Searcharxiv⌕ Search

arXiv subjects

Yan Jiang

Publications and source records attributed to Yan Jiang.

At least 19 recordsLinked to original sources
arXiv2026

Limiter-based fully-discrete entropy stable explicit DG schemes for ideal MHD equations

We propose a class of high-order fully-discrete entropy stable (ES) explicit discontinuous Galerkin (DG) solvers for the compressible ideal magnetohydrodynamics (MHD) equations. Our main theoretical contribution is the introduction of a novel generalized-path-decomposition framework for MHD equations in Godunov's symmetric form. By innovatively interpreting the interior volume integral of the non-conservative source term as a path integral along a generalized path constructed by the solution polynomial, we establish the weak cell entropy inequality for the fully-discrete DG schemes. This overarching framework also accommodates other existing DG solvers based on the symmetric form. Combined with a carefully designed ES limiter, the proposed scheme satisfies the genuine fully-discrete cell entropy inequality. With this property, a Lax--Wendroff-type theorem can be obtained to show that the solution limit satisfies the entropy condition. Finally, the scheme is naturally compatible with the locally divergence-free space. Extensive numerical experiments demonstrate the scheme's low numerical dissipation and strong robustness.

math.NA↗
arXiv2026

Membership Determination of 45 Open Clusters Beyond 3 kpc

Context. Open clusters (OCs) are fundamental tracers for studying the structure and chemical evolution of the Galactic disc. Reliable identification of cluster members, particularly at the faint end of the main sequence, remains challenging owing to severe field-star contamination and the declining photometric completeness for distant, obscured systems. Aims. We aim to identify and characterise distant OC candidates at heliocentric distances $d \gtrsim 3$ kpc using Gaia DR3 astrometry, with emphasis on improving the recovery of faint candidate members in highly contaminated stellar fields. Methods. We apply a probabilistic membership method based on Gaia DR3 proper motions and parallaxes. Candidate members are selected through combined astrometric criteria and refined via spatial filtering using radial density profiles, with photometric data serving as a consistency check. For clusters affected by significant extinction, near-infrared photometry from 2MASS is incorporated to compensate for the limitations of optical data. Results. We analyse a sample of 45 targets, comprising 30 previously reported OCs and 15 newly identified candidates, all located at $d \gtrsim 3$ kpc. The method yields more compact astrometric distributions and improves the recovery of faint candidate members in several systems. However, residual field contamination remains non-negligible for the most obscured clusters projected against the Galactic plane. Conclusions. Gaia DR3 astrometry provides an effective basis for the exploratory identification and first-order characterisation of distant OC candidates. Dedicated near-infrared follow-up observations will be essential for robust membership assessment in high extincted regions.

astro-ph.GA↗
arXiv2026

Global recovery of Lorentzian principal geometry from the hyperbolic Dirichlet-to-Neumann map

We prove that the full Dirichlet-to-Neumann map on a finite time interval globally determines the Lorentzian metric \(\mathbf G_{g,c}=-c(x,t)^2\mathrm{d}t^2+g(x)\) encoded by the principal symbol of the wave operator. The result holds in spatial dimensions \(n\geq3\) for multiplicatively separable wave speeds \(c(x,t)=a(x)b(t)\), provided the accumulated effective time during the experiment exceeds the maximal travel time from the boundary to the interior and back. The data determine both the unknown Riemannian metric \(g(x)\) and the wave speed \(c(x,t)\) throughout the observation cylinder, up to a spatial change of coordinates that fixes the boundary and leaves the measured time unchanged. In particular, the temporal factor \(b\) is not prescribed but is recovered from the same measurements. We also construct several examples demonstrating that the dimensional and visibility conditions for uniqueness are sharp.

math.AP↗
arXiv2026

A Weyl-type law for surface-localized eigenfunctions of the Maxwell transmission problem

This work studies surface-localized transmission eigenfunctions for time-harmonic electromagnetic scattering. Prior results on this phenomenon are mostly qualitative, proving existence without quantifying distribution. Here we provide a quantitative analysis for the Maxwell transmission eigenvalue problem, covering both TE and TM modes. We first establish a Weyl asymptotic law for the full counting function, with cubic growth with respect to the radius $R$. We then prove Weyl-type upper and lower bounds for the counting functions restricted to surface-localized modes, and demonstrate that they share the same growth order three. To our knowledge, this is the first quantitative result of its kind, demonstrating that surface-localized eigenfunctions form a non-negligible fraction of the high-frequency spectrum.

math.AP↗
arXiv2026

Physics-Informed Learning of Probabilistic Gegenbauer Reconstruction for Transport-Dominated Problems

Transport-dominated problems remain challenging for data-driven methods, which often exhibit severe numerical oscillations near shocks or steep gradients due to globally supported basis functions or overly smooth hypothesis spaces. Gegenbauer reconstruction has shown promise in mitigating such oscillations, but its effectiveness critically depends on the reconstruction parameters, particularly the weight parameter $\lambda$ and truncation order $m$. For data-driven models, variations in governing problems, training data, and model architectures make systematic parameter selection particularly challenging. To address this issue, we propose a physics-informed machine-learning framework that predicts probability distributions over candidate Gegenbauer parameter pairs, enabling probabilistically weighted reconstruction while accounting for parameter uncertainty. A two-stage strategy is adopted, in which a general predictor is first pre-trained and then fine-tuned for target problems to balance accuracy and computational cost. The framework is evaluated for reduced-order and neural operator models, represented by POD-Galerkin and DeepONet, respectively. Numerical experiments on one- and two-dimensional transport-dominated problems show that the framework learns effective spatially adaptive parameter distributions. Compared with conventional reconstruction strategies, it reduces numerical errors by up to one to two orders of magnitude and achieves a more favorable accuracy--cost trade-off than problem-specific model retraining.

math.NA↗
arXiv2026

Quasianalyticity and geometric rigidity in anisotropic Calder\'on's problem

The anisotropic Calder\'on problem in dimensions $n\ge3$ remains open for general smooth metrics~\cite{Uhlmann2009}. We establish uniqueness results in two complementary regimes. In the first, the identity principle for quasianalytic functions propagates boundary information and yields uniqueness in general geometry, including a partial-boundary consequence; under a prescribed normal geometry, quasianalyticity is needed only in the distinguished direction. In the second, suitable symmetry or one-sided ordering assumptions lead to uniqueness at $C^\infty$ regularity with full or restricted boundary access. Taken together, the results exhibit a tradeoff among regularity, geometric structure, and boundary access: quasianalyticity supplies continuation in general geometry, while symmetry or one-sided order replaces that continuation at $C^\infty$ regularity.

math.AP↗
arXiv2026

An Asymptotic-Preserving Dynamical Low-Rank Semi-Lagrangian Method for Multiscale Linear Kinetic Transport Equations

In this paper, we develop an asymptotic-preserving (AP) dynamical low-rank semi-Lagrangian method for multiscale linear kinetic transport equations. The method combines the large-time-step capability of semi-Lagrangian discretizations with the storage and cost reduction provided by low-rank representations. The proposed scheme couples an approximate macroscopic density update with the basis update Galerkin integrator for the kinetic distribution. To retain the reduced complexity in the semi-Lagrangian flux evaluation, the flux derivative is computed through a sampled angular quadrature strategy. We establish an unconditional stability analysis of the full-quadrature low-rank scheme in the constant-coefficient case. The error induced by angular sampling in the flux derivative is quantified. The resulting scheme is shown to be AP in the diffusive limit. Numerical experiments, including high-dimensional test cases, demonstrate that the proposed method is AP, stable under large time steps, and computationally efficient across kinetic and diffusive regimes.

math.NA↗
arXiv2026

Weighted Inverse Lax-Wendroff Boundary Treatment of Discontinuous Galerkin Methods for Conservation Laws

In this paper, we propose a weighted inverse Lax-Wendroff (WILW) boundary treatment for the discontinuous Galerkin (DG) method on unfitted meshes to efficiently solve hyperbolic conservation laws in complex geometries. The proposed method employs the standard DG scheme for interior cells and reconstructs high-order approximation polynomials via the ILW principle for cut cells near boundaries to impose numerical boundary conditions, effectively eliminating the time-step restriction typically caused by small cut cells. In particular, to address the sensitivity of numerical errors to the geometric size of cut cells in the basic ILW scheme, we raise the reconstruction order at the boundary, ensuring that accuracy becomes independent of the cut-cell size. Furthermore, it incorporates a weighted least-squares reconstruction to reduce the need for complex high-order boundary derivatives during construction. As a result, the method maintains high-order accuracy while significantly improving computational efficiency for multi-dimensional problems. Finally, the stability of the proposed method is theoretically validated through linear stability analysis, and the effectiveness and robustness of the proposed scheme are numerically verified through a series of one-dimensional and two-dimensional numerical experiments for scalar and system equations.

math.NA↗
arXiv2026

MathCoPilot: An Interactive System for Human-AI Symbiotic Paradigm of Mathematical Research

Existing LLM-based theorem provers have achieved impressive results on formal mathematics benchmarks, yet they remain confined to acting as autonomous agents that prove a stated proposition. In this paper, we propose MathCoPilot, a human-in-the-loop system that embodies a new human--AI symbiotic paradigm for mathematical research, in which the mathematician steers the high-level mathematical direction while AI agents carry out the detailed formalization and proof work under continuous human guidance. MathCoPilot unifies three core capabilities: (1) an interactive workbench where the mathematician and AI agents collaborate through a living proof blueprint that decomposes a proof into navigable steps the human can directly inspect, direct, and refine; (2) automated proving skill orchestration with adaptive knowledge base search and Lean-integrated iterative verification; and (3) topic-driven paper retrieval and automated formalization into a verified Lean knowledge base. Using MathCoPilot, we systematically compare four state-of-the-art LLMs, including Gemini~3.1~Pro, GPT-5.4, and Claude~Opus~4.7, on a FormalMATH subset and on two real PDE theorems requiring deep domain expertise, evaluating their ability to produce verified Lean~4 proofs and to identify errors in deliberately incorrect proofs. Our results show that while current models can handle undergraduate-level problems with high success rates under favorable autoformalization conditions, substantial challenges remain for domain-specific theorems requiring genuine mathematical understanding.

cs.AI↗
arXiv2026

Transient Depth Thermography for Probing Heat Transport

Directly probing heat propagation inside materials remains challenging because conventional measurements are predominantly sensitive to surface temperature. Depth thermography has enabled non-contact reconstruction of subsurface temperature profiles from spectrally resolved thermal radiation under steady-state conditions. Here, we extend this approach into the time domain, establishing transient depth thermography to resolve the evolution of internal temperature during heat transport. By exploiting wavelength-dependent optical penetration depth, time-resolved thermal-radiation spectra provide access to temperature as a function of both depth and time. Tracking this spatiotemporal temperature field enables direct probing of heat propagation and quantitative determination of out-of-plane thermal conductivity and interfacial thermal resistance. We demonstrate the approach in fused silica, obtaining thermal conductivity within 2% of established values, and measure the temperature-dependent thermal conductivity of MgF2 over a broad temperature range where existing data are sparse and inconsistent. Numerical simulations further demonstrate its extension to multilayer thin films for probing interfacial thermal resistance. By extending depth-resolved thermal spectroscopy from steady-state to transient heat transport, this work establishes a new optical route for non-contact characterization of thermal dynamics in bulk and layered materials.

physics.optics↗
arXiv2026

Post-Processing Reduced-Order Models for Transport-Dominated Problems by Gegenbauer Reconstruction

In this paper, we develop a physics-based post-processing technique for data-driven reduced-order models (ROMs) of transport-dominated problems. Besides the slow decay of the Kolmogorov n-width, ROMs based on globally supported bases often produce unphysical oscillations when approximating solutions with shocks or sharp gradients, a phenomenon analogous to Gibbs oscillations in spectral approximations. To address this issue, we introduce a post-processing framework based on Gegenbauer polynomial reconstruction. The key idea is to re-project the ROM solution onto a Gegenbauer polynomial basis over each interval of analyticity. Originally developed for spectral approximations, Gegenbauer reconstruction achieves spectral accuracy while effectively suppressing Gibbs oscillations. We extend this technique to data-driven ROMs and consider three representative approaches: Proper Orthogonal Decomposition (POD)-Galerkin ROM, Operator Inference (OpInf), and nonlinear manifold ROMs based on convolutional autoencoders (CAE). Numerical results show that the proposed post-processing consistently removes spurious oscillations and substantially improves solution quality for all three ROMs. For one-dimensional problems, the method is straightforward to implement once discontinuities are detected. We further develop a practical extension to two-dimensional problems using line-by-line reconstruction in each coordinate direction. Extensive numerical experiments demonstrate that the proposed method reduces errors by up to one or two orders of magnitude for inviscid transport problems and significantly outperforms total variation regularization in both numerical accuracy and the sharp resolution of discontinuities.

math.NA↗
arXiv2026

Are LLMs Ready to Assist Physicians? PhysAssistBench for Interactive Doctor-Patient-EHR Assistance

The most plausible near-term role of medical LLMs is to assist rather than replace physicians, yet current evaluations often test isolated capabilities: clinical knowledge, EHR system interaction, or patient communication. Physician assistance instead requires coordinating these capabilities within the same interaction, where physicians issue underspecified requests, patients describe symptoms ambiguously, and EHR systems demand precise tool use. We introduce PhysAssistBench, a benchmark for interactive doctor-patient-EHR assistance. Built from real MIMIC-IV cases, PhysAssistBench uses a scalable pipeline to construct agentic patients: interactive, record-grounded agents that turn static EHR records into multi-turn clinical scenarios while preserving clinical factuality. PhysAssistBench provides a curated bilingual evaluation set of 1,296 manually reviewed and physician-validated turns. Experiments with leading LLMs show that current models remain unreliable in this setting, which exposes a key bottleneck for clinical LLMs: reliable assistance requires coordination across knowledge, communication, and systems, not isolated gains in any of them.

cs.CL↗
arXiv2026

RAG-Match: Retrieval-Augmented Knowledge Injection and Hierarchical Reasoning for Calibrated Semantic Relevance

Semantic relevance judgment for search is particularly challenging in knowledge-intensive scenarios, where accurate ranking requires not only semantic matching but also background grounding, multi-step reasoning, and well-calibrated decision boundaries. Existing relevance models mainly rely on direct label supervision or shallow semantic similarity, which limits their ability to handle implicit intent, factual equivalence, and fine-grained relevance distinctions. To address this issue, we propose \textsc{RAG-Match}, a three-stage framework that integrates knowledge-augmented pretraining, hierarchical reasoning alignment, and preference-based decision calibration for relevance modeling. The key idea is to first strengthen query-centered semantic grounding, then align the model with structured relevance reasoning, and finally correct decision-level inconsistencies in difficult boundary cases. Experimental results on a real-world search relevance benchmark show that \textsc{RAG-Match} consistently outperforms strong LLM-based baselines across multiple ranking metrics, demonstrating the effectiveness of combining knowledge injection, reasoning supervision, and preference optimization for fine-grained relevance judgment.

cs.IR↗
arXiv2026

A Comparative Evaluation of Structural Topic Models and BERTopic for Short, Open-Ended Survey Responses

Topic modeling in applied psychology increasingly spans two methodological traditions: probabilistic bag-of-words models and newer embedding-based approaches. Yet many evaluations of these methods rely on longer and cleaner benchmark corpora, leaving less guidance for short, open-ended survey responses. This paper compares Structural Topic Models (STM), a probabilistic topic model, and BERTopic, an embedding-based model, for analyzing open-ended survey responses. We evaluated three STM conditions and five BERTopic conditions, varying typographical correction, stemming, embedding choice, and contextual augmentation, a strategy we introduced to provide additional semantic context for very short responses. Results indicate that BERTopic consistently produced higher topic coherence than STM, with contextual augmentation yielding the strongest performance gains. In contrast, higher-dimensional embeddings alone did not improve coherence and were associated with greater data loss. Qualitative evaluation showed that BERTopic generated more interpretable and stable topics, while STM topics were often broader and more mixed. However, STM provides stronger support for inferential covariate analysis, whereas BERTopic covariate comparisons are primarily descriptive. These findings suggest that STM and BERTopic offer complementary strengths. We conclude with practical guidance for selecting and combining topic modeling approaches in applied social science research.

cs.CL↗
arXiv2026

GFMate: Empowering Graph Foundation Models with Test-time Prompt Tuning

Graph prompt tuning has shown great potential in graph learning by introducing trainable prompts to enhance the model performance in conventional single-domain scenarios. Recent research has extended graph prompts to improve Graph Foundation Models (GFMs) by few-shot tuning auxiliary prompts. Despite their progress, most existing methods embed source-domain information into prompts, which serve either as input to GFMs or encoded during model pre-training. Such prompt entanglement with specific source domains and GFM pre-training strategy restricts their generalisability to other domains and different GFMs. Furthermore, existing GFM prompts merely rely on few-shot tuning for adaptation, neglecting the rich information in unlabelled target domain test data. Motivated by these insights, this paper aims to empower GFMs with pre-training-agnostic test-time graph prompt tuning, named GFMate. GFMate introduces centroid and layer prompts applied after pre-training on target domains, avoiding entanglement with specific source domains and model pre-training. In addition, a test-time complementary learning objective is devised to exploit both labelled and unlabelled target domain data for effective test-time prompt tuning. Extensive experiments on 12 benchmark datasets demonstrate the superior performance and efficiency of GFMate, achieving improvements of up to 30.63%. Code is available at https://github.com/YanJiangJerry/GFMate.

cs.LG↗
arXiv2026

Hierarchical Attacks for Multi-Modal Multi-Agent Reasoning

Multi-modal multi-agent systems (MM-MAS) have gained increasing attention for their capacity to enable complex reasoning and coordination across diverse modalities. As these systems continue to expand in scale and functionality, investigating their potential vulnerabilities has become increasingly important. However, existing studies on adversarial attacks in multi-agent systems primarily focus on isolated agents or unimodal settings, leaving the vulnerabilities of MM-MAS largely underexplored. To bridge this gap, we introduce HAM$^{3}$, a Hierarchical Attack framework for multi-modal multi-agent systems that decomposes attacks into three interconnected layers. Specifically, at the perception layer, HAM$^{3}$ mounts attacks by perturbing visual inputs, textual inputs, and their fused visual-textual representations. At the communication layer, it performs communication-level attacks that corrupt message content and interaction topology, such as manipulating shared context or communication links to distort collective information flow. At the reasoning layer, it conducts reasoning-level attacks that interfere with each agent's cognitive pipeline, biasing reasoning trajectories and ultimately compromising final decisions. We evaluate HAM$^{3}$ on the GQA benchmark through multi-agent systems built on distinct reasoning paradigms including ReAct, Plan-and-Solve, and Reflexion. Experiments demonstrate that our framework achieves an Attack Success Rate of up to 78.3%, with reasoning-layer attacks being the most effective. More than half of the successful attacks lead multiple agents to produce consistent errors. These findings offer valuable insights for building more robust and interpretable multi-agent intelligence.

cs.AI↗
arXiv2026

Block-R1: Rethinking the Role of Block Size in Multi-domain Reinforcement Learning for Diffusion Large Language Models

Recently, reinforcement learning (RL) has been widely applied during post-training for diffusion large language models (dLLMs) to enhance reasoning with block-wise semi-autoregressive generation. Block size has therefore become a vital factor in dLLMs, since it determines the parallel decoding granularity and affects the rollout trajectories during RL optimisation, e.g., GRPO. Instead of investigating the effect of block size during inference on individual domains, this paper studies block size from a domain conflict perspective for dLLM RL post-training in multi-domain scenarios. The main contributions are: (1) a formulation of domain block size conflict in multi-domain RL for dLLMs, which will largely affect the post-training effectiveness for rollout-based RL methods; (2) a novel dataset, Block-R1-41K is constructed with a best-improved training block size for each sample, which also induces a Block Size Conflict Score to quantitatively measure the domain conflict; (3) a new benchmark, Block-R1, for flexible RL post-training for dLLMs in both single and cross domain; and (4) a simple yet powerful cross-domain post-training method with sample-level best-improved training block sizes. Extensive experiments on 13 distinct datasets, 7 latest RL algorithms and diverse dLLM backbones are comprehensively covered in Block-R1. The benchmark is open-sourced at https://github.com/YanJiangJerry/Block-R1 with the dataset released at https://huggingface.co/datasets/YanJiangJerry/Block-R1-41K.

cs.LG↗
arXiv2026

Break the Block: Dynamic-size Reasoning Blocks for Diffusion Large Language Models via Monotonic Entropy Descent with Reinforcement Learning

Recent diffusion large language models (dLLMs) have demonstrated both effectiveness and efficiency in reasoning via a block-based semi-autoregressive generation paradigm. Despite their progress, the fixed-size block generations remain a critical bottleneck for effective and coherent reasoning. 1. From a global perspective, different reasoning tasks would correspond to different optimal decoding block sizes, which makes a ``one-size-fits-all'' assumption ineffective. 2. Even within a single reasoning task, the rigid block partitioning would break the logical flow and reduce reasoning coherence. Through empirical observations, we reveal that for block-wise entropy, incorrect reasoning exhibits a fluctuating and unsteady trend between blocks, whereas the correctly generated tasks follow a consistent descending trend. Therefore, this paper proposes b1, a novel post-training framework for dLLMs that learns dynamic-size reasoning blocks via a Monotonic Entropy Descent objective with reinforcement learning to enhance reasoning coherence.b1 integrates seamlessly as a plug-and-play module with existing dLLM's post-training algorithms. Extensive experiments across various reasoning benchmarks showcase b1's consistent improvement over existing fixed-size block baselines. Our code has been released at https://github.com/YanJiangJerry/Block-R1.

cs.LG↗