arXiv subjects

Tao Yin

Publications and source records attributed to Tao Yin.

At least 19 recordsLinked to original sources

arXiv2026

From multi-layered problems to multiple two-layered problems: a novel frequency-time hybrid multiple-scattering integral equation solver

This paper proposes a novel frequency-time hybrid multiple scattering (FTH-MS) integral equation solver for time-dependent wave equation problems in general multi-layered media, with remarkable scalability with respect to the number of layers $N$. In light of the finite speed of wave propagation, the new methodology provides an innovative multiple-scattering idea of re-modeling the original $N$-layered problem into a sequence of $N-1$ two-layered sub-problems, for which the main advantages lie in that (i) each sub-problem enjoys much simpler wave scattering properties compared with the complicated problem in a multi-layered medium, (ii) it enables to develop high-accuracy solver utilizing Fourier transform and frequency-domain boundary integral equation (BIE) method; and (iii) numerical evaluation of the sub-problems in each multiple scattering step can be parallelized. Both multiplicative- and additive-type strategies are developed and equivalence results, which indicate that the $M$-th order multiple scattering sums can provide equivalent representations of the solutions up to a certain time $T(M)$, are rigorously derived. Owing to the existed result of exponential convergence of the perfectly-matched-layer (PML) truncation for two-layered problem, all the sub-problems is numerically resolved by means of the FTH method based on the Fourier transform and the PML-BIE method whose numerical evaluation is addressed utilizing the Chebyshev-based rectangular-polar solver with high accuracy. Numerical examples are presented to validate the efficiency and accuracy of the proposed method.

math.NA↗

arXiv2026

A Uniformly High-Accuracy PML-BIE Method for Scattering by Periodic Arrays of Obstacles: The 2D Case

This paper presents a novel frequency-robust perfectly matched layer (PML) boundary integral equation (BIE) method for solving two-dimensional electromagnetic scattering problems involving periodic arrays of obstacles. In periodic scattering problems, standard BIE formulations based on the quasi-periodic Green's function require the evaluation of lattice sums or challenging Sommerfeld-type integrals, which diverge at Rayleigh--Wood (RW) anomalies. An alternative is to use BIE formulations based on the Helmholtz free-space Green's function, but these are defined on unbounded unit-cell boundaries and therefore require suitable truncation strategies, such as the Windowed Green Function (WGF) method. Although such approaches avoid the use of expensive quasi-periodic Green's functions, they also suffer from breakdowns at RW anomalies unless an appropriate mode correction is incorporated. Similarly, the direct application of PML-BIE techniques to periodic structures experiences comparable difficulties near RW anomalies due to the destruction of exponential convergence near RW anomalies for fixed PML parameters. To overcome this challenge, we propose a modified PML-BIE method that combines the PML technique with a finite-mode correction, ensuring both high accuracy and robustness at and around RW-anomalies. Convergence of the PML-truncated boundary integral operators is proved and several numerical examples are presented to validate the efficiency and performance of the proposed method.

math.NA↗

arXiv2026

DeepGuard: Secure Code Generation via Multi-Layer Semantic Aggregation

Large Language Models (LLMs) for code generation can replicate insecure patterns from their training data. To mitigate this, a common strategy for security hardening is to fine-tune models using supervision derived from the final transformer layer. However, this design may suffer from a final-layer bottleneck: vulnerability-discriminative cues can be distributed across layers and become less detectable near the output representations optimized for next-token prediction. To diagnose this issue, we perform layer-wise linear probing. We observe that vulnerability-related signals are most detectable in a band of intermediate-to-upper layers yet attenuate toward the final layers. Motivated by this observation, we introduce DeepGuard, a framework that leverages distributed security-relevant cues by aggregating representations from multiple upper layers via an attention-based module. The aggregated signal powers a dedicated security analyzer within a multi-objective training objective that balances security enhancement and functional correctness, and further supports a lightweight inference-time steering strategy. Extensive experiments across five code LLMs demonstrate that DeepGuard improves the secure-and-correct generation rate by an average of 11.9% over strong baselines such as SVEN. It also preserves functional correctness while exhibiting generalization to held-out vulnerability types. Our code is public at https://github.com/unknownhl/DeepGuard.

cs.SE↗

arXiv2025

Intention Chain-of-Thought Prompting with Dynamic Routing for Code Generation

Large language models (LLMs) exhibit strong generative capabilities and have shown great potential in code generation. Existing chain-of-thought (CoT) prompting methods enhance model reasoning by eliciting intermediate steps, but suffer from two major limitations: First, their uniform application tends to induce overthinking on simple tasks. Second, they lack intention abstraction in code generation, such as explicitly modeling core algorithmic design and efficiency, leading models to focus on surface-level structures while neglecting the global problem objective. Inspired by the cognitive economy principle of engaging structured reasoning only when necessary to conserve cognitive resources, we propose RoutingGen, a novel difficulty-aware routing framework that dynamically adapts prompting strategies for code generation. For simple tasks, it adopts few-shot prompting; for more complex ones, it invokes a structured reasoning strategy, termed Intention Chain-of-Thought (ICoT), which we introduce to guide the model in capturing task intention, such as the core algorithmic logic and its time complexity. Experiments across three models and six standard code generation benchmarks show that RoutingGen achieves state-of-the-art performance in most settings, while reducing total token usage by 46.37% on average across settings. Furthermore, ICoT outperforms six existing prompting baselines on challenging benchmarks.

cs.AI↗

arXiv2025

MoRA: On-the-fly Molecule-aware Low-Rank Adaptation Framework for LLM-based Multi-Modal Molecular Assistant

Effectively integrating molecular graph structures with Large Language Models (LLMs) is a key challenge in drug discovery. Most existing multi-modal alignment methods typically process these structures by fine-tuning the LLM or adding a static adapter simultaneously. However, these approaches have two main limitations: (1) it optimizes a shared parameter space across all molecular inputs, limiting the model's ability to capture instance-specific structural features; and (2) fine-tuning the LLM for molecular tasks can lead to catastrophic forgetting, undermining its general reasoning capabilities. In this paper, instead of static task-oriented adaptation, we propose an instance-specific parameter space alignment approach for each molecule on-the-fly. To this end, we introduce Molecule-aware Low-Rank Adaptation (MoRA) that produces a unique set of low-rank adaptation weights for each input molecular graph. These weights are then dynamically injected into a frozen LLM, allowing the model to adapt its reasoning to the structure of each molecular input, while preserving the LLM's core knowledge. Extensive experiments demonstrate that on key molecular tasks, such as chemical reaction prediction and molecular captioning, MoRA's instance-specific dynamic adaptation outperforms statically adapted baselines, including a 14.1% relative improvement in reaction prediction exact match and a 22% reduction in error for quantum property prediction. The code is available at https://github.com/jk-sounds/MoRA.

cs.LG↗

arXiv2025

ScatterAD: Temporal-Topological Scattering Mechanism for Time Series Anomaly Detection

One main challenge in time series anomaly detection for industrial IoT lies in the complex spatio-temporal couplings within multivariate data. However, traditional anomaly detection methods focus on modeling spatial or temporal dependencies independently, resulting in suboptimal representation learning and limited sensitivity to anomalous dispersion in high-dimensional spaces. In this work, we conduct an empirical analysis showing that both normal and anomalous samples tend to scatter in high-dimensional space, especially anomalous samples are markedly more dispersed. We formalize this dispersion phenomenon as scattering, quantified by the mean pairwise distance among sample representations, and leverage it as an inductive signal to enhance spatio-temporal anomaly detection. Technically, we propose ScatterAD to model representation scattering across temporal and topological dimensions. ScatterAD incorporates a topological encoder for capturing graph-structured scattering and a temporal encoder for constraining over-scattering through mean squared error minimization between neighboring time steps. We introduce a contrastive fusion mechanism to ensure the complementarity of the learned temporal and topological representations. Additionally, we theoretically show that maximizing the conditional mutual information between temporal and topological views improves cross-view consistency and enhances more discriminative representations. Extensive experiments on multiple public benchmarks show that ScatterAD achieves state-of-the-art performance on multivariate time series anomaly detection. Code is available at this repository: https://github.com/jk-sounds/ScatterAD.

cs.LG↗

arXiv2025

On the direct and inverse electromagnetic scattering in a parallel-plate waveguide

This paper devotes to providing rigorous theoretical analysis of the wellposedness of the direct problem and the uniqueness of the inverse problem of electromagnetic scattering in a parallel-plate waveguide. The direct problem is reduced to an equivalent boundary value problem on a bounded domain by introducing an exact transparent boundary condition in terms of the electric-to-magnetic Calderón operator which can be explicitly represented as a series expansion. Then the wellopsedness of the reduced problem in appropriate Sobolev spaces is proved via the variational approach provided by some necessary properties of the Calderón operator and Helmholtz decomposition. Relying on the Green's representation formula and a reciprocity relation, the probe method, finally, is utilized to show the uniqueness of the inverse obstacle problem.

math.AP↗

arXiv2025

LRCTI: A Large Language Model-Based Framework for Multi-Step Evidence Retrieval and Reasoning in Cyber Threat Intelligence Credibility Verification

Verifying the credibility of Cyber Threat Intelligence (CTI) is essential for reliable cybersecurity defense. However, traditional approaches typically treat this task as a static classification problem, relying on handcrafted features or isolated deep learning models. These methods often lack the robustness needed to handle incomplete, heterogeneous, or noisy intelligence, and they provide limited transparency in decision-making-factors that reduce their effectiveness in real-world threat environments. To address these limitations, we propose LRCTI, a Large Language Model (LLM)-based framework designed for multi-step CTI credibility verification. The framework first employs a text summarization module to distill complex intelligence reports into concise and actionable threat claims. It then uses an adaptive multi-step evidence retrieval mechanism that iteratively identifies and refines supporting information from a CTI-specific corpus, guided by LLM feedback. Finally, a prompt-based Natural Language Inference (NLI) module is applied to evaluate the credibility of each claim while generating interpretable justifications for the classification outcome. Experiments conducted on two benchmark datasets, CTI-200 and PolitiFact show that LRCTI improves F1-Macro and F1-Micro scores by over 5%, reaching 90.9% and 93.6%, respectively, compared to state-of-the-art baselines. These results demonstrate that LRCTI effectively addresses the core limitations of prior methods, offering a scalable, accurate, and explainable solution for automated CTI credibility verification

cs.CR↗

arXiv2025

Multi-patch/multiple-scattering frequency-time hybrid solver for interior and exterior wave equation problems

This paper proposes a new multiple-scattering frequency-time hybrid (FTH-MS) integral equation solver for problems of wave scattering by obstacles in two dimensional space, including interior problems in closed cavities and problems exterior to a set of disconnected open or closed scattering obstacles. The multiple-scattering FTH-MS method is based on a partition of the domain boundary into a user-prescribed set of overlapping open arcs, along with a corresponding sequence of multiple-scattering problems that effectively decompose the interior problem into a series of open-arc wave equation subproblems. The new strategy provides a significant extension of the original FTH-MS algorithm originally presented in [22], in that (1) By allowing for use of an arbitrary of number of component arcs, and not just two as in the previous contribution, the new approach affords (1a) A significantly increased geometric flexibility, as well as, (1b) The use of partitions for which each open arc leads to small numbers of iterations if iterative linear-algebra solvers are employed; and, (2) It facilitates parallelization -- as the subproblem solutions that are needed at each multiple scattering step can be evaluated in an embarrassingly parallel fashion. Utilizing a suitably-implemented Fourier transformation, each sub-problem is reduced to a Helmholtz frequency-domain problem that is tackled via a uniquely-solvable boundary integral equation. Similar FTH-MS methods are also presented for problems exterior to a number of bounded obstacles. All of the algorithms considered incorporate the previously introduced ``time-windowing and recentering'' methodology (that enables both treatment of incident signals of long duration and long time simulation), as well as a high-frequency Fourier transform algorithm that delivers numerically dispersionless, spectrally-accurate time evolution for arbitrarily long times.

math.NA↗

arXiv2025

Regularized boundary integral equation methods for open-arc scattering problems in thermoelasticity

This paper devotes to developing novel boundary integral equation (BIE) solvers for the problem of thermoelastic scattering by open-arcs with four different boundary conditions in two dimensions. The proposed methodology is inspired by the Calderón formulas, whose eigenvalues are shown to accumulate at particular points depending only on Lamé parameters, satisfied by the thermoelastic boundary integral operators (BIOs) on both closed- and open-surfaces. Regularized BIEs in terms of weighted BIOs on open-arc that explicitly exhibits the edge singularity behavior, depending on the types of boundary conditions, of the unknown potentials are constructed to effectively reduce the required iteration number to solve the corresponding discretized linear systems. We implement the new formulations utilizing regularizations of singular integrals, which reduces the strongly- and hyper-singular integrals into weakly-singular integrals. Combined with spectrally accurate quadrature rules, numerical examples are presented to illustrate the accuracy and efficiency of the proposed solvers.

math.NA↗

arXiv2025

Factorization method for near-field inverse scattering problems in elastodynamics

Consider a time-harmonic elastic point source incident on a bounded obstacle which is embedded in an open space filled with a homogeneous and isotropic elastic medium. This paper is concerned with the inverse problem of recovering the location and shape of the obstacle from near-field data generated by infinitely many incident point source waves at a fixed energy. The incident point sources and the receivers for recording scattered signals are both located on a spherical closed surface, on which an outgoing-to-incoming operator is defined for facilitating the factorization of the near-field operator. Numerical examples in 2D are presented to show the validity and accuracy of the inversion algorithm.

math.AP↗

arXiv2025

Out-of-Distribution Detection in Heterogeneous Graphs via Energy Propagation

Graph neural networks (GNNs) are proven effective in extracting complex node and structural information from graph data. While current GNNs perform well in node classification tasks within in-distribution (ID) settings, real-world scenarios often present distribution shifts, leading to the presence of out-of-distribution (OOD) nodes. OOD detection in graphs is a crucial and challenging task. Most existing research focuses on homogeneous graphs, but real-world graphs are often heterogeneous, consisting of diverse node and edge types. This heterogeneity adds complexity and enriches the informational content. To the best of our knowledge, OOD detection in heterogeneous graphs remains an underexplored area. In this context, we propose a novel methodology for OOD detection in heterogeneous graphs (OODHG) that aims to achieve two main objectives: 1) detecting OOD nodes and 2) classifying all ID nodes based on the first task's results. Specifically, we learn representations for each node in the heterogeneous graph, calculate energy values to determine whether nodes are OOD, and then classify ID nodes. To leverage the structural information of heterogeneous graphs, we introduce a meta-path-based energy propagation mechanism and an energy constraint to enhance the distinction between ID and OOD nodes. Extensive experimental findings substantiate the simplicity and effectiveness of OODHG, demonstrating its superiority over baseline models in OOD detection tasks and its accuracy in ID node classification.

cs.LG↗

arXiv2024

Can Efficient Fourier-Transform Techniques Favorably Impact on Broadband Computational Electromagnetism?

In view of recently demonstrated joint use of novel Fourier-transform techniques and effective high-accuracy frequency domain solvers related to the Method of Moments, it is argued that a set of transformative innovations could be developed for the effective, accurate and efficient simulation of problems of wave propagation and scattering of broadband, time-dependent wavefields. This contribution aims to convey the character of these methods and to highlight their applicability in computational modeling of electromagnetic configurations across various fields of science and engineering.

physics.comp-ph↗

arXiv2024

Cascaded two-stage feature clustering and selection via separability and consistency in fuzzy decision systems

Feature selection is a vital technique in machine learning, as it can reduce computational complexity, improve model performance, and mitigate the risk of overfitting. However, the increasing complexity and dimensionality of datasets pose significant challenges in the selection of features. Focusing on these challenges, this paper proposes a cascaded two-stage feature clustering and selection algorithm for fuzzy decision systems. In the first stage, we reduce the search space by clustering relevant features and addressing inter-feature redundancy. In the second stage, a clustering-based sequentially forward selection method that explores the global and local structure of data is presented. We propose a novel metric for assessing the significance of features, which considers both global separability and local consistency. Global separability measures the degree of intra-class cohesion and inter-class separation based on fuzzy membership, providing a comprehensive understanding of data separability. Meanwhile, local consistency leverages the fuzzy neighborhood rough set model to capture uncertainty and fuzziness in the data. The effectiveness of our proposed algorithm is evaluated through experiments conducted on 18 public datasets and a real-world schizophrenia dataset. The experiment results demonstrate our algorithm's superiority over benchmarking algorithms in both classification accuracy and the number of selected features.

cs.LG↗

arXiv2024

PML-based boundary integral equation method for electromagnetic scattering problems in a layered-medium

This paper proposes a new boundary integral equation (BIE) methodology based on the perfectly matched layer (PML) truncation technique for solving the electromagnetic scattering problems in a multi-layered medium. Instead of using the original PML stretched fields, artificial fields which are also equivalent to the solutions in the physical region are introduced. This significantly simplifies the study of the proposed methodology to derive the PML problem. Then some PML transformed layer potentials and the associated boundary integral operators (BIOs) are defined and the corresponding jump relations are shown. Under the assumption that the fields vanish on the PML boundary, the solution representations, as well as the related BIEs and regularization of the hyper-singular operators, in terms of the current density functions on the truncated interface, are derived. Numerical experiments are presented to demonstrate the efficiency and accuracy of the method.

math.NA↗

arXiv2023

On a Robin-type non-singular coupling scheme for solving the wave scattering problems

This paper studies a non-singular coupling scheme for solving the acoustic and elastic wave scattering problems and its extension to the problems of Laplace and Lamé equations and the problem with a compactly supported inhomogeneity is also briefly discussed. Relying on the solution representation of the wave scattering problem, a Robin-type artificial boundary condition in terms of layer potentials whose kernels are non-singular, is introduced to obtain a reduced problem on a bounded domain. The wellposedness of the reduced problems and the a priori error estimates of the corresponding finite element discretization are proved. Numerical examples are presented to demonstrate the accuracy and efficiency of the proposed method.

math.NA↗

arXiv2023

Helmholtz decomposition based windowed Green function methods for elastic scattering problems on a half-space

This paper proposes a new Helmholtz decomposition based windowed Green function (HD-WGF) method for solving the time-harmonic elastic scattering problems on a half-space with Dirichlet boundary conditions in both 2D and 3D. The Helmholtz decomposition is applied to separate the pressure and shear waves, which satisfy the Helmholtz and Helmholtz/Maxwell equations, respectively, and the corresponding boundary integral equations of type $(\mathbb{I}+\mathbb{T})\bsϕ=\bs f$, that couple these two waves on the unbounded surface, are derived based on the free-space fundamental solution of Helmholtz equation. This approach avoids the treatment of the complex elastic displacement tensor and traction operator that involved in the classical integral equation method for elastic problems. Then a smooth ``slow-rise'' windowing function is introduced to truncate the boundary integral equations and a ``correction'' strategy is proposed to ensure the uniformly fast convergence for all incident angles of plane incidence. Numerical experiments for both two and three dimensional problems are presented to demonstrate the accuracy and efficiency of the proposed method.

physics.comp-ph↗

arXiv2023

Mathematical and numerical study of an inverse source problem for the biharmonic wave equation

In this paper, we study the inverse source problem for the biharmonic wave equation. Mathematically, we characterize the radiating sources and non-radiating sources at a fixed wavenumber. We show that a general source can be decomposed into a radiating source and a non-radiating source. The radiating source can be uniquely determined by Dirichlet boundary measurements at a fixed wavenumber. Moreover, we derive a Lipschitz stability estimate for determining the radiating source. On the other hand, the non-radiating source does not produce any scattered fields outside the support of the source function. Numerically, we propose a novel source reconstruction method based on Fourier series expansion by multi-wavenumber boundary measurements. Numerical experiments are presented to verify the accuracy and efficiency of the proposed method.

math.NA↗