Sparsification of long range force networks for molecular dynamics simulations

Area of Science:

• Materials Science
• Computational Physics
• Network Theory

Background:

• Atomic interactions in solids are complex and computationally intensive to model.
• Network theory provides a framework to analyze system dynamics based on interactions.
• Existing methods for simplifying atomistic models often involve approximations that can introduce errors.

Purpose of the Study:

• To develop and evaluate a spectral sparsification technique for constructing sparse atomic interaction networks.
• To compare the accuracy and efficiency of spectral sparsification against the common thresholding method.
• To quantify error propagation from local approximations to global continuum scales.

Main Methods:

• Application of network theory to model atomic interactions in solid materials.
• Development of a spectral sparsification algorithm to create sparse interaction networks.
• Comparison of spectral sparsification with a cut-off radius (threshold) method.
• Quantification of interatomic force approximation errors and their propagation.
• Implementation on surface relaxation and tensile test simulations.

Main Results:

• Spectral sparsification reduces computational complexity while preserving macroscopic conservation properties.
• For short-range potentials (Lennard-Jones), spectral sparsification yields results comparable to thresholding.
• For long-range potentials (Coulomb), spectral sparsification shows improved performance over thresholding.
• Error propagation from local approximations to global scales is assessed.

Conclusions:

• Spectral sparsification is a viable and efficient technique for modeling atomic interactions in solids.
• This method offers advantages over traditional thresholding, particularly for systems with long-range interactions.
• The network-theoretic approach provides a robust framework for materials simulations.