arXiv subjects

Juan Zhang

Publications and source records attributed to Juan Zhang.

At least 19 recordsLinked to original sources

arXiv2026

Data-driven accelerated multigrid method for Riesz space fractional diffusion equations

The multigrid method is one of the most efficient iterative methods for solving large structured linear systems, and its efficiency stems from the complementarity between the smoother and the coarse grid correction. In this paper, we consider the block Toeplitz linear system obtained by discretizing time dependent Riesz space fractional diffusion equations, and employ the weighted Jacobi iterative method as a smoother. The weighted Jacobi smoother features a simple structure and low computational cost, yet its smoothing property is highly dependent on the relaxation parameter. We adopt Gaussian process regression to select the relaxation parameter to accelerate the convergence of the multigrid method. Numerical experiments confirm the theoretical analysis, which simultaneously verifies the effectiveness and superiority of the data-driven parameter selection strategy.

math.NA↗

arXiv2026

Flux Evolution of PSR B0540--69 and the Spectral Energy Distribution of its Pulsar Wind Nebula

The young Crab-like pulsar PSR B0540--69, located in the Large Magellanic Cloud, underwent a spin-down rate transition (SRT) in 2011 December, after which its pulsar wind nebula (PWN) was reported to brighten up to 2018. In this work, we extend the study of its X-ray and $γ$-ray flux evolution through 2026 by combining observations from multiple X-ray instruments with data from the Fermi Large Area Telescope, thereby constructing a flux history of the PSR$+$PWN system spanning more than two decades. We find that the enhanced X-ray luminosity of the PSR$+$PWN system has persisted for more than 14 yr after the SRT, up to early 2026, whereas the pulsed X-ray flux remains unchanged across all epochs. This confirms that the brightening originates from the PWN. In the $γ$-ray band, neither the pulsed nor the non-pulsed flux shows any detectable long-term variation between 2008 and 2025. Together, these results imply that the additional spin-down energy released at the SRT has been continuously injected into the PWN over decades, placing strong constraints on the energy budget and physical mechanism of the transition. Combining the non-pulsed X-ray and $γ$-ray fluxes measured here with previously published radio-to-UV data, we further construct a broadband spectral energy distribution of the PWN, which shows properties markedly different from those of the Crab Nebula.

astro-ph.HE↗

arXiv2026

In-flight Timing Calibration of the Follow-up X-Ray Telescope on Board the Einstein Probe

After the launch of Einstein Probe (EP), pulsars are observed to calibrate the timing system of the onboard Follow-up X-ray Telescope (FXT) by measuring the times of arrival (TOAs). FXT has two independently operating modules, namely FXTA and FXTB, each equipped with the Wolter-I optics and the pnCCD camera. For scientific observations, each pnCCD has three distinct readout modes that differ in frame cycles, the full frame mode (FF, 50 ms per frame), the partial windowed mode (PW, 2.2 ms per frame), and the timing mode (TM, 23.68 $μ$s per row, 9.4352 ms per frame). Thus, 1RXS J170849.0--400910 with the spin period of 11 s is observed in FF, PSR B1509--58 (150 ms) in PW, and Crab pulsar (33 ms) in TM as well as PSR B1821--24 (3.05 ms) and PSR B1937+21 (1.56 ms). The TOAs of these pulsars measured by FXTA and FXTB are compared with the results of NICER, and for Crab pulsar with the Jodrell Bank Monthly Ephemeris (JBE). Results verify that the timing system of FXTA and FXTB in FF, PW, and TM modes are consistent with each other, and are in good alignment with NICER. The measured advance of the Crab pulsar's main peak relative to JBE is $357^{\pm14(stat)}_{\pm54(sys)} μ$s in FXTA and $394^{\pm14(stat)}_{\pm67(sys)} μ$s in FXTB. Based on measurements of PSR B1821--24 and PSR B1937+21, the preliminary absolute timing accuracy is estimated to be 6 $μ$s for FXTA and 31 $μ$s for FXTB in TM mode. Additionally, the systematic delay of FXTA timing results relative to FXTB is found to be $20^{\pm19(stat)}_{\pm21(sys)} μ$s.

astro-ph.IM↗

arXiv2026

A High-Accuracy Numerical Homogenization Method for Quasiperiodic Hamilton--Jacobi Equations

In this work, we develop an accurate numerical homogenization method for computing effective Hamiltonians of quasiperiodic Hamilton--Jacobi equations (QHJEs) with convex Hamiltonians of the form $H(x,p) = |p|^k/{k}-f(x), ~k>1$, where $f$ is quasiperiodic. Computing effective Hamiltonians in the quasiperiodic setting requires solving QHJEs posed on the whole space. Their solutions generally possess neither translational symmetry nor decay and may exhibit low regularity. These features pose substantial challenges for numerical computation. To address these difficulties, we introduce a quasiperiodic boundary condition, which allows the original whole-space problem to be treated on a bounded domain while preserving quasiperiodicity at the boundary. We then propose an SL--FPR scheme that combines a semi-Lagrangian (SL) approximation with the finite points recovery (FPR) method and establish stability and error estimates for the resulting scheme. We also extend the quasiperiodic homogenization result from the quadratic case to general $k>1$ and apply the proposed method to accurately approximate the corresponding effective Hamiltonians. Numerical experiments illustrate the convergence and applicability of the method and validate the extended homogenization results.

math.NA↗

arXiv2026

Candidate X-ray Counterparts of Ultra-High-Energy Emission of the Galactic Microquasar V4641 Sgr Revealed by Einstein Probe

Microquasars have emerged as promising PeVatron candidates capable of accelerating particles to PeV energies, with recent observations revealing ultra-high-energy (UHE) $γ$-ray emission from extended structures associated with these systems. Multi-wavelength studies of such extended structures are crucial for understanding the acceleration, transport, and radiation processes of UHE cosmic rays (CRs), yet observational evidence remains limited. Here, we report the discovery of diffuse X-ray structures spatially coincident with the TeV $γ$-ray emission regions to the north and south of the microquasar V4641 Sgr, using the Follow-up X-ray Telescope (FXT) onboard the Einstein Probe. We identify X-ray structures located $\sim20$-$40$ pc from V4641 Sgr, extending over several arcminutes. These structures exhibit X-ray fluxes of $\sim1$-$3\times10^{-13}$ erg s$^{-1}$ cm$^{-2}$ and photon indices of $Γ\sim2$-3 in 0.5-8 keV per individual knot. Under the one-zone leptonic interpretation, the weak X-ray emission implies a magnetic field of order $1-2 μ$G. Stronger fields remain possible if only part of the TeV-PeV emission is produced by inverse Compton scattering, with the remaining emission arising from hadronic interactions. The EP-FXT observations support the presence of relativistic electrons on tens-of-parsec scales, while the origin of the UHE $γ$-ray emission remains open.

astro-ph.HE↗

arXiv2026

A Two-level Filtered Subspace Iterative Method for Generalized Hermitian Interior Eigenvalue Problems

We propose a two-level filtered subspace iterative (TLFSI) method for computing all eigenpairs whose eigenvalues in the interval of interest $[a,b]$ after finite element discretization of self-adjoint PDE eigenvalue problems. The method combines a two-level approach with a modern filtered subspace iteration framework. In this paper, we use contour integral filtering as an example. The two-level method constructs a coarse space according to the spectral location of the eigenvalues of interest and obtains from it an approximation to the target invariant subspace. We prove that the distance between the approximate and target subspaces depends only on the separation between the spectral region of interest and the remainder of the spectrum, together with the coarse mesh size $H$. Numerical experiments on benchmark elasticity problems confirm the theoretical predictions.

math.NA↗

arXiv2026

Squeeze10-LLM: Squeezing LLMs' Weights by 10 Times via a Staged Mixed-Precision Quantization Method

Deploying large language models (LLMs) is challenging due to their massive parameters and high computational costs. Ultra low-bit quantization can significantly reduce storage and accelerate inference, but extreme compression (i.e., mean bit-width <= 2) often leads to severe performance degradation. To address this, we propose Squeeze10-LLM, effectively "squeezing" 16-bit LLMs' weights by 10 times. Specifically, Squeeze10-LLM is a staged mixed-precision post-training quantization (PTQ) framework and achieves an average of 1.6 bits per weight by quantizing 80% of the weights to 1 bit and 20% to 4 bits. We introduce Squeeze10LLM with two key innovations: Post-Binarization Activation Robustness (PBAR) and Full Information Activation Supervision (FIAS). PBAR is a refined weight significance metric that accounts for the impact of quantization on activations, improving accuracy in low-bit settings. FIAS is a strategy that preserves full activation information during quantization to mitigate cumulative error propagation across layers. Experiments on LLaMA and LLaMA2 show that Squeeze10-LLM achieves state-of-the-art performance for sub-2bit weight-only quantization, improving average accuracy from 43% to 56% on six zero-shot classification tasks--a significant boost over existing PTQ methods.

cs.LG↗

arXiv2026

LieDiscover: Adaptive Symbolic Library Construction for Explicit Open-form Symmetry Discovery

Discovering underlying symmetries from data has emerged as a crucial challenge in scientific discovery. Existing data-driven methods for symmetry discovery fail to determine the exact number and mathematical form of unknown infinitesimal generators. Recent explicit methods represent generators using a predefined function library and identify them through algebraic optimization, but they often struggle to capture complex symmetries involving high-order polynomials or transcendental functions. To address this limitation, we formulate symmetry discovery as a joint optimization problem over the function library and coefficients. We propose a novel framework that leverages an encoder-decoder architecture to dynamically generate symbolic expressions and expand the library. This generation process is optimized via reinforcement learning, which accelerates the exploration of the symbolic search space through step-wise rewards. Experiments demonstrate that LieDiscover can successfully uncover open-form infinitesimal generators involving high-order polynomials or transcendental functions, which remain intractable for existing methods. The discovered symmetries also improve performance in downstream PDE solving and discovery tasks.

cs.SC↗

arXiv2026

Proof of Nobori's generalized Böttcher-Wenzel inequality conjecture

Let $m,n\ge 2$. For $m\times n$ complex matrices $A$, $C$ and an $n\times m$ matrix $B$, Nobori (Linear Algebra Appl. 725 (2025) 135--144) proposed the following conjecture on the generalized Böttcher-Wenzel inequality: $$ \|ABC-CBA\|_F^2 \le 2\|B\|_2^2\|A\|_{(2),2}^2\|C\|_F^2, $$ where $\|\cdot\|_F$ is the Frobenius norm, $\|\cdot\|_2$ is the spectral norm, and $\|\cdot\|_{(2),2}$ is the $(2,2)$-norm defined by $\|X\|_{(2),2}=\sqrt{σ_1(X)^2+σ_2(X)^2}$, in which $σ_1(X)$ and $σ_2(X)$ are the largest and second largest singular values of $X$, respectively. This paper proves the conjecture and, as a consequence, establishes the Kronecker product inequality that Nobori derived from it. In addition, we show that for each fixed $m,~n\ge 2$, the constant $2$ is sharp. We also give necessary and sufficient conditions for equality, namely, the equality condition in the Böttcher--Wenzel inequality and some matrix identities derived from a fixed singular value decomposition.

math.RA↗

arXiv2026

A counterexample to Huang's weak majorization conjecture

We give a counterexample to a weak majorization problem, proposed by Z. Huang (Linear Algebra Appl., 434 (2) (2011) 457--462), for singular values of Hadamard products of nonnegative matrices. The problem asks whether, for all nonnegative matrices $A$ and $B$, \begin{equation*} \bigl\{s_j^2(A\Had B)\bigr\} \prec_w \bigl\{s_j(A\Had A)s_j(B\Had B)\bigr\} \end{equation*} holds, where $\Had$ denotes the Hadamard product, $\prec_w$ means weak majorization, and $s_j(\cdot)$ is the $j$th largest singular value of a matrix. To answer this problem, we construct two $3\times3$ entrywise positive symmetric matrices. We give rigorous upper and lower bounds for the relevant singular-value sums by Sturm's theorem, and show that the inequality fails for the partial sum with $k=2$.

math.RA↗

arXiv2026

A $3\times 3$ counterexample to Lin and Wimmer's rank-minimization conjecture associated with Roth's similarity theorem

We give a $3\times 3$ counterexample, valid over every field, to a rank-minimization conjecture of Lin and Wimmer (Bull. Aust. Math. Soc., 84 (3) (2011), 441--443) related to Roth's similarity theorem for the Sylvester matrix equation. We also prove that, over the complex field, no counterexample can occur when one of the two matrix sizes is less than $3$. Hence the example is dimensionally minimal over the complex field.

math.RA↗

arXiv2026

Ab initio-based Deep-Learning Prediction of Carrier Mobility in Strongly Anharmonic Materials

Predicting charge transport in strongly anharmonic materials, particularly ultralow thermal conductors, remains a major challenge for first-principles methods. In such systems, perturbative treatments of electron-phonon interactions and the harmonic phonon picture often break down, necessitating non-perturbative approaches. The ab initio Kubo-Greenwood(aiKG) formalism provides a rigorous framework for evaluating temperature-dependent carrier transport beyond the harmonic approximation. Nevertheless, its practical application is computationally demanding because it requires large supercells, extensive statistical sampling, and extrapolation to the zero-frequency limit. In this work, we introduce an artificial-intelligence(AI)-assisted aiKG framework that incorporates the deep-learning Hamiltonian model. By predicting the Kohn-Sham Hamiltonian with sub-meV accuracy for supercells of up to 250 atoms, the model bypasses the costly iterative self-consistent field calculations while retaining first-principles reliability within the scope of effects captured by the training data. Using a strongly anharmonic thermal insulator, potassium iodide(KI) as a benchmark system, we demonstrate that the proposed approach enables efficient simulations of electronic structure and transport properties from a large supercell. The framework reproduces temperature-dependent carrier mobilities, spectral functions, and effective masses in close agreement with the underlying density functional theory while reducing computational cost to 10%. These results suggest that the AI-assisted aiKG framework can make non-perturbative transport calculations tractable for strongly anharmonic materials, opening a scalable route towards realistic simulations and accelerated discovery of new functional materials.

cond-mat.mtrl-sci↗

arXiv2026

A Structure-Exploiting Implicit-Explicit Trust Region Method for Computing Second-Order Stationary Points of the Landau-Brazovskii Model

This work focuses on the reliable computation of second-order stationary points in the high-dimensional nonconvex energy landscape of the Landau-Brazovskii (LB) model, a fundamental model for studying phases and phase transitions. For this purpose, we develop an efficient implicit-explicit trust region (IMEX-TR) method. Trust region (TR) methods can avoid saddle-point stagnation and guarantee convergence to second-order stationary points under appropriate conditions. However, their direct application to the LB model has been impractical because the Hessian is dense if treated directly. The proposed IMEX-TR method overcomes this difficulty by exploiting the Hessian's special structure: the linear interaction part is diagonal in reciprocal space, whereas the nonlinear bulk-energy part is diagonal in physical space. Based on this structure, we design an efficient solver for the TR subproblem that with globally convergent guarantee and enjoys FFT-based acceleration, with $\mathcal O(N \log N)$ complexity per iteration. Existing first-order gradient-based methods for the LB model only guarantee convergence to first-order stationary points and may stagnate at saddle points. In contrast, the proposed IMEX-TR method inherits the theoretical guarantee of converging to second-order stationary points while remaining computationally practical. Numerical experiments verify the theoretical properties of the algorithm and demonstrate its robustness in locating stable phases from different initial conditions. Numerical results also show that IMEX-TR can escape unstable stationary states reached by first-order schemes and converge to physically meaningful second-order stationary points. These results suggest that targeting second-order stationary points provides an effective computational paradigm for exploring complex free-energy landscapes and identifying stable or metastable states.

math.NA↗

arXiv2026

NanoBTE: Fast Iterative Solution of the Phonon Boltzmann Transport Equation for Nanoscale Heat Transport

Nanoscale heat dissipation has become a critical challenge in advanced semiconductor devices, where phonon transport can strongly deviate from the classical Fourier description due to the boundary scattering and ballistic effects. In this work, we propose NanoBTE, a deterministic finite-volume solver for the non-gray phonon Boltzmann transport equation under the relaxation-time approximation. The solver supports complex two- and three-dimensional geometries, band-resolved phonon properties, discrete-ordinates angular quadrature, volumetric heat generation, and multiple phonon boundary conditions, including thermalizing, diffuse, and specular reflections. %To improve the efficiency of multiscale simulations, both sequential and synthetic iterative schemes are implemented, where the latter couples the microscopic phonon transport equation with a macroscopic diffusion-type temperature equation to accelerate convergence in near-diffusive regimes. Both sequential and synthetic iterative options are implemented for the steady-state solution. Furthermore, NanoBTE adopts a band-direction task decomposition strategy, enabling efficient MPI-based CPU parallelization and GPU acceleration of the dominant sparse transport operations.

cond-mat.mtrl-sci↗

arXiv2026

Newton-Based Mixed Precision Iterative Refinement for Large-Scale Sparse Continuous-Time Algebraic Riccati Equations

We propose a Newton-based mixed precision iterative refinement framework for solving large-scale sparse continuous-time algebraic Riccati equations (CAREs). The framework computes the initial approximation and the inner Lyapunov correction equations in lower precision, while evaluating residuals and updating the solution in higher precision. To handle indefinite residuals and Newton correction terms in low-rank form, we introduce factor decomposition procedures with truncation strategies that preserve positive semidefiniteness and control rank growth. A first-order rounding error analysis derives a residual recurrence for the refinement process and relates stable mixed precision refinement to a Lyapunov operator conditioning threshold governed by the unit roundoff of the lower precision inner solves. We then present a concrete ADI-based realization, using NLR-ADI for the initial CARE approximation and LR-ADI for the inner Lyapunov correction equations. Compared with dense Lyapunov correction implementations, this realization reduces the main computations to shifted linear solves and low-rank factor operations, and we provide a solver-dependent complexity analysis. Numerical experiments on dense CARE over a range of condition numbers illustrate the conditioning effect described by the error analysis, and experiments on large-scale sparse CAREs show that the mixed precision framework is faster than the full double precision implementation while maintaining the same level of accuracy.

math.NA↗

arXiv2026

InfraNet: Quality-Aware RGB Guidance for Efficient Infrared Object Detection

Robust object detection under adverse visual conditions remains a long-standing challenge for multi-modal perception systems. Existing fusion-based methods typically require both RGB and infrared (IR) inputs, and treat them equally during both training and inference, which compromises their robustness when the RGB modality becomes unreliable or unavailable. In this case, we propose \textbf{InfraNet}, an IR-centric quality-aware framework that regulates RGB guidance during training and supports flexible RGB--IR or IR-only deployment. InfraNet employs an asymmetric architecture where the primary IR pathway extracts multi-scale infrared features for predictions, while the auxiliary RGB pathway provides reliability-controlled supervisory signals. The core of InfraNet is \textbf{QualGate}, a quality-aware fusion module that learns a task-oriented control signal to suppress unreliable RGB guidance and compensate IR features during cross-modal training. Built upon InfraNet, we design two architectural variants: a lightweight IR-only architecture InfraNet-IR and an RGB--IR architecture InfraNet-RGB-IR. Our method is evaluated through extensive experiments on four benchmark datasets (LLVIP, FLIR-Aligned, M$^3$FD, and DroneVehicle), showing strong or competitive accuracy in challenging low-light and adverse weather conditions. Notably, InfraNet maintains high efficiency in IR-only inference, making it both accurate and computationally efficient.

cs.CV↗

arXiv2026

Teaching Vision-Language-Action Models What to See and Where to Look

Vision-Language-Action (VLA) models have emerged as a promising paradigm for end-to-end autonomous driving. However, existing VLAs' training relies heavily on text-centric visual question answering and chain-of-thought reasoning data, which emphasizes linguistic reasoning rather than action-grounded planning. As a result, the learned representations capture semantic knowledge but lack spatial dependencies crucial for reliable trajectory prediction. We propose DriveTeach-VLA, a framework that explicitly teaches VLAs what to see and where to look. Driving-aware Vision Distillation (DVD) injects driving-specific perceptual priors into the vision encoder, while 2D Trajectory-Guided Prompts (2D-TGP) provide spatial conditioning aligned with feasible driving trajectories. Together, they form a vision-guided learning pipeline: what to see (DVD pretraining) - where to look (TGP-guided SFT) - how to act (TGP-guided GRPO). DriveTeach-VLA achieves the state-of-the-art performance on NAVSIM and nuScenes. Our code is available at: https://github.com/ShivaTeam/DriveTeach-VLA.

cs.CV↗

arXiv2026

Kernel-learning parameter prediction and evaluation in algebraic multigrid method for several PDEs

This paper explores the application of kernel learning methods for parameter prediction and evaluation in the Algebraic Multigrid Method (AMG), focusing on several Partial Differential Equation (PDE) problems. AMG is an efficient iterative solver for large-scale sparse linear systems, particularly those derived from elliptic and parabolic PDE discretizations. However, its performance heavily relies on numerous parameters, which are often set empirically and are highly sensitive to AMG's effectiveness. Traditional parameter optimization methods are either computationally expensive or lack theoretical support. To address this, we propose a Gaussian Process Regression (GPR)-based strategy to optimize AMG parameters and introduce evaluation metrics to assess their effectiveness. Trained on small-scale datasets, GPR predicts nearly optimal parameters, bypassing the time-consuming parameter sweeping process. We also use kernel learning techniques to build a kernel function library and determine the optimal kernel function through linear combination, enhancing prediction accuracy. In numerical experiments, we tested typical PDEs such as the constant-coefficient Poisson equation, variable-coefficient Poisson equation, diffusion equation, and Helmholtz equation. Results show that GPR-predicted parameters match grid search results in iteration counts while significantly reducing computational time. A comprehensive analysis using metrics like mean squared error, prediction interval coverage, and Bayesian information criterion confirms GPR's efficiency and reliability. These findings validate GPR's effectiveness in AMG parameter optimization and provide theoretical support for AMG's practical application.

math.NA↗