arXiv subjects

Guoyu Zhang

Publications and source records attributed to Guoyu Zhang.

9 recordsLinked to original sources

arXiv2026

Green's matching: an efficient approach to parameter estimation in complex dynamic systems

Parameters of differential equations are essential to characterize intrinsic behaviors of dynamic systems. Numerous methods for estimating parameters in dynamic systems are computationally and/or statistically inadequate, especially for complex systems with general-order differential operators, such as motion dynamics. This article presents Green's matching, a computationally tractable and statistically efficient two-step method, which only needs to approximate trajectories in dynamic systems but not their derivatives due to the inverse of differential operators by Green's function. This yields a statistically optimal guarantee for parameter estimation in general-order equations, a feature not shared by existing methods, and provides an efficient framework for broad statistical inferences in complex dynamic systems.

stat.ME↗

arXiv2025

A Pick function approach for designing energy-decay preserving schemes of the Maxwell equations in Havriliak-Negami dispersive media

This work proposes a novel approach for designing high-order energy-decaying schemes for Maxwell's equations in Havriliak-Negami dispersive media. It is shown that conventional convolution quadrature (CQ) methods, which rely directly on the generating function of linear multistep methods, cannot generate completely monotonic sequences beyond first-order accuracy. We rigorously prove that for any linear multistep method of second-or higher-order, the associated generating function $δ(ζ)$ cannot satisfy both that $-δ(ζ)$ is a Pick function and that it is analytic on $(-\infty,1)$ - a key requirement for constructing completely monotonic sequences. To overcome this fundamental limitation, we introduce a reconstruction of the generating function's structure. By strategically incorporating the theory of Pick functions, we successfully construct a second-order completely monotonic sequence. This theoretical advance leads to a discrete scheme that inherits the continuous model's energy decay property, guaranteeing unconditional stability. Numerical experiments confirm the convergence rates and energy dissipation behavior of the proposed method.

math.NA↗

arXiv2025

Analysis of discrete energy-decay preserving schemes for Maxwell's equations in Cole-Cole dispersive medium

This work investigates the design and analysis of energy-decay preserving numerical schemes for Maxwell's equations in a Cole-Cole (C-C) dispersive medium. A continuous energy-decay law is first established for the C-C model through a modified energy functional. Subsequently, a novel $θ$-scheme is proposed for temporal discretization, which is rigorously proven to preserve a discrete energy dissipation property under the condition $θ\in [\fracα{2}, \frac{1}{2}]$. The temporal convergence rate of the scheme is shown to be first-order for $θ\neq 0.5$ and second-order for $θ= 0.5$. Extensive numerical experiments validate the theoretical findings, including convergence tests and energy-decay comparisons. The proposed SFTR-$θ$ scheme demonstrates superior performance in maintaining monotonic energy decay compared to an alternative 2nd-order fractional backward difference formula, particularly in long-time simulations, highlighting its robustness and physical fidelity.

math.NA↗

arXiv2025

Machine learning-driven elasticity prediction in advanced inorganic materials via convolutional neural networks

Inorganic crystal materials have broad application potential due to excellent physical and chemical properties, with elastic properties (shear modulus, bulk modulus) crucial for predicting materials' electrical conductivity, thermal conductivity and mechanical properties. Traditional experimental measurement suffers from high cost and low efficiency, while theoretical simulation and graph neural network-based machine learning methods--especially crystal graph convolutional neural networks (CGCNNs)--have become effective alternatives, achieving remarkable results in predicting material elastic properties. This study trained two CGCNN models using shear modulus and bulk modulus data of 10987 materials from the Matbench v0.1 dataset, which exhibit high accuracy (mean absolute error <13, coefficient of determination R-squared close to 1) and good generalization ability. Materials were screened to retain those with band gaps between 0.1-3.0 eV and exclude radioactive element-containing compounds. The final predicted dataset comprises two parts: 54359 crystal structures from the Materials Project database and 26305 crystal structures discovered by Merchant et al. (2023 Nature 624 80). Ultimately, this study completed the prediction of shear modulus and bulk modulus for 80664 inorganic crystals. This work enriches existing material elastic data resources and provides robust support for material design, with all data openly available at https://doi.org/10.57760/sciencedb.j00213.00104.

cond-mat.mtrl-sci↗

arXiv2025

Computational Efficient and Minimax Optimal Nonignorable Matrix Completion

While the matrix completion problem has attracted considerable attention over the decades, few works address the nonignorable missing issue and all have their limitations. In this article, we propose a nuclear norm regularized row- and column-wise matrix U-statistic loss function for the generalized nonignorable missing mechanism, a flexible and generally applicable missing mechanism which contains both ignorable and nonignorable missing mechanism assumptions. The proposed method achieves computational efficiency comparable to the existing missing-at-random approaches, while providing the near minimax optimal statistical convergence rate guarantees for the more general nonignorable missing case. We propose an accelerated proximal gradient algorithm to solve the associated optimization problem, and characterize the interaction between algorithmic and statistical convergence. Simulations and real data analyzes further support the practical utility of the proposed method.

stat.ML↗

arXiv2025

Universal Bootstrap for Spectral Statistics: Beyond Gaussian Approximation

Spectral analysis plays a crucial role in high-dimensional statistics, where determining the asymptotic distribution of various spectral statistics remains a challenging task. Due to the difficulties of deriving the analytic form, recent advances have explored data-driven bootstrap methods for this purpose. However, widely used Gaussian approximation-based bootstrap methods, such as the empirical bootstrap and multiplier bootstrap, have been shown to be inconsistent in approximating the distributions of spectral statistics in high-dimensional settings. To address this issue, we propose a universal bootstrap procedure based on the concept of universality from random matrix theory. Our method consistently approximates a broad class of spectral statistics across both high- and ultra-high-dimensional regimes, accommodating scenarios where the dimension-to-sample-size ratio $p/n$ converges to a nonzero constant or diverges to infinity without requiring structural assumptions on the population covariance matrix, such as eigenvalue decay or low effective rank. We showcase this universal bootstrap method for high-dimensional covariance inference. Extensive simulations and a real-world data study support our findings, highlighting the favorable finite sample performance of the proposed universal bootstrap procedure.

math.ST↗

arXiv2023

Convolution quadrature for Hadamard fractional calculus and correction methods for the subdiffusion with singular source terms

The convolution quadrature method originally developed for the Riemann-Liouville fractional calculus is extended in this work to the Hadamard fractional calculus by using the exponential type meshes. Local truncation error analysis is presented for singular solutions. By adopting the fractional BDF-$p(1\leq p \leq 6)$ for the Caputo-Hadamard fractional derivative in solving subdiffusion problem with singular source terms, and using the finite element method to discretize the space variable, we carry out the sharp error analysis rigorously and obtain the optimal accuracy by the novel correction technique. Our correction method is a natural generalization of the one developed for subdiffusion problems with smooth source terms. Numerical tests confirm the correctness of our theoretical results.

math.NA↗

arXiv2023

A high-order discrete energy decay and maximum-principle preserving scheme for time fractional Allen-Cahn equation

The shifted fractional trapezoidal rule (SFTR) with a special shift is adopted to construct a finite difference scheme for the time-fractional Allen-Cahn (tFAC) equation. Some essential key properties of the weights of SFTR are explored for the first time. Based on these properties, we rigorously demonstrate the discrete energy decay property and maximum-principle preservation for the scheme. Numerical investigations show that the scheme can resolve the intrinsic initial singularity of such nonlinear fractional equations as tFAC equation on uniform meshes without any correction. Comparison with the classic fractional BDF2 and L2-1$_σ$ method further validates the superiority of SFTR in solving the tFAC equation. Experiments concerning both discrete energy decay and discrete maximum-principle also verify the correctness of the theoretical results.

math.NA↗

arXiv2022

Construction of high-order robust theta-methods with applications in anomalous models

A general conversion strategy by involving a shifted parameter $θ$ is proposed to construct high-order accuracy difference formulas for fractional calculus operators. By converting the second-order backward difference formula with such strategy, a novel $θ$-scheme with correction terms is developed for the subdiffusion problem with nonsmooth data, which is robust even for very small $α$ and can resolve the initial singularity.The optimal error estimates are carried out with essential arguments and are verified by numerical tests.

math.NA↗