5 papers
Convergence of high-index saddle dynamics for degenerate saddle points on critical manifolds
Tao Luo, Jianyuan Yin, Lei Zhang +1
The high-index saddle dynamics (HiSD) method provides a powerful framework for finding saddle points and constructing solution landscapes. While originally derived for nondegenerat…
Optimal Error Estimates of a Linearized Backward Euler Localized Orthogonal Decomposition for the Landau-Lifshitz Equation
Zetao Ma, Rui Du, Lei Zhang
We introduce a novel spatial discretization technique for the reliable and efficient simulation of magnetization dynamics governed by the Landau-Lifshitz (LL) equation. The overall…
Higher-Order Boundary Conditions for Atomistic Dislocation Simulations
Xinyi Wei, Julian Braun, Yangshuai Wang +1
We present a higher-order boundary condition for atomistic simulations of dislocations that address the slow convergence of standard supercell methods. The method is based on a mul…
Numerical Homogenization of Landau-Lifshitz Equation with Rough Coefficients
Zetao Ma, Jingrun Chen, Rui Du +1
In this work, we develop a numerical homogenization approach for the fully nonlinear Landau-Lifshitz equation with rough coefficients, including non-periodicity and nonseparable sc…
Enhancing Accuracy in Deep Learning Using Random Matrix Theory
Leonid Berlyand, Etienne Sandier, Yitzchak Shmalo +1
We explore the applications of random matrix theory (RMT) in the training of deep neural networks (DNNs), focusing on layer pruning that is reducing the number of DNN parameters (w…