arXiv subjects

Liu Liu

Publications and source records attributed to Liu Liu.

At least 127 records · Page 7Linked to original sources

arXiv2025

Mode-Matched Inverse Gamma Priors for Variance Components in Bayesian Multilevel Models

We introduce a strategy for specifying informative inverse-gamma (IG) priors for variance components in Bayesian multilevel models (MLMs), derived via transformations from chi-square to gamma to inverse-gamma distributions. A Monte Carlo simulation compared frequentist (maximum likelihood) estimation and Bayesian estimation using uninformative, weakly informative, and strongly informative variance priors across varied conditions (clusters J = 10, 30, 100; cluster sizes M = 5, 30; intraclass correlations 0.01, 0.20, 0.40; levels of explained variance at L1 and L2 R^2 = 0, 0.2, 0.4). The simulation results indicated that strongly informative IG priors (with hyperparameters set so the prior mode equals a plausible true variance) yielded more accurate and stable variance estimates with reduced bias and narrower credible intervals than flat/uninformative or weak IG(0.01, 0.01) priors. In an empirical example using the TIMSS 2019 Grade 8 science achievement data, both the full sample (273 schools) and small subsample (30 schools) were analyzed. The small-sample analysis with an informative variance prior anchored near the full-sample variance while considerably reducing the uncertainty of estimates. Findings suggest that carefully calibrated informative variance priors improve the precision and accuracy of parameter estimates, particularly when the number of higher-level units is limited.

stat.ME↗

arXiv2025

Leveraging 3D Technologies for Hardware Security: Opportunities and Challenges

3D die stacking and 2.5D interposer design are promising technologies to improve integration density, performance and cost. Current approaches face serious issues in dealing with emerging security challenges such as side channel attacks, hardware trojans, secure IC manufacturing and IP piracy. By utilizing intrinsic characteristics of 2.5D and 3D technologies, we propose novel opportunities in designing secure systems. We present: (i) a 3D architecture for shielding side-channel information; (ii) split fabrication using active interposers; (iii) circuit camouflage on monolithic 3D IC, and (iv) 3D IC-based security processing-in-memory (PIM). Advantages and challenges of these designs are discussed, showing that the new designs can improve existing countermeasures against security threats and further provide new security features.

cs.CR↗

arXiv2025

Explainable AI for Predicting and Understanding Mathematics Achievement: A Cross-National Analysis of PISA 2018

Understanding the factors that shape students' mathematics performance is vital for designing effective educational policies. This study applies explainable artificial intelligence (XAI) techniques to PISA 2018 data to predict math achievement and identify key predictors across ten countries (67,329 students). We tested four models: Multiple Linear Regression (MLR), Random Forest (RF), CATBoost, and Artificial Neural Networks (ANN), using student, family, and school variables. Models were trained on 70% of the data (with 5-fold cross-validation) and tested on 30%, stratified by country. Performance was assessed with R^2 and Mean Absolute Error (MAE). To ensure interpretability, we used feature importance, SHAP values, and decision tree visualizations. Non-linear models, especially RF and ANN, outperformed MLR, with RF balancing accuracy and generalizability. Key predictors included socio-economic status, study time, teacher motivation, and students' attitudes toward mathematics, though their impact varied across countries. Visual diagnostics such as scatterplots of predicted vs actual scores showed RF and CATBoost aligned closely with actual performance. Findings highlight the non-linear and context-dependent nature of achievement and the value of XAI in educational research. This study uncovers cross-national patterns, informs equity-focused reforms, and supports the development of personalized learning strategies.

cs.AI↗

arXiv2025

IGFuse: Interactive 3D Gaussian Scene Reconstruction via Multi-Scans Fusion

Reconstructing complete and interactive 3D scenes remains a fundamental challenge in computer vision and robotics, particularly due to persistent object occlusions and limited sensor coverage. Multiview observations from a single scene scan often fail to capture the full structural details. Existing approaches typically rely on multi stage pipelines, such as segmentation, background completion, and inpainting or require per-object dense scanning, both of which are error-prone, and not easily scalable. We propose IGFuse, a novel framework that reconstructs interactive Gaussian scene by fusing observations from multiple scans, where natural object rearrangement between captures reveal previously occluded regions. Our method constructs segmentation aware Gaussian fields and enforces bi-directional photometric and semantic consistency across scans. To handle spatial misalignments, we introduce a pseudo-intermediate scene state for unified alignment, alongside collaborative co-pruning strategies to refine geometry. IGFuse enables high fidelity rendering and object level scene manipulation without dense observations or complex pipelines. Extensive experiments validate the framework's strong generalization to novel scene configurations, demonstrating its effectiveness for real world 3D reconstruction and real-to-simulation transfer. Our project page is available online.

cs.CV↗

arXiv2025

On a class of multi-fidelity methods for the semiclassical Schrödinger equation with uncertainties

In this paper, we study the semiclassical Schrödinger equation with random parameters and develop several robust multi-fidelity methods. We employ the time-splitting Fourier pseudospectral (TSFP) method for the high-fidelity solver, and consider different low-fidelity solvers including the meshless method like frozen Gaussian approximation (FGA) and the level set (LS) method for the semiclassical limit of the Schrödinger equation. With a careful choice of the low-fidelity model, we obtain an error estimate for the bi-fidelity method. We conduct numerous numerical experiments and validate the accuracy and efficiency of our proposed multi-fidelity methods, by comparing the performance of a class of bi-fidelity and tri-fidelity approximations.

math.NA↗

arXiv2025

YOLO-PRO: Enhancing Instance-Specific Object Detection with Full-Channel Global Self-Attention

This paper addresses the inherent limitations of conventional bottleneck structures (diminished instance discriminability due to overemphasis on batch statistics) and decoupled heads (computational redundancy) in object detection frameworks by proposing two novel modules: the Instance-Specific Bottleneck with full-channel global self-attention (ISB) and the Instance-Specific Asymmetric Decoupled Head (ISADH). The ISB module innovatively reconstructs feature maps to establish an efficient full-channel global attention mechanism through synergistic fusion of batch-statistical and instance-specific features. Complementing this, the ISADH module pioneers an asymmetric decoupled architecture enabling hierarchical multi-dimensional feature integration via dual-stream batch-instance representation fusion. Extensive experiments on the MS-COCO benchmark demonstrate that the coordinated deployment of ISB and ISADH in the YOLO-PRO framework achieves state-of-the-art performance across all computational scales. Specifically, YOLO-PRO surpasses YOLOv8 by 1.0-1.6% AP (N/S/M/L/X scales) and outperforms YOLO11 by 0.1-0.5% AP in critical N/M/L/X groups, while maintaining competitive computational efficiency. This work provides practical insights for developing high-precision detectors deployable on edge devices.

cs.CV↗

arXiv2025

Machine learning-based moment closure model for the linear Boltzmann equation with uncertainties

The Boltzmann equation, a fundamental equation in kinetic theory, serves as a bridge between microscopic particle dynamics and macroscopic continuum mechanics. However, deriving closed macroscopic moment systems from the Boltzmann equation remains a long-standing challenge due to the intrinsic non-closure of the moment hierarchy. In this paper, we propose a machine learning (ML)-based moment closure model for the linear Boltzmann equation, addressing both the deterministic and stochastic settings. Our approach leverages neural networks to learn the spatial gradient of the unclosed highest-order moment, enabling effective training through natural output normalization. For the deterministic problem, to ensure global hyperbolicity and stability, we derive and apply the constraints that enforce symmetrizable hyperbolicity of the system. For the stochastic problem, we adopt the generalized polynomial chaos (gPC)-based stochastic Galerkin method to discretize the random variables, resulting in a system for which the approach in the deterministic case can be used similarly. Several numerical experiments are shown to demonstrate the effectiveness and accuracy of our ML-based moment closure model for the linear Boltzmann equation with or without uncertainties.

math.NA↗

arXiv2025

Efficient numerical methods for the uncertain Boltzmann equation based on a hybrid solver

In this work, we propose and compare several approaches to solve the Boltzmann equation with uncertain parameters, including multi-level Monte Carlo and multi-fidelity methods that employ an asymptotic-preserving-hybrid (APH) scheme (Filbet and Rey, 2015) for the deterministic Boltzmann model. By constructing a hierarchy of models from finer to coarser meshes in phase space for the APH scheme and adopting variance reduction techniques, the MLMC method is able to allocate computational resources across different hierarchies quasi-optimally. On the other hand, in the bi-fidelity method we choose the APH scheme for the Boltzmann equation as the high-fidelity solver, and a finite volume scheme for the compressible Euler system as the low-fidelity model. Since both methods are non-intrusive, they can preserve the physical properties of the deterministic solver. Extensive numerical experiments demonstrate that our APH-based MLMC and multi-fidelity methods are significantly faster than standard approaches, while maintaining accuracy. We also provide practical guidelines for selection between APH-based MLMC and multi-fidelity approaches, based on solution smoothness and computational resource availability.

math.NA↗

arXiv2025

A Bi-fidelity numerical method for velocity discretization of Boltzmann equations

In this paper, we introduce a bi-fidelity algorithm for velocity discretization of Boltzmann-type kinetic equations under multiple scales. The proposed method employs a simpler and computationally cheaper low-fidelity model to capture a small set of significant velocity points through the greedy approach, then evaluates the high-fidelity model only at these few velocity points and to reconstruct a bi-fidelity surrogate. This novel method integrates a simpler collision term of relaxation type in the low-fidelity model and an asymptotic-preserving scheme in the high-fidelity update step. Both linear Boltzmann under diffusive scaling and the nonlinear full Boltzmann in hyperbolic scaling are discussed. We show the weak asymptotic-preserving property and empirical error bound estimates. Extensive numerical experiments on linear semiconductor and nonlinear Boltzmann problems with smooth or discontinuous initial conditions and under various regimes have been carefully studied, which demonstrates the effectiveness and robustness of our proposed scheme.

math.NA↗

arXiv2025

GeoFlow-SLAM: A Robust Tightly-Coupled RGBD-Inertial and Legged Odometry Fusion SLAM for Dynamic Legged Robotics

This paper presents GeoFlow-SLAM, a robust and effective Tightly-Coupled RGBD-inertial SLAM for legged robotics undergoing aggressive and high-frequency motions.By integrating geometric consistency, legged odometry constraints, and dual-stream optical flow (GeoFlow), our method addresses three critical challenges:feature matching and pose initialization failures during fast locomotion and visual feature scarcity in texture-less scenes.Specifically, in rapid motion scenarios, feature matching is notably enhanced by leveraging dual-stream optical flow, which combines prior map points and poses. Additionally, we propose a robust pose initialization method for fast locomotion and IMU error in legged robots, integrating IMU/Legged odometry, inter-frame Perspective-n-Point (PnP), and Generalized Iterative Closest Point (GICP). Furthermore, a novel optimization framework that tightly couples depth-to-map and GICP geometric constraints is first introduced to improve the robustness and accuracy in long-duration, visually texture-less environments. The proposed algorithms achieve state-of-the-art (SOTA) on collected legged robots and open-source datasets. To further promote research and development, the open-source datasets and code will be made publicly available at https://github.com/HorizonRobotics/GeoFlowSlam

cs.RO↗

arXiv2025

Efficient numerical method for the Schrödinger equation with high-contrast potentials

In this paper, we study the Schrödinger equation in the semiclassical regime and with multiscale potential function. We develop the so-called constraint energy minimization generalized multiscale finite element method (CEM-GMsFEM), in the framework of Crank-Nicolson (CN) discretization in time. The localized multiscale basis functions are constructed by addressing the spectral problem and a constrained energy minimization problem related to the Hamiltonian norm. A first-order convergence in the energy norm and second-order convergence in the $L^2$ norm for our numerical scheme are shown, with a relation between oversampling number in the CEM-GMsFEM method, spatial mesh size and the semiclassical parameter provided. Furthermore, we demonstrate the convergence of the proposed Crank-Nicolson CEM-GMsFEM scheme. The convergence requires $H/\sqrtΛ=O(\varepsilon^{\frac{5}{4}})$, $Δt=O(\varepsilon^{\frac{5}{4}})$ if $\varepsilon\leq δ$; while if $δ<\varepsilon$, the convergence requires $H/\sqrtΛ=O(\varepsilon^{\frac{1}{4}}δ)$, $Δt=O(\frac{δ^2}{\varepsilon^{3/4}})$ (where $H$ represents the maximum diameter of coarse elements, $Λ$ is the minimal eigenvalue associated with the eigenvector not included in the auxiliary space, $Δt$ is the time step, $0 < \varepsilon\ll 1$ is the Planck constant and $δ$ describes the multiscale structure of the potential).Several numerical examples including 1D and 2D in space, with high-contrast potential are conducted to demonstrate the efficiency and accuracy of our proposed scheme.

math.NA↗

arXiv2025

An efficient Asymptotic-Preserving scheme for the Boltzmann mixture with disparate mass

In this paper, we develop and implement an efficient asymptotic-preserving (AP) scheme to solve the gas mixture of Boltzmann equations under the disparate mass scaling relevant to the so-called "epochal relaxation" phenomenon. The disparity in molecular masses, ranging across several orders of magnitude, leads to significant challenges in both the evaluation of collision operators and the designing of time-stepping schemes to capture the multi-scale nature of the dynamics. A direct implementation of the spectral method faces prohibitive computational costs as the mass ratio increases due to the need to resolve vastly different thermal velocities. Unlike [I. M. Gamba, S. Jin, and L. Liu, Commun. Math. Sci., 17 (2019), pp. 1257-1289], we propose an alternative approach based on proper truncation of asymptotic expansions of the collision operators, which significantly reduces the computational complexity and works well for small $\varepsilon$. By incorporating the separation of three time scales in the model's relaxation process [P. Degond and B. Lucquin-Desreux, Math. Models Methods Appl. Sci., 6 (1996), pp. 405-436], we design an AP scheme that captures the specific dynamics of the disparate mass model while maintaining computational efficiency. Numerical experiments demonstrate the effectiveness of the proposed scheme in handling large mass ratios of heavy and light species, as well as capturing the epochal relaxation phenomenon.

math.NA↗

arXiv2025

SFOOD: A Multimodal Benchmark for Comprehensive Food Attribute Analysis Beyond RGB with Spectral Insights

With the rise and development of computer vision and LLMs, intelligence is everywhere, especially for people and cars. However, for tremendous food attributes (such as origin, quantity, weight, quality, sweetness, etc.), existing research still mainly focuses on the study of categories. The reason is the lack of a large and comprehensive benchmark for food. Besides, many food attributes (such as sweetness, weight, and fine-grained categories) are challenging to accurately percept solely through RGB cameras. To fulfill this gap and promote the development of intelligent food analysis, in this paper, we built the first large-scale spectral food (SFOOD) benchmark suite. We spent a lot of manpower and equipment costs to organize existing food datasets and collect hyperspectral images of hundreds of foods, and we used instruments to experimentally determine food attributes such as sweetness and weight. The resulting benchmark consists of 3,266 food categories and 2,351 k data points for 17 main food categories. Extensive evaluations find that: (i) Large-scale models are still poor at digitizing food. Compared to people and cars, food has gradually become one of the most difficult objects to study; (ii) Spectrum data are crucial for analyzing food properties (such as sweetness). Our benchmark will be open source and continuously iterated for different food analysis tasks.

cs.CV↗

arXiv2025

ArtGS:3D Gaussian Splatting for Interactive Visual-Physical Modeling and Manipulation of Articulated Objects

Articulated object manipulation remains a critical challenge in robotics due to the complex kinematic constraints and the limited physical reasoning of existing methods. In this work, we introduce ArtGS, a novel framework that extends 3D Gaussian Splatting (3DGS) by integrating visual-physical modeling for articulated object understanding and interaction. ArtGS begins with multi-view RGB-D reconstruction, followed by reasoning with a vision-language model (VLM) to extract semantic and structural information, particularly the articulated bones. Through dynamic, differentiable 3DGS-based rendering, ArtGS optimizes the parameters of the articulated bones, ensuring physically consistent motion constraints and enhancing the manipulation policy. By leveraging dynamic Gaussian splatting, cross-embodiment adaptability, and closed-loop optimization, ArtGS establishes a new framework for efficient, scalable, and generalizable articulated object modeling and manipulation. Experiments conducted in both simulation and real-world environments demonstrate that ArtGS significantly outperforms previous methods in joint estimation accuracy and manipulation success rates across a variety of articulated objects. Additional images and videos are available on the project website: https://sites.google.com/view/artgs/home

cs.RO↗

arXiv2025

GLS: Geometry-aware 3D Language Gaussian Splatting

Recently, 3D Gaussian Splatting (3DGS) has achieved impressive performance on indoor surface reconstruction and 3D open-vocabulary segmentation. This paper presents GLS, a unified framework of 3D surface reconstruction and open-vocabulary segmentation based on 3DGS. GLS extends two fields by improving their sharpness and smoothness. For indoor surface reconstruction, we introduce surface normal prior as a geometric cue to guide the rendered normal, and use the normal error to optimize the rendered depth. For 3D open-vocabulary segmentation, we employ 2D CLIP features to guide instance features and enhance the surface smoothness, then utilize DEVA masks to maintain their view consistency. Extensive experiments demonstrate the effectiveness of jointly optimizing surface reconstruction and 3D open-vocabulary segmentation, where GLS surpasses state-of-the-art approaches of each task on MuSHRoom, ScanNet++ and LERF-OVS datasets. Project webpage: https://jiaxiongq.github.io/GLS_ProjectPage.

cs.CV↗

arXiv2025

PhysicsSolver: Transformer-Enhanced Physics-Informed Neural Networks for Forward and Forecasting Problems in Partial Differential Equations

Time-dependent partial differential equations are a significant class of equations that describe the evolution of various physical phenomena over time. One of the open problems in scientific computing is predicting the behaviour of the solution outside the given temporal region. Most traditional numerical methods are applied to a given time-space region and can only accurately approximate the solution of the given region. To address this problem, many deep learning-based methods, basically data-driven and data-free approaches, have been developed to solve these problems. However, most data-driven methods require a large amount of data, which consumes significant computational resources and fails to utilize all the necessary information embedded underlying the partial differential equations (PDEs). Moreover, data-free approaches such as Physics-Informed Neural Networks (PINNs) may not be that ideal in practice, as traditional PINNs, which primarily rely on multilayer perceptrons (MLPs) and convolutional neural networks (CNNs), tend to overlook the crucial temporal dependencies inherent in real-world physical systems. We propose a method denoted as \textbf{PhysicsSolver} that merges the strengths of two approaches: data-free methods that can learn the intrinsic properties of physical systems without using data, and data-driven methods, which are effective at making predictions. Extensive numerical experiments have demonstrated the efficiency and robustness of our proposed method. We provide the code at \href{https://github.com/PhysicsSolver/PhysicsSolver}{https://github.com/PhysicsSolver}.

math.NA↗

arXiv2025

Efficient stochastic asymptotic-preserving scheme for tumor growth models with uncertain parameters

In this paper, we investigate a class of tumor growth models governed by porous medium-type equations with uncertainties arisen from the growth function, initial condition, tumor support radius or other parameters in the model. We develop a stochastic asymptotic preservation (s-AP) scheme in the generalized polynomial chaos-stochastic Galerkin (gPC-SG) framework, which remains robust for all index parameters $m\geq 2$. The regularity of the solution to porous medium equations in the random space is studied, and we show the s-AP property, ensuring the convergence of SG system on the continuous level to that of Hele-Shaw dynamics as $m \to \infty$. Our numerical experiments, including capturing the behaviors such as finger-like projection, proliferating, quiescent and dead cell's evolution, validate the accuracy and efficiency of our designed scheme. The numerical results can describe the impact of stochastic parameters on tumor interface evolutions and pattern formations.

math.NA↗

arXiv2025

Research on Graph-Retrieval Augmented Generation Based on Historical Text Knowledge Graphs

This article addresses domain knowledge gaps in general large language models for historical text analysis in the context of computational humanities and AIGC technology. We propose the Graph RAG framework, combining chain-of-thought prompting, self-instruction generation, and process supervision to create a The First Four Histories character relationship dataset with minimal manual annotation. This dataset supports automated historical knowledge extraction, reducing labor costs. In the graph-augmented generation phase, we introduce a collaborative mechanism between knowledge graphs and retrieval-augmented generation, improving the alignment of general models with historical knowledge. Experiments show that the domain-specific model Xunzi-Qwen1.5-14B, with Simplified Chinese input and chain-of-thought prompting, achieves optimal performance in relation extraction (F1 = 0.68). The DeepSeek model integrated with GraphRAG improves F1 by 11% (0.08-0.19) on the open-domain C-CLUE relation extraction dataset, surpassing the F1 value of Xunzi-Qwen1.5-14B (0.12), effectively alleviating hallucinations phenomenon, and improving interpretability. This framework offers a low-resource solution for classical text knowledge extraction, advancing historical knowledge services and humanities research.

cs.CL↗