arXiv subjects

Zhiguo Yang

Publications and source records attributed to Zhiguo Yang.

At least 19 recordsLinked to original sources

arXiv2026

A geometric reformulation and structure-preserving rotational discrete gradient scheme for the full Ericksen-Leslie model

In this paper, we present a structure-preserving rotational discrete gradient method of the full Ericksen-Leslie model for nematic liquid crystal flows with general anisotropic Oseen-Frank elasticity and full Leslie stress. The main difficulty resides in preserving both the pointwise unit-length constraint on the director field and the energy-dissipation at the discrete level, which involves high nonlinearities in the interplay between the length constraint, anisotropic elastic energy, and hydrodynamic couplings. To address this issue, we first reformulate the Ericksen-Leslie system into an equivalent rotational form in which the director evolution is intrinsically tangent to the unit sphere and the coupling terms in the Leslie and Ericksen stresses are reorganized so that the energy exchange and dissipation structure become explicit. Based on this reformulation, we construct rotational discrete gradient schemes that preserve the director length and satisfy an unconditional discrete energy law, together with a fully discrete scheme based on an exact divergence-free spectral approximation. Numerical experiments verify the accuracy, unit-length preservation and energy-stability of the proposed method, and illustrate dynamical effects induced by anisotropic elastic coefficients and shear flow in the full Ericksen-Leslie model.

math.NA↗

arXiv2026

TeleCom-Bench: How Far Are Large Language Models from Industrial Telecommunication Applications?

While Large Language Models have achieved remarkable integration in various vertical scenarios, their deployment in the telecommunications domain remains exploratory due to the lack of a standardized evaluation framework. Current telecom benchmarks primarily focus on static, foundational knowledge and isolated atomic skills, neglecting the equipment-specific documentation and end-to-end industrial workflows essential for real-world production systems. To bridge this gap, we present TeleCom-Bench, a comprehensive benchmark comprising 12 evaluation sets with 22,678 curated samples, which evaluates LLMs across a synergistic hierarchy: (1) Multi-dimensional Knowledge Comprehension, which integrates telecommunication fundamentals, 3GPP protocols, and 5G network architecture with proprietary product knowledge across wired, core, and wireless networks via knowledge graph-driven synthesis; and (2)End-to-End Knowledge Application, which formalizes six core tasks on authentic trajectories from live network agent workflows, including intent recognition, entity extraction, event verification, tool invocation, root cause analysis, and solution generation-across network optimization and fault maintenance scenarios. Evaluations of eight state-of-the-art LLMs reveal a universal Execution Wall: while models achieve 90% accuracy in linguistic interface tasks such as intent recognition and entity extraction, performance collapses to approximately 30% in procedural execution tasks like solution generation. This capability gap demonstrates that current LLMs function competently as diagnosticians but fail as field engineers. TeleCom-Bench provides standardized diagnostics to precisely pinpoint this deficit, offering actionable guidance for domain-specific alignment toward production-ready telecom agents. The dataset and evaluation code have been released at https://github.com/ZTE-AICloud/TeleCom-Bench.

cs.AI↗

arXiv2026

Bridging SFT and RL: Dynamic Policy Optimization for Robust Reasoning

Post-training paradigms for Large Language Models (LLMs), primarily Supervised Fine-Tuning (SFT) and Reinforcement Learning (RL), face a fundamental dilemma: SFT provides stability (low variance) but suffers from high fitting bias, while RL enables exploration (low bias) but grapples with high gradient variance. Existing unified optimization strategies often employ naive loss weighting, overlooking the statistical conflict between these distinct gradient signals. In this paper, we provide a rigorous theoretical analysis of this bias-variance trade-off and propose \textbf{DYPO} (Dynamic Policy Optimization), a unified framework designed to structurally mitigate this conflict. DYPO integrates three core components: (1) a \textit{Group Alignment Loss (GAL)} that leverages intrinsic group dynamics to significantly reduce RL gradient variance; (2) a \textit{Multi-Teacher Distillation} mechanism that corrects SFT fitting bias via diverse reasoning paths; and (3) a \textit{Dynamic Exploitation-Exploration Gating} mechanism that adaptively arbitrates between stable SFT and exploratory RL based on reward feedback. Theoretical analysis confirms that DYPO linearly reduces fitting bias and minimizes overall variance. Extensive experiments demonstrate that DYPO significantly outperforms traditional sequential pipelines, achieving an average improvement of 4.8\% on complex reasoning benchmarks and 13.3\% on out-of-distribution tasks. Our code is publicly available at https://github.com/Tocci-Zhu/DYPO.

cs.LG↗

arXiv2025

Revisiting the Data Sampling in Multimodal Post-training from a Difficulty-Distinguish View

Recent advances in Multimodal Large Language Models (MLLMs) have spurred significant progress in Chain-of-Thought (CoT) reasoning. Building on the success of Deepseek-R1, researchers extended multimodal reasoning to post-training paradigms based on reinforcement learning (RL), focusing predominantly on mathematical datasets. However, existing post-training paradigms tend to neglect two critical aspects: (1) The lack of quantifiable difficulty metrics capable of strategically screening samples for post-training optimization. (2) Suboptimal post-training paradigms that fail to jointly optimize perception and reasoning capabilities. To address this gap, we propose two novel difficulty-aware sampling strategies: Progressive Image Semantic Masking (PISM) quantifies sample hardness through systematic image degradation, while Cross-Modality Attention Balance (CMAB) assesses cross-modal interaction complexity via attention distribution analysis. Leveraging these metrics, we design a hierarchical training framework that incorporates both GRPO-only and SFT+GRPO hybrid training paradigms, and evaluate them across six benchmark datasets. Experiments demonstrate consistent superiority of GRPO applied to difficulty-stratified samples compared to conventional SFT+GRPO pipelines, indicating that strategic data sampling can obviate the need for supervised fine-tuning while improving model accuracy. Our code will be released at https://github.com/qijianyu277/DifficultySampling.

cs.CV↗

arXiv2025

Beyond Scaling Law: A Data-Efficient Distillation Framework for Reasoning

Large language models (LLMs) demonstrate remarkable reasoning capabilities in tasks such as algorithmic coding and mathematical problem-solving. Recent methods have improved reasoning through expanded corpus and multistage training combining reinforcement learning and supervised fine-tuning. Although some methods suggest that small but targeted dataset can incentivize reasoning via only distillation, a reasoning scaling laws is still taking shape, increasing computational costs. To address this, we propose a data-efficient distillation framework (DED) that optimizes the Pareto frontier of reasoning distillation. Inspired by the on-policy learning and diverse roll-out strategies of reinforcement learning, the key idea of our approach is threefold: (1) We identify that benchmark scores alone do not determine an effective teacher model. Through comprehensive comparisons of leading reasoning LLMs, we develop a method to select an optimal teacher model. (2) While scaling distillation can enhance reasoning, it often degrades out-of-domain performance. A carefully curated, smaller corpus achieves a balanced trade-off between in-domain and out-of-domain capabilities. (3) Diverse reasoning trajectories encourage the student model to develop robust reasoning skills. We validate our method through evaluations on mathematical reasoning (AIME 2024/2025, MATH-500) and code generation (LiveCodeBench), achieving state-of-the-art results with only 0.8k carefully curated examples, bypassing the need for extensive scaling. Our systematic analysis demonstrates that DED outperforms existing methods by considering factors beyond superficial hardness, token length, or teacher model capability. This work offers a practical and efficient pathway to advanced reasoning while preserving general capabilities.

cs.LG↗

arXiv2025

Structure-Aware Corpus Construction and User-Perception-Aligned Metrics for Large-Language-Model Code Completion

Code completion technology based on large language model has significantly improved the development efficiency of programmers. However, in practical applications, there remains a gap between current commonly used code completion evaluation metrics and users' actual perception. To address this issue, we propose two evaluation metrics for code completion tasks--LCP and ROUGE-LCP, from the perspective of probabilistic modeling. Furthermore, to tackle the lack of effective structural semantic modeling and cross-module dependency information in LLMs for repository-level code completion scenarios, we propose a data processing method based on a Structure-Preserving and Semantically-Reordered Code Graph (SPSR-Graph). Through theoretical analysis and experimental validation, we demonstrate the superiority of the proposed evaluation metrics in terms of user perception consistency, as well as the effectiveness of the data processing method in enhancing model performance.

cs.SE↗

arXiv2024

A divergence-free projection method for quasiperiodic photonic crystals in three dimensions

This paper presents a point-wise divergence-free projection method for numerical approximations of photonic quasicrystals problems. The original three-dimensional quasiperiodic Maxwell's system is transformed into a periodic one in higher dimensions through a variable substitution involving the projection matrix, such that periodic boundary condition can be readily applied. To deal with the intrinsic divergence-free constraint of the Maxwell's equations, we present a quasiperiodic de Rham complex and its associated commuting diagram, based on which a point-wise divergence-free quasiperiodic Fourier spectral basis is proposed. With the help of this basis, we then propose an efficient solution algorithm for the quasiperiodic source problem and conduct its rigorous error estimate. Moreover, by analyzing the decay rate of the Fourier coefficients of the eigenfunctions, we further propose a divergence-free reduced projection method for the quasiperiodic Maxwell eigenvalue problem, which significantly alleviates the computational cost. Several numerical experiments are presented to validate the efficiency and accuracy of the proposed method.

math.NA↗

arXiv2024

Reduced projection method for photonic moiré lattices

This paper presents a reduced projection method for the solution of quasiperiodic Schrödinger eigenvalue problems for photonic moiré lattices. Using the properties of the Schrödinger operator in higher-dimensional space via a projection matrix, we rigorously prove that the generalized Fourier coefficients of the eigenfunctions exhibit faster decay rate along a fixed direction associated with the projection matrix. An efficient reduction strategy of the basis space is then proposed to reduce the degrees of freedom significantly. Rigorous error estimates of the proposed reduced projection method are provided, indicating that a small portion of the degrees of freedom is sufficient to achieve the same level of accuracy as the classical projection method. We present numerical examples of photonic moiré lattices in one and two dimensions to demonstrate the accuracy and efficiency of our proposed method.

math.NA↗

arXiv2024

Highly efficient Gauss's law-preserving spectral algorithms for Maxwell's double-curl source and eigenvalue problems based on eigen-decomposition

In this paper, we present Gauss's law-preserving spectral methods and their efficient solution algorithms for curl-curl source and eigenvalue problems in two and three dimensions arising from Maxwell's equations. Arbitrary order $H(curl)$-conforming spectral basis functions in two and three dimensions are firstly proposed using compact combination of Legendre polynomials. A mixed formulation involving a Lagrange multiplier is then adopted to preserve the Gauss's law in the weak sense. To overcome the bottleneck of computational efficiency caused by the saddle-point nature of the mixed scheme, we present highly efficient solution algorithms based on reordering and decoupling of the resultant linear algebraic system and numerical eigen-decomposition of one dimensional mass matrix. The proposed solution algorithms are direct methods requiring only several matrix-matrix or matrix-tensor products of $N$-by-$N$ matrices, where $N$ is the highest polynomial order in each direction. Compared with other direct methods, the computational complexities are reduced from $O(N^6)$ and $O(N^9)$ to $O(N^3)$ and $O(N^4)$ with small and constant pre-factors for 2D and 3D cases, respectively, and can further be accelerated to $O(N^{2.807})$ and $O(N^{3.807})$, when boosted with the Strassen's matrix multiplication algorithm. Moreover, these algorithms strictly obey the Helmholtz-Hodge decomposition, thus totally eliminate the spurious eigen-modes of non-physical zero eigenvalues. Extensions of the proposed methods and algorithms to problems in complex geometries with variable coefficients and inhomogeneous boundary conditions are discussed to deal with more general situations. Ample numerical examples for solving Maxwell's source and eigenvalue problems are presented to demonstrate the accuracy and efficiency of the proposed methods.

math.NA↗

arXiv2023

An exact divergence-free spectral method for incompressible and resistive magneto-hydrodynamic equations in two and three dimensions

In this paper, we present exact divergence-free spectral method for solving the incompressible and resistive magneto-hydrodynamic (MHD) equations in two and three dimensions, as well as the efficient solution algorithm and unconditionally energy-stable fully-discretized numerical schemes. We introduce new ideas of constructing two families of exact divergence-free vectorial spectral basis functions on domains diffeomorphic to squares or cubes. These bases are obtained with the help of orthogonality and derivative relation of generalised Jacobi polynomials, several de Rham complexes, as well as the property of contravariant Piola transformation. They are well-suited for discretizing the velocity and magnetic fields, respectively, thereby ensuring point-wise preservation of the incompressibility condition and the magnetic Gauss's law. With the aid of these bases, we propose a family of exact divergence-free implicit-explicit $k$-step backward differentiation formula (DF-BDF-$k$) fully-discretized schemes for the MHD system. These schemes naturally decouple the pressure field from the velocity field. Consequently, the stability of the space-time fully-discretized numerical schemes based on these bases are significantly enhanced. These schemes exhibit unconditional stability for $k=1,2$, and demonstrate exceptional stability and accuracy for $k=3,4$, verified with extensive numerical results for long time simulations using large time step sizes. Furthermore, we present efficient solution algorithms for these two decoupled equations for the velocity and magnetic fields, respectively, by exploiting the sparsity and structure of the resultant linear algebraic systems. Ample numerical examples in two and three dimensions are provided to demonstrate the distinctive accuracy, efficiency and stability of our proposed method.

math.NA↗

arXiv2023

A second-order SO(3)-preserving and energy-stable scheme for orthonormal frame gradient flow model of biaxial nematic liquid crystals

In this paper, we present a novel second-order generalised rotational discrete gradient scheme for numerically approximating the orthonormal frame gradient flow of biaxial nematic liquid crystals. This scheme relies on reformulating the original gradient flow system into an equivalent generalised "rotational" form. A second-order discrete gradient approximation of the energy variation is then devised such that it satisfies an energy difference relation. The proposed numerical scheme has two remarkable properties: (i) it strictly obeys the orthonormal property of the tensor field and (ii) it satisfies the energy dissipation law at the discrete level, regardless of the time step sizes. We provide ample numerical results to validate the accuracy, efficiency, unconditional stability and SO(3)-preserving property of this scheme. In addition, comparisons of the simulation results between the biaxial orthonormal frame gradient flow model and uniaxial Oseen-Frank gradient flow are made to demonstrate the ability of the former to characterize non-axisymmetric local anisotropy.

math.NA↗

arXiv2023

A highly efficient and accurate divergence-free spectral method for curl-curl equation in two and three dimensions

In this paper, we present a fast divergence-free spectral algorithm (FDSA) for the curl-curl problem. Divergence-free bases in two and three dimensions are constructed by using the generalized Jacobi polynomials. An accurate spectral method with exact preservation of the divergence-free constraint point-wisely is then proposed, and its corresponding error estimate is established. We then present a highly efficient solution algorithm based on a combination of matrix-free preconditioned Krylov subspace iterative method and a fully diagonalizable auxiliary problem, which is derived from the spectral discretisations of generalized eigenvalue problems of Laplace and biharmonic operators. We rigorously prove that the dimensions of the invariant subspace of the preconditioned linear system resulting from the divergence-free spectral method with respect to the dominate eigenvalue $1$, are $(N-3)^2$ and $2(N-3)^3$ for two- and three-dimensional problems with $(N-1)^2$ and $2(N-1)^3$ unknowns, respectively. Thus, the proposed method usually takes only several iterations to converge, and astonishingly, as the problem size (polynomial order) increases, the number of iterations will decrease, even for highly indefinite system and oscillatory solutions. As a result, the computational cost of the solution algorithm is only a small multiple of $N^3$ and $N^4$ floating number operations for 2D and 3D problems, respectively. Plenty of numerical examples for solving the curl-curl problem with both constant and variable coefficients in two and three dimensions are presented to demonstrate the accuracy and efficiency of the proposed method.

math.NA↗

arXiv2023

A second-order length-preserving and unconditionally energy stable rotational discrete gradient method for Oseen-Frank gradient flows

We present a second-order strictly length-preserving and unconditionally energy-stable rotational discrete gradient (Rdg) scheme for the numerical approximation of the Oseen-Frank gradient flows with anisotropic elastic energy functional. Two essential ingredients of the Rdg method are reformulation of the length constrained gradient flow into an unconstrained rotational form and discrete gradient discretization for the energy variation. Besides the well-known mean-value and Gonzalez discrete gradients, we propose a novel Oseen-Frank discrete gradient, specifically designed for the solution of Oseen-Frank gradient flow. We prove that the proposed Oseen-Frank discrete gradient satisfies the energy difference relation, thus the resultant Rdg scheme is energy stable. Numerical experiments demonstrate the efficiency and accuracy of the proposed Rdg method and its capability for providing reliable simulation results with highly disparate elastic coefficients.

math.NA↗

arXiv2023

Pythagoras Superposition Principle for Localized Eigenstates of 2D Moiré Lattices

Moiré lattices are aperiodic systems formed by a superposition of two periodic lattices with a relative rotational angle. In optics, the photonic moiré lattice has many appealing properties such as its ability to localize light, thus attracting much attention on exploring features of such a structure. One fundamental research area for photonic moiré lattices is the properties of eigenstates, particularly the existence of localized eigenstates and the localization-to-delocalization transition in the energy band structure. Here we propose an accurate algorithm for the eigenproblems of aperiodic systems by combining plane wave discretization and spectral indicator validation under the higher-dimensional projection, allowing us to explore energy bands of fully aperiodic systems. A localization-delocalization transition regarding the intensity of the aperiodic potential is observed and a novel Pythagoras superposition principle for localized eigenstates of 2D moiré lattices is revealed by analyzing the relationship between the aperiodic and its corresponding periodic eigenstates. This principle sheds light on exploring the physics of localizations for moiré lattice.

physics.optics↗

arXiv2022

An Energy-Conserving Fourier Particle-in-Cell Method with Asymptotic-Preserving Preconditioner for Vlasov-Ampère System with Exact Curl-Free Constraint

We present an efficient and accurate energy-conserving implicit particle-in-cell~(PIC) algorithm for the electrostatic Vlasov system, with particular emphasis on its high robustness for simulating complex plasma systems with multiple physical scales. This method consists of several indispensable elements: (\romannumeral1) the reformulation of the original Vlasov-Poisson system into an equivalent Vlasov-Ampère system with divergence-/curl-free constraints; (\romannumeral2) a novel structure-preserving Fourier spatial discretization, which exactly preserves these constraints at the discrete level; (\romannumeral3) a preconditioned Anderson-acceleration algorithm for the solution of the highly nonlinear system; and (\romannumeral4) a linearized and uniform approximation of the implicit Crank-Nicolson scheme for various Debye lengths, based on the generalized Ohm's law, which serves as an asymptotic-preserving preconditioner for the proposed method. Numerical experiments are conducted, and comparisons are made among the proposed energy-conserving scheme, the classical leapfrog scheme, and a Strang operator-splitting scheme to demonstrate the superiority of the proposed method, especially for plasma systems crossing physical scales.

physics.comp-ph↗

arXiv2022

An Asymptotic-Preserving and Energy-Conserving Particle-In-Cell Method for Vlasov-Maxwell Equations

In this paper, we develop an asymptotic-preserving and energy-conserving (APEC) Particle-In-Cell (PIC) algorithm for the Vlasov-Maxwell system. This algorithm not only guarantees that the asymptotic limiting of the discrete scheme is a consistent and stable discretization of the quasi-neutral limit of the continuous model, but also preserves Gauss's law and energy conservation at the same time, thus it is promising to provide stable simulations of complex plasma systems even in the quasi-neutral regime. The key ingredients for achieving these properties include the generalized Ohm's law for electric field such that the asymptotic-preserving discretization can be achieved, and a proper decomposition of the effects of the electromagnetic fields such that a Lagrange multiplier method can be appropriately employed for correcting the kinetic energy. We investigate the performance of the APEC method with three benchmark tests in one dimension, including the linear Landau damping, the bump-on-tail problem and the two-stream instability. Detailed comparisons are conducted by including the results from the classical explicit leapfrog and the previously developed asymptotic-preserving PIC schemes. Our numerical experiments show that the proposed APEC scheme can give accurate and stable simulations both kinetic and quasi-neutral regimes, demonstrating the attractive properties of the method crossing scales.

physics.plasm-ph↗

arXiv2020

gPAV-Based Unconditionally Energy-Stable Schemes for the Cahn-Hilliard Equation: Stability and Error Analysis

We present several first-order and second-order numerical schemes for the Cahn-Hilliard equation with discrete unconditional energy stability. These schemes stem from the generalized Positive Auxiliary Variable (gPAV) idea, and require only the solution of linear algebraic systems with a constant coefficient matrix. More importantly, the computational complexity (operation count per time step) of these schemes is approximately a half of those of the gPAV and the scalar auxiliary variable (SAV) methods in previous works. We investigate the stability properties of the proposed schemes to establish stability bounds for the field function and the auxiliary variable, and also provide their error analyses. Numerical experiments are presented to verify the theoretical analyses and also demonstrate the stability of the schemes at large time step sizes.

math.NA↗

arXiv2020

On time-domain NRBC for Maxwell's equations and its application in accurate simulation of electromagnetic invisibility cloaks

In this paper, we present analytic formulas of the temporal convolution kernel functions involved in the time-domain non-reflecting boundary condition (NRBC) for the electromagnetic scattering problems. Such exact formulas themselves lead to accurate and efficient algorithms for computing the NRBC for domain reduction of the time-domain Maxwell's system in $\mathbb R^3$. A second purpose of this paper is to derive a new time-domain model for the electromagnetic invisibility cloak. Different from the existing models, it contains only one unknown field and the seemingly complicated convolutions can be computed as efficiently as the temporal convolutions in the NRBC. The governing equation in the cloaking layer is valid for general geometry, e.g., a spherical or polygonal layer. Here, we aim at simulating the spherical invisibility cloak. We take the advantage of radially stratified dispersive media and special geometry, and develop an efficient vector spherical harmonic (VSH)-spectral-element method for its accurate simulation. Compared with limited results on FDTD simulation, the proposed method is optimal in both accuracy and computational cost. Indeed, the saving in computational time is significant.

math.NA↗