arXiv subjects

Jiaojiao Zhang

Publications and source records attributed to Jiaojiao Zhang.

22 records · Page 2Linked to original sources

arXiv2022

Variance-Reduced Stochastic Quasi-Newton Methods for Decentralized Learning: Part I

In this work, we investigate stochastic quasi-Newton methods for minimizing a finite sum of cost functions over a decentralized network. In Part I, we develop a general algorithmic framework that incorporates stochastic quasi-Newton approximations with variance reduction so as to achieve fast convergence. At each time each node constructs a local, inexact quasi-Newton direction that asymptotically approaches the global, exact one. To be specific, (i) A local gradient approximation is constructed by using dynamic average consensus to track the average of variance-reduced local stochastic gradients over the entire network; (ii) A local Hessian inverse approximation is assumed to be positive definite with bounded eigenvalues, and how to construct it to satisfy these assumptions will be given in Part II. Compared to the existing decentralized stochastic first-order methods, the proposed general framework introduces the second-order curvature information without incurring extra sampling or communication. With a fixed step size, we establish the conditions under which the proposed general framework linearly converges to an exact optimal solution.

math.OC↗

arXiv2020

Diagnosis of electron density and temperature by using collisional radiative model in capacitively coupled Ar plasmas I: triple-frequency discharges

An 18-level argon collisional radiative model (CRM) suitable for low pressure was established. The model can be solved by combining the optical emission spectroscopy (OES) with Langmuir probe calibration. In the capacitively coupled plasmas (CCPs) with different frequency and power, the electron temperature and density obtained by the model were compared with those measured by Langmuir probe. It is found that the calibration point at any frequency or power is suitable for the fixed pressure. This method was then applied to the diagnosis of triple-frequency (TF) CCPs, it is shown that the high frequency (HF) power mainly controls the electron density, the low frequency (LF) power mainly controls the electron temperature, and the intermediate frequency (IF) power was between the two. Compared with the dual-frequency (DF) CCPs, it is found that with the increase of IF power, the HF power can control the electron density more independently with less influence on the electron temperature.

physics.plasm-ph↗

arXiv2020

A Newton Tracking Algorithm with Exact Linear Convergence Rate for Decentralized Consensus Optimization

This paper considers the decentralized consensus optimization problem defined over a network where each node holds a second-order differentiable local objective function. Our goal is to minimize the summation of local objective functions and find the exact optimal solution using only local computation and neighboring communication. We propose a novel Newton tracking algorithm, where each node updates its local variable along a local Newton direction modified with neighboring and historical information. We investigate the connections between the proposed Newton tracking algorithm and several existing methods, including gradient tracking and second-order algorithms. Under the strong convexity assumption, we prove that it converges to the exact optimal solution at a linear rate. Numerical experiments demonstrate the efficacy of Newton tracking and validate the theoretical findings.

math.OC↗

arXiv2014

Electronic properties and stability of three new kinds of single-atom-thick SIC graphyne sheets

Three new single-atom-thick silicon-carbon stable systems have been found by using of SCED-LCAO and DFT methods. An important position, named bone position, is proposed in these structures. For SiC and Si1C9 system, the bone positions are partially occupied by Si atoms, the plane structure is kept and electronic gap is opened with 0.955 eV and 0.689 eV respectively. For Si2C8 system, the bone positions are fully occupied by Si atoms. It shows a buckled structure with a buckling of 0.05 Å and a Dirac cone at M point. Moreover, the sp hybridization between Si and C atoms in SiC system is found and the co-existence of sp, sp2 and sp3 hybridization is also found in Si2C8 system. The thermal stability for these three systems is certified.

cond-mat.mtrl-sci↗