom of THKF and atoms on the interface. By doing so, the dynamics simulation without considering virtual atoms will be equivalent to the original full MD simulation.
In a broad sense, multiscale interface (MI) from this study is a two-way implicit interface across real domains, which is not limited to the number of real domains and the way of coupling. However, in the special case of single real domain, multiscale interface reduces to the classical absorbing boundary condition (ABC). There is some key difference between these two applications. ABC totally ignores the information of the virtual domain, thus the time-cutoff of convolution can reduce the computational cost and maintain the bound of the non-reflecting system. On the other hand, due to the transition of the information between different real domains, the simulation of MI will result in spurious wave reflection if THKF are interfered by the time-cutoff. In addition, THKF analyzed from the MI has strong physical meanings of real space that contains the size effect, which can be further developed to resolve length scale limitation in MD.
In this thesis, we also explore the possibility of applying machine learning (ML) in ABC based on the function form in THKF. The preliminary verification has been completed and ML for ABC can reduce the computational efforts substantially. This poses a good direction to develop ML for MI in the future.

Reference ( 31 ) 〈TOP〉

[1] E. T. Jaynes, “Information Theory and Statistical Mechanics,” Physical Review, vol. 106, no. 4, pp. 620-630, 1957.
[2] M. C. Payne, M. P. Teter, D. C. Allan, T. A. Arias, and J. D. Joannopoulos, “Iterative minimization techniques forab initiototal-energy calculations: molecular dynamics and conjugate gradients,” Reviews of Modern Physics, vol. 64, no. 4, pp. 1045-1097, 1992.
[3] R. Lustig, “Statistical thermodynamics in the classical molecular dynamics ensemble. I. Fundamentals,” The Journal of Chemical Physics, vol. 100, no. 4, pp. 3048-3059, 1994.
[4] R. Car and M. Parrinello, “Unified approach for molecular dynamics and density-functional theory,” Phys Rev Lett, vol. 55, no. 22, pp. 2471-2474, 1985.
[5] C. Wei, D. Srivastava, and K. Cho, “Thermal Expansion and Diffusion Coefficients of Carbon Nanotube-Polymer Composites,” Nano Letters, vol. 2, pp. 647-650, 2002.

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