arXiv subjects

Xiaoxu Li

Publications and source records attributed to Xiaoxu Li.

At least 19 recordsLinked to original sources

arXiv2026

Momentum-Resolved Electronic Structure for Quasicrystals: Full-Band Spectra and Chern Number

Quasicrystals lack the translational symmetry that underlies Bloch decomposition and Brillouin-zone integration, making full-band momentum-resolved electronic structure difficult to formulate and compute. We develop a systematically convergent reciprocal-space tight-binding framework for a broad class of quasicrystals. The method combines two systematically refinable components: a Fourier-module scattering-channel Hamiltonian that yields local spectral and current-current correlation quantities at each physical momentum, and an expanding hierarchy of pseudo-Brillouin zones that converts the resulting local quantities into bulk thermodynamic observables through an exact local-to-global relation. Applied to the Penrose and Ammann-Beenker models, the framework uncovers full-band momentum-resolved quasibands and a multichannel mechanism for pseudogap formation, both beyond the scope of low-energy effective models. It further resolves Zeeman-driven gap closings and reopenings, quantized Chern plateaus, and the phason invariance of bulk spectral and topological observables. This framework provides a unified reciprocal-space route to full-band spectral and topological properties of quasicrystals.

cond-mat.mtrl-sci↗

arXiv2026

ARDepth: Auto-regressive Monocular Depth Estimation with Progressive Visual Conditioning

Diffusion models have recently become the dominant paradigm for monocular depth estimation (MDE). However, they implicitly assume that depth can be recovered as a globally smooth field through iterative denoising, which does not explicitly reflect the piecewise and scale-dependent organization of scene geometry. In practice, geometric structure emerges progressively across spatial scales, where coarse layout, surfaces, and boundaries are constructed in a hierarchical manner. Motivated by this observation, we introduce ARDepth, which formulates depth estimation as structured auto-regressive generation. Instead of recovering depth through global refinement, ARDepth progressively constructs depth representations as spatial resolution increases. To support this generative process, we introduce Scale-Progressive Conditioning (SPC) to inject multi-scale visual features at each generation stage, and Semantic-Aware Guidance (SAG) to provide scene-level semantic priors that enhance global structural consistency. Together, these designs enable the model to capture fine-grained local details while maintaining coherent global geometry. Empirical results demonstrate that our approach achieves strong performance and produces structurally consistent depth predictions across scales, validating auto-regressive generation as a promising alternative paradigm for geometric modeling.

cs.CV↗

arXiv2026

A Hybrid Discontinuous Galerkin Method with Isogeometric-Planewaves Coupling for Periodic Full-Potential Electronic Structure Calculations

Full-potential electronic structure calculations for periodic systems retain the Coulomb singularity at the nuclei, which induces cusp behavior of the orbitals near the nuclei while leaving the interstitial region smooth. This multiscale regularity motivates a hybrid discretization framework that combines localized real-space discretizations in atomic patches with plane waves in the interstitial region. In this work, we employ tensor-product B-splines in the atomic patches and couple the two approximation spaces through a symmetric interior penalty discontinuous Galerkin formulation, yielding the isogeometric-plane wave (IGA-PW) method. To efficiently evaluate the restricted plane wave integrals, we develop a combined fast Fourier transform and Chebyshev correction strategy. We also construct a trace-block DG preconditioner to alleviate the conditioning deterioration caused by the SIPG penalty terms and accelerate the iterative eigensolver. In addition, we establish {\it a priori} error estimates for the corresponding linear eigenvalue problem, showing algebraic convergence near the nuclei and superalgebraic convergence in the interstitial region. Numerical experiments demonstrate the accuracy and efficiency of the proposed method.

math.NA↗

arXiv2025

A Multi-Level Monte Carlo Tree Search Method for Configuration Generation in Crystalline Systems

In this paper, we study the construction of structural models for the description of substitutional defects in crystalline materials. Predicting and designing the atomic structures in such systems is highly challenging due to the combinatorial growth of atomic arrangements and the ruggedness of the associated landscape. We develop a multi-level Monte Carlo tree search algorithm to generate the "optimal" configuration within a supercell. Our method explores the configuration space with an expanding search tree through random sampling, which further incorporates a hierarchical decomposition of the crystalline structure to accelerate exploration and reduce redundancy. We perform numerical experiments on some typical crystalline systems to demonstrate the efficiency of our method in identifying optimal configurations.

physics.comp-ph↗

arXiv2025

Data-Driven Insights into Rare Earth Mineralization: Machine Learning Applications Using Functional Material Synthesis Data

Quantitative understanding of rare earth element (REE) mineralization mechanisms, crucial for improving industrial separation, remains limited. This study leverages 1239 hydrothermal synthesis datapoints from material science as a surrogate for natural REE mineralization. We trained machine learning models (KNN, RF, XGBoost) using precursor, additive, and reaction data to predict product elements and phases, validating predictions with new experiments. XGBoost exhibited the highest accuracy, with feature importance analysis indicating thermodynamic properties were critical for predictions. Observed correlations among reaction parameters aligned with classical crystallization theory. Further XGBoost models successfully predicted reaction temperature and pH from precursor/product data. Our findings demonstrate the cross-disciplinary utility of material science data for geochemical understanding, underscore the need for research on less-studied REE minerals (e.g., carbonates, heavy REEs), and suggest potential to accelerate REE resource development.

cond-mat.mtrl-sci↗

arXiv2024

Approximations of the Green's Function in Multiple Scattering Theory for Crystalline Systems

The multiple scattering theory (MST) is a Green's function method that has been widely used in electronic structure calculations for crystalline disordered systems. The key property of the MST method is the scattering path matrix (SPM) that characterizes the Green's function within a local solution representation. This paper studies various approximations of the SPM, under the condition that an appropriate reference is used for perturbation. In particular, we justify the convergence of the SPM approximations with respect to the size of scattering region and the length of scattering path, which are the central numerical parameters to achieve a linear-scaling MST method. We present numerical experiments on several typical systems to support the theory.

physics.comp-ph↗

arXiv2024

Numerical Analysis of Multi-patch Discontinuous Galerkin Isogeometric Method for Full-potential Electronic Structure Calculations

In this paper, we study the multi-patch discontinuous Galerkin isogeometric (DG-IGA) approximations for full-potential electronic structure calculations. We decompose the physical domain into several subdomains, represent each part of the wavefunction separately using B-spline basis functions, possibly with different degrees, on varying mesh sizes, and then combine them by DG methods. We also provide a rigorous {\em a priori} error analysis of the DG-IGA approximations for linear eigenvalue problems. Furthermore, this work offers a unified analysis framework for the DG-IGA method applied to a class of elliptic eigenvalue problems. Finally, we present several numerical experiments to verify our theoretical results.

math.NA↗

arXiv2023

Unified analysis of finite-size error for periodic Hartree-Fock and second order Møller-Plesset perturbation theory

Despite decades of practice, finite-size errors in many widely used electronic structure theories for periodic systems remain poorly understood. For periodic systems using a general Monkhorst-Pack grid, there has been no comprehensive and rigorous analysis of the finite-size error in the Hartree-Fock theory (HF) and the second order Møller-Plesset perturbation theory (MP2), which are the simplest wavefunction based method, and the simplest post-Hartree-Fock method, respectively. Such calculations can be viewed as a multi-dimensional integral discretized with certain trapezoidal rules. Due to the Coulomb singularity, the integrand has many points of discontinuity in general, and standard error analysis based on the Euler-Maclaurin formula gives overly pessimistic results. The lack of analytic understanding of finite-size errors also impedes the development of effective finite-size correction schemes. We propose a unified analysis to obtain sharp convergence rates of finite-size errors for the periodic HF and MP2 theories. Our main technical advancement is a generalization of the result of [Lyness, 1976] for obtaining sharp convergence rates of the trapezoidal rule for a class of non-smooth integrands. Our result is applicable to three-dimensional bulk systems as well as low dimensional systems (such as nanowires and 2D materials). Our unified analysis also allows us to prove the effectiveness of the Madelung-constant correction to the Fock exchange energy, and the effectiveness of a recently proposed staggered mesh method for periodic MP2 calculations [Xing, Li, Lin, J. Chem. Theory Comput. 2021]. Our analysis connects the effectiveness of the staggered mesh method with integrands with removable singularities, and suggests a new staggered mesh method for reducing finite-size errors of periodic HF calculations.

physics.comp-ph↗

arXiv2023

Atomic-scale Mapping Unravel Anisotropic Dissolution Behaviors of Gibbsite Nanosheets

This study examines the anisotropic dissolution of the basal plane gibbsite (γ-Al(OH)3) nanoplates in sodium hydroxide solution using in situ atomic force microscopy (AFM) and density functional theory (DFT) calculations. In the surface-reaction controlled regime, in situ AFM measurements reveal anisotropic dissolution of hillocks and etch pits on the gibbsite basal plane, with preferred dissolution directions alternating between layers. The mirror-symmetric pattern of dissolution preference between adjacent gibbsite aluminum hydroxide sheet, observed along the crystallographic a-c plane, results from the matching symmetry between the structures of the adjacent (001) and (002) crystal planes. Consequently, the overall dissolution rate of gibbsite nanoplates exhibits crystallographic a-c plane symmetry, as the rate of parallel steps is governed by the slower ones. DFT calculations suggest that the anisotropic dissolution is partially due to the orientation and strength of Al-OH-Al linkages pair within gibbsite surface structure. These findings offer a comprehensive understanding of anisotropic dissolution behavior of gibbsite and illuminate the mechanisms behind preferential dissolution.

cond-mat.mtrl-sci↗

arXiv2023

Machine learning assisted phase and size-controlled synthesis of iron oxides

The controllable synthesis of iron oxides particles is a critical issue for materials science, energy storage, biomedical applications, environmental science, and earth science. However, synthesis of iron oxides with desired phase and size are still a time-consuming and trial-and-error process. This study presents solutions for two fundamental challenges in materials synthesis: predicting the outcome of a synthesis from specified reaction parameters and correlating sets of parameters to obtain products with desired outcomes. Four machine learning algorithms, including random forest, logistic regression, support vector machine, and k-nearest neighbor, were trained to predict the phase and particle size of iron oxide based on experimental conditions. Among the models, random forest exhibited the best performance, achieving 96% and 81% accuracy when predicting the phase and size of iron oxides in the test dataset. Premutation feature importance analysis shows that most models (except logistic regression) rely on known features such as precursor concentration, pH, and temperature to predict the phases from synthesis conditions. The robustness of the random forest models was further verified by comparing prediction and experimental results based on 24 randomly generated methods in additive and non-additive systems not included in the datasets. The predictions of product phase and particle size from the models are in good agreement with the experimental results. Additionally, a searching and ranking algorithm was developed to recommend potential synthesis parameters for obtaining iron oxide products with desired phase and particle size from previous studies in the dataset.

cond-mat.mtrl-sci↗

arXiv2023

Bi-directional Feature Reconstruction Network for Fine-Grained Few-Shot Image Classification

The main challenge for fine-grained few-shot image classification is to learn feature representations with higher inter-class and lower intra-class variations, with a mere few labelled samples. Conventional few-shot learning methods however cannot be naively adopted for this fine-grained setting -- a quick pilot study reveals that they in fact push for the opposite (i.e., lower inter-class variations and higher intra-class variations). To alleviate this problem, prior works predominately use a support set to reconstruct the query image and then utilize metric learning to determine its category. Upon careful inspection, we further reveal that such unidirectional reconstruction methods only help to increase inter-class variations and are not effective in tackling intra-class variations. In this paper, we for the first time introduce a bi-reconstruction mechanism that can simultaneously accommodate for inter-class and intra-class variations. In addition to using the support set to reconstruct the query set for increasing inter-class variations, we further use the query set to reconstruct the support set for reducing intra-class variations. This design effectively helps the model to explore more subtle and discriminative features which is key for the fine-grained problem in hand. Furthermore, we also construct a self-reconstruction module to work alongside the bi-directional module to make the features even more discriminative. Experimental results on three widely used fine-grained image classification datasets consistently show considerable improvements compared with other methods. Codes are available at: https://github.com/PRIS-CV/Bi-FRN.

cs.CV↗

arXiv2022

Deep Metric Learning for Few-Shot Image Classification: A Review of Recent Developments

Few-shot image classification is a challenging problem that aims to achieve the human level of recognition based only on a small number of training images. One main solution to few-shot image classification is deep metric learning. These methods, by classifying unseen samples according to their distances to few seen samples in an embedding space learned by powerful deep neural networks, can avoid overfitting to few training images in few-shot image classification and have achieved the state-of-the-art performance. In this paper, we provide an up-to-date review of deep metric learning methods for few-shot image classification from 2018 to 2022 and categorize them into three groups according to three stages of metric learning, namely learning feature embeddings, learning class representations, and learning distance measures. With this taxonomy, we identify the novelties of different methods and problems they face. We conclude this review with a discussion on current challenges and future trends in few-shot image classification.

cs.CV↗

arXiv2021

Numerical Analysis of the Multiple Scattering Theory for Electronic Structure Calculations

The multiple scattering theory (MST) is one of the most widely used methods in electronic structure calculations. It features a perfect separation between the atomic configurations and site potentials, and hence provides an efficient way to simulate defected and disordered systems. This work studies the MST methods from a numerical point of view and shows the convergence with respect to the truncation of the angular momentum summations, which is a fundamental approximation parameter for all MST methods. We provide both rigorous analysis and numerical experiments to illustrate the efficiency of the MST methods within the angular momentum representations.

math.NA↗

arXiv2021

TLRM: Task-level Relation Module for GNN-based Few-Shot Learning

Recently, graph neural networks (GNNs) have shown powerful ability to handle few-shot classification problem, which aims at classifying unseen samples when trained with limited labeled samples per class. GNN-based few-shot learning architectures mostly replace traditional metric with a learnable GNN. In the GNN, the nodes are set as the samples embedding, and the relationship between two connected nodes can be obtained by a network, the input of which is the difference of their embedding features. We consider this method of measuring relation of samples only models the sample-to-sample relation, while neglects the specificity of different tasks. That is, this method of measuring relation does not take the task-level information into account. To this end, we propose a new relation measure method, namely the task-level relation module (TLRM), to explicitly model the task-level relation of one sample to all the others. The proposed module captures the relation representations between nodes by considering the sample-to-task instead of sample-to-sample embedding features. We conducted extensive experiments on four benchmark datasets: mini-ImageNet, tiered-ImageNet, CUB-$200$-$2011$, and CIFAR-FS. Experimental results demonstrate that the proposed module is effective for GNN-based few-shot learning.

cs.CV↗

arXiv2021

The Devil is in the Channels: Mutual-Channel Loss for Fine-Grained Image Classification

Key for solving fine-grained image categorization is finding discriminate and local regions that correspond to subtle visual traits. Great strides have been made, with complex networks designed specifically to learn part-level discriminate feature representations. In this paper, we show it is possible to cultivate subtle details without the need for overly complicated network designs or training mechanisms -- a single loss is all it takes. The main trick lies with how we delve into individual feature channels early on, as opposed to the convention of starting from a consolidated feature map. The proposed loss function, termed as mutual-channel loss (MC-Loss), consists of two channel-specific components: a discriminality component and a diversity component. The discriminality component forces all feature channels belonging to the same class to be discriminative, through a novel channel-wise attention mechanism. The diversity component additionally constraints channels so that they become mutually exclusive on spatial-wise. The end result is therefore a set of feature channels that each reflects different locally discriminative regions for a specific class. The MC-Loss can be trained end-to-end, without the need for any bounding-box/part annotations, and yields highly discriminative regions during inference. Experimental results show our MC-Loss when implemented on top of common base networks can achieve state-of-the-art performance on all four fine-grained categorization datasets (CUB-Birds, FGVC-Aircraft, Flowers-102, and Stanford-Cars). Ablative studies further demonstrate the superiority of MC-Loss when compared with other recently proposed general-purpose losses for visual classification, on two different base networks. Code available at https://github.com/dongliangchang/Mutual-Channel-Loss

cs.CV↗

arXiv2021

Staggered mesh method for correlation energy calculations of solids: Second order Møller-Plesset perturbation theory

The calculation of the MP2 correlation energy for extended systems can be viewed as a multi-dimensional integral in the thermodynamic limit, and the standard method for evaluating the MP2 energy can be viewed as a trapezoidal quadrature scheme. We demonstrate that existing analysis neglects certain contributions due to the non-smoothness of the integrand, and may significantly underestimate finite-size errors. We propose a new staggered mesh method, which uses two staggered Monkhorst-Pack meshes for occupied and virtual orbitals, respectively, to compute the MP2 energy. The staggered mesh method circumvents a significant error source in the standard method, in which certain quadrature nodes are always placed on points where the integrand is discontinuous. One significant advantage of the proposed method is that there are no tunable parameters, and the additional numerical effort needed can be negligible compared to the standard MP2 calculation. Numerical results indicate that the staggered mesh method can be particularly advantageous for quasi-1D systems, as well as quasi-2D and 3D systems with certain symmetries.

physics.comp-ph↗

arXiv2020

BSNet: Bi-Similarity Network for Few-shot Fine-grained Image Classification

Few-shot learning for fine-grained image classification has gained recent attention in computer vision. Among the approaches for few-shot learning, due to the simplicity and effectiveness, metric-based methods are favorably state-of-the-art on many tasks. Most of the metric-based methods assume a single similarity measure and thus obtain a single feature space. However, if samples can simultaneously be well classified via two distinct similarity measures, the samples within a class can distribute more compactly in a smaller feature space, producing more discriminative feature maps. Motivated by this, we propose a so-called \textit{Bi-Similarity Network} (\textit{BSNet}) that consists of a single embedding module and a bi-similarity module of two similarity measures. After the support images and the query images pass through the convolution-based embedding module, the bi-similarity module learns feature maps according to two similarity measures of diverse characteristics. In this way, the model is enabled to learn more discriminative and less similarity-biased features from few shots of fine-grained images, such that the model generalization ability can be significantly improved. Through extensive experiments by slightly modifying established metric/similarity based networks, we show that the proposed approach produces a substantial improvement on several fine-grained image benchmark datasets. Codes are available at: https://github.com/spraise/BSNet

cs.CV↗

arXiv2020

CC-Loss: Channel Correlation Loss For Image Classification

The loss function is a key component in deep learning models. A commonly used loss function for classification is the cross entropy loss, which is a simple yet effective application of information theory for classification problems. Based on this loss, many other loss functions have been proposed,~\emph{e.g.}, by adding intra-class and inter-class constraints to enhance the discriminative ability of the learned features. However, these loss functions fail to consider the connections between the feature distribution and the model structure. Aiming at addressing this problem, we propose a channel correlation loss (CC-Loss) that is able to constrain the specific relations between classes and channels as well as maintain the intra-class and the inter-class separability. CC-Loss uses a channel attention module to generate channel attention of features for each sample in the training stage. Next, an Euclidean distance matrix is calculated to make the channel attention vectors associated with the same class become identical and to increase the difference between different classes. Finally, we obtain a feature embedding with good intra-class compactness and inter-class separability.Experimental results show that two different backbone models trained with the proposed CC-Loss outperform the state-of-the-art loss functions on three image classification datasets.

cs.CV↗