arXiv subjects

Lu Chen

Publications and source records attributed to Lu Chen.

At least 19 recordsLinked to original sources

arXiv2026

Coupled thermoacoustic resolvent analysis of a model two-stream coaxial combustor

We derived a resolvent operator to analyze the coupled flame-acoustic effect in a model two-stream coaxial combustor. The theoretical analysis accommodates both the hydrodynamic effect of the active flame and chamber acoustic effect, as well as their coupling effect. Utilizing the coupled thermoacoustic resolvent, we are able to identify the optimal forcing of different mechanisms and their corresponding optimal responses. When this new modeling tool is applied to a two-stream coaxial model combustor, it reveals distinctly different forcing-response characteristics in the coupled system compared to those in a purely hydrodynamic linear system. Acoustic energy peaks, indicative of resonance, are observed. Additionally, it has been found that the acoustic forcing does not maintain a rank-one property. Furthermore, the modes most receptive to the flame-acoustic coupling effect can be identified using a novel sensitivity analysis approach. Interestingly, by employing the coupled thermoacoustic resolvent, we demonstrate that forcing can be designed to negate or counteract perturbations caused by the forcing of another attribute, potentially aiding in the development of effective thermoacoustic control strategies.

physics.flu-dyn↗

arXiv2026

A $C^2$-Perturbative Bernstein Theorem for Anisotropic Entire Minimal Graphs

We prove a Bernstein theorem for $\Phi$-anisotropic minimal hypersurfaces in dimensions $1\leq n\leq 7$ that the only entire smooth solutions $u$ of $\Phi$-anisotropic minimal hypersurfaces equation are affine functions provided the anisotropic area functional integrand $\Phi$ is sufficiently $C^{2}$--close to the Euclidean area integrand. This settles the $C^2$ entire--graph version of anisotropic Bernstein problem posed by Mooney and Yang \cite{MooneyYang2024}, and the proof uses a compactness--rigidity argument combined with Figalli's regularity theorem established in \cite{Figalli2017}.

math.AP↗

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

Chart2SVG: Editable SVG Generation from Raster Chart Images

We present Chart2SVG, a multimodal large language model that converts static raster charts into structurally organized, semantically enriched SVGs that support programmatic editing. By incorporating chart-specific semantic tokens into a vision-language model, Chart2SVG captures both geometric primitives and their functional roles. To support robust structural recovery, we introduce Beagle+, a dataset of 33K canonicalized and structurally distilled chart samples. Our approach combines specialized training objectives with a rendering-aware post-training phase, producing SVGs that are both visually accurate and structurally consistent. To facilitate higher-level manipulations, we construct a Chart Structure Graph (CSG) that exposes visual dependencies, enabling tasks such as interactive exploration, chart repurposing, and layout reuse. Experiments show that Chart2SVG substantially outperforms baselines in reconstruction fidelity and downstream editing utility, advancing the development of intelligent and interactive visualization tools.

cs.LG↗

arXiv2026

ASIL: Replacing Screenshot-and-Click with Structured State and Semantic Actions

Powerful code agents can execute scripts, call tools, and manage files, yet many important applications remain accessible primarily through graphical user interfaces. We argue that screenshot-and-click is an inefficient interface for software-operating agents: screenshots are state-incomplete, and GUI actions are brittle, semantically weak, and poorly matched to long-horizon planning. We introduce ASIL (Agent-Software Interaction Layer), an agent-native interface that exposes software through structured JSON observations and code-executable semantic actions, realized through the deepest feasible access path for each application. We instantiate ASIL across 15 applications and a benchmark of 300 single-application and 80 multi-application tasks. ASIL reaches above 80 with closed models while executing fewer than five actions per task. Under a repaired runtime and a 50-step screenshot budget, the same tasks yield 6.6 and 26.6 strict success under screenshot-and-click control, rising to 15.0 and 53.3 on an easier OSWorld-comparable band. Against application-native interfaces on matched tasks, ASIL exceeds LibreOffice's UNO API by 28-38 strict points but only matches draw.io's MCP content contract. The structured modality also suits training: small-scale SFT raises Qwen3.5-2B from 58.0 to 72.1 and Qwen3.5-9B from 66.6 to 80.4, and resource-limited on-policy RL further raises them to 74.4 and 82.2.

cs.AI↗

arXiv2026

StrategyBench: Evaluating Explicit Strategy Induction in Large Language Models

As large language models are increasingly used in data-scarce and evolving task scenarios, few-shot in-context learning (ICL) has become a key paradigm for task adaptation. However, direct ICL often uses a small set of examples without explicitly abstracting task rules, making it sensitive to example construction. In contrast, human learners often reduce such sensitivity by first summarizing task rules from examples and then applying them to new instances. To evaluate this ability, we propose StrategyBench, which selects strategy-inducible tasks from BIG-Bench, constructs reference strategies, and defines evaluation metrics along two dimensions: strategy quality and downstream utility. We further analyze strategy induction from three perspectives: task variation, model configuration, and adaptation setting, covering category-wise differences, generator-executor choices, demonstration design, and SFT-based adaptation. Experiments show that explicit strategy utility differs substantially across task categories and depends on both strategy generation and execution conditions. The benchmark is released at: https://anonymous.4open.science/r/StrategyBench-D53C.

cs.AI↗

arXiv2026

Boundary Spectral Inequalities from Measurable Sets and Heat Observability on $C^{1,1}$ Domains

In this paper, we consider the boundary control problem. For bounded connected $C^{1,1}$ domains, we establish quantitative boundary spectral inequalities for both Dirichlet and Neumann eigenfunctions. Moreover, on the basis of the spectral inequality, we study the boundary control of the solution of the heat equation and get the following observability inequality $\|u(T)\|_{L^2(\Omega)}^2 \leq C\int_{\mathcal J}|\partial_\nu u(x,t)|^2 \, d\sigma \, dt,$ where the observation domain $\mathcal J\subset\partial\Omega\times(0,T)$ is measurable with $|\mathcal J|>0$. The proof of the observability inequality combines quantitative continuation from positive-measure boundary sets with low-frequency spectral concentration. This result shows that boundary observability of solutions to the heat equation can also be achieved in $C^{1,1}$ domains.

math.AP↗

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

A diffusion model for time-dependent compositional data

We introduce a stochastic process for modeling the evolution in time of compositional measurements (i.e., a vector of non-negative values that add up to a total of 1). This model is a diffusion, as it is defined as the solution for a stochastic differential equation in the Ito sense, and it has a Dirichlet distribution as its steady distribution. We have named this process Dirichlet Diffusion (DD). As the process is confined to a manifold and the coefficients of the equation are not globally Lipschitz, the usual theorems do not apply directly and establishing the existence and properties of solutions requires a somewhat delicate analysis. We establish the existence of strong solutions under the assumption that all the parameters of the Dirichlet distribution are greater than 2; for the general case we were only able to establish the existence of weak solutions, but also that these solutions remain confined to the closed simplex without need for reflecting boundaries. A useful feature of DD that it inherits from the Dirichlet distribution is the property of aggregation: If components are combined to create a coarser composition, the resulting process is also a DD. This makes it useful, for example, for jointly modeling the evolution of a microbiome grouping the microbe species at different taxonomic levels.

math.PR↗

arXiv2026

LigBench: A Unified and Human-Aligned Benchmark for LLM-based Research Idea Generation

With the rapid advancement of large language models (LLMs), research idea generation has attracted increasing attention. Existing approaches enable LLMs to retrieve relevant literature and propose novel ideas for research areas. However, current evaluation practices for idea generation remain fragmented and lack objective standards, often relying on direct LLM scoring, which limits their ability to provide unified and reliable assessments across a coherent distribution of generated ideas. To address this challenge, we propose LigBench, an automated evaluation benchmark that enables fine-grained and reliable evaluation of AI research ideas, consistently applicable across different generation distributions. In addition, we introduce PAIR-IQ, a dataset tailored for training pairwise idea judgment models and serving as an auxiliary reference to support more objective comparative evaluation. Extensive experiments demonstrate that LigBench achieves stable and interpretable evaluations, significantly improving alignment with expert judgments. Furthermore, models trained on PAIR-IQ exhibit enhanced ranking accuracy and robustness, establishing a principled standard for scalable and objective research idea assessment.

cs.CL↗

arXiv2026

JAPE: Joint Anomaly Prediction and Intrinsic Explanation in Multivariate Time Series

Multivariate time-series anomaly prediction aims to identify whether and when anomalies will occur over a future horizon from historical observations. Existing methods primarily characterize anomalies as deviations in future numerical values, which may overlook subtle dependency changes induced by weak anomaly precursors and provide no native variable-level explanation together with the alert. To bridge these gaps, we propose JAPE, a Joint Anomaly Prediction and Explanation framework that lifts anomaly prediction from numerical-deviation modeling to dependency-structure modeling. JAPE is the first anomaly prediction framework to explicitly model evolving dependency structures for both point-wise alerting and native variable-level explanation. Specifically, JAPE (i) proposes a Decoupled Spatio-Temporal Representation (DSTR) backbone that decouples temporal and spatial modeling and captures lag-aware dependencies via learnable lag aggregation, thereby perceiving structural precursors before numerical deviations emerge; (ii) designs a dual-view alerting mechanism that fuses numerical forecasts with evolving dependency graphs for point-wise anomaly prediction, capturing structural evidence even under subtle numerical deviations; and (iii) presents Native Predictive Explanation (NPE), which directly reuses the predicted dependency graphs to rank variables by structural deviations without additional models or training. Extensive experiments on five real-world benchmarks across three prediction horizons demonstrate that JAPE improves average F1 and AUC-PR by 19.7% and 41.3%, respectively, while improving explainability with 26.6% gain in MRR.

cs.LG↗

arXiv2026

A complete characterization of the existence of extremals for the Trudinger-Moser inequality on $\mathbb{R}^2$ under sharp $L^p$-perturbations

In this paper, we investigate the following critical Trudinger--Moser inequality on $\mathbb R^2$ under sharp $L^p$-perturbations: $$ S(\lambda,p) := \sup_{\substack{u\in H^{1}(\mathbb R^{2})\\ \int_{\mathbb R^2}(|\nabla u|^2+|u|^2)\,dx\le 1}} \int_{\mathbb R^2} \left(e^{4\pi u^2}-1-\lambda |u|^p\right)\,dx . $$ For $2 \lambda^{\ast}$. Moreover, we show that the nonattainment in this range is caused by a vanishing phenomenon. For $p=2$, combining our analysis with the nonexistence results for $L^2$-perturbed Trudinger--Moser inequalities obtained in \cite{Chenluzhu}, we establish the existence of two finite thresholds $\lambda_{\ast}>-\infty$ and $\lambda^{\ast}<+\infty$ such that $S(\lambda,2)$ is attained when $\lambda_{\ast}<\lambda<\lambda^{\ast}$, and is not attained when $\lambda<\lambda_{\ast}$ or $\lambda>\lambda^{\ast}$. In contrast, for $p>4$, we prove that $S(\lambda,p)$ is attained for all admissible values of $\lambda$. Our results indicate that, in the whole-space setting, the $L^p$-perturbation term affects the existence and nonexistence of extremals through either concentration or vanishing phenomena, which is fundamentally different from the bounded-domain case, where existence or nonexistence is governed solely by concentration phenomena. These results provide a complete characterization of how sharp $L^p$ perturbations determine the existence and nonexistence of extremals for critical Trudinger--Moser inequalities on the entire $\mathbb R^2$. The resulting existence and nonexistence theory exhibits a threshold structure with respect to the $L^p$ pertubation reminiscent of the classical Brezis--Nirenberg phenomenon in the whole space $\mathbb R^2$.

math.AP↗

arXiv2026

From Enumeration to Covering: Near-Optimal Densest P-Partite Subgraph Search over Large Heterogeneous Information Networks

Given a heterogeneous information network (HIN) and a query meta-path P of length i, the densest P-partite subgraph problem finds the subgraph, spanning the i typed layers of P, that maximizes a parameter-free density: the number of meta-path instances over the geometric mean of the layer sizes. It has applications across bibliographic, e-commerce, and biomedical networks. The state-of-the-art approximation linearizes the geometric-mean objective by fixing per-layer weights, but solves one subproblem for every feasible weight set, of which there are $O((n/i)^i)$, and on each achieves only a $1/i$ approximation. We show that neither the exhaustive enumeration nor the loose guarantee is necessary. First, we replace enumeration by covering: polylogarithmically many representative weight sets, localized further by a data-dependent bound, cover all feasible ones while losing only a tunable factor $1+\eta$ in density. Second, we cast each fixed-weight subproblem as a weighted supermodular densest-subgraph instance and solve it near-optimally, lifting the overall guarantee to $(1-\delta)/(1+\eta)$. To our knowledge, this is the first near-optimal density approximation beyond the bipartite ($i=2$) case, and it yields a PTAS for every fixed i. Algorithmically, our solver is an adaptive peeling scheme that never materializes the meta-path instances, whose number can exceed the graph size by orders of magnitude. An incumbent-driven reduction further discards representative weight sets before their subproblems are solved. Experiments on five real HINs show that our algorithms achieve substantial speedups over enumeration-based baselines and can further certify the near-optimality of the returned subgraph.

cs.DS↗

arXiv2026

Data-DPO: Direct Preference Optimization for Target Model Data Selection in LLM Post-Training

Data selection in supervised fine-tuning aims to select a small set of effective samples from large-scale candidate data, reducing training cost while preserving model performance. However, existing methods usually treat data value as a relatively static property, and pay limited attention to the compatibility between data and the capability distribution of the target model. To address this issue, we propose Data-DPO, a target model-oriented SFT data selection method. Data-DPO observes the local training feedback of the target model on different samples through one-step probing, transforms activation differences among samples into pairwise data preferences, and trains a lightweight reward model to learn target-model-aware data preferences. In the final selection stage, Data-DPO further combines target model preference, external quality scores, and marginal diversity to construct a more stable and effective training subset. Experimental results on Vision-Flan and LLaVA-CoT show that Data-DPO consistently outperforms existing data selection baselines under multiple data budgets and stably surpasses full data training performance.

cs.LG↗

arXiv2026

Hierarchical Data Selection via Manifold Coverage and Sparse Feature Coverage in LLM Post-training

As supervised fine-tuning data continues to scale, selecting high-value subsets from large candidate pools is crucial for reducing training cost and improving model performance. Existing methods often measure diversity directly in the original embedding space, where geometric metrics entangle dominant semantic directions, fine-grained supervision differences, and local noise. We address this limitation by formulating data selection as a coarse-to-fine hierarchical coverage problem and propose MASS. MASS learns low-dimensional principal manifold coordinates with a dense autoencoder for coarse semantic grouping, and then performs quality-aware sparse feature coverage within each group using a TopK sparse autoencoder. Experiments on Vision Flan and LLaVA-CoT show that MASS consistently outperforms strong data selection baselines across multiple budgets, and in several settings matches or surpasses full data training with only a small subset of data.

cs.LG↗

arXiv2026

MinerU.Chem: A High-Precision System for Optical Chemical Structure and Reaction Recognition

In organic chemistry papers and patents, molecular structures, reaction schemes, and experimental conditions are often presented as molecular structure depictions, reaction diagrams, and complex tables or figures. Such information is difficult for general-purpose document parsing systems to directly convert into machine-readable data. This limits data production for organic chemistry knowledge base construction and for AI for Chemistry tasks such as reaction prediction, retrosynthesis, condition recommendation, molecular property prediction, and drug molecule design. This report introduces MinerU-Chem, a document parsing system for organic chemistry literature integrated into the MinerU online platform. Built on top of MinerU's general document parsing pipeline, MinerU-Chem adds five chemistry-specific modules: chemistry relevance filtering, molecular structure detection, molecule identifier extraction, molecular structure recognition, and reaction scheme parsing. Together, these modules convert organic-chemistry-related image regions in documents into a Molecule Summary List and a Reaction Summary List. For molecular structure recognition, MinerU-Chem uses CARBON (Complex Atomic Representation and Bonding Object Notation) as its core representation. CARBON enables recognition results to preserve both the visual layout of the original image and complex chemical semantics, while supporting the export of standard downstream formats such as MolFile and SMILES. On the SMILES-evaluable subset of MolRecBench-Wild (N=2,392), MinerU-Chem's molecular structure recognition module achieves a SMILES exact-match accuracy of 93.02%, outperforming the best evaluated comparison system, GPT-5.6-Sol (74.87%), by 18.15 percentage points. The system has been integrated into the MinerU online platform and is available at https://mineru.net/OpenSourceTools/Extractor .

cs.CV↗

arXiv2026

Anisotropic minimal surface equation with Dirichlet boundary condition

This paper investigates the Dirichlet problem for the anisotropic minimal surface equation in a bounded domain. Under the natural assumption of non-negative boundary anisotropic mean curvature, we establish the unique solvability of the Dirichlet problem for continuous boundary data. To achieve this, an essential a priori gradient estimate is established, which also allows us to prove a weak version of Bernstein's theorem for entire solutions under a sharp, one-sided linear growth assumption. Moreover, using the direct method in the calculus of variations, we prove the existence and local Lipschitz regularity of generalized minimizers in $BV(\Omega)$ with $L^1(\partial\Omega)$ boundary data. We also find that this variational formulation naturally yields a Neumann-type boundary condition, geometrically explaining why the Neumann problem requires no boundary curvature constraints.

math.AP↗

arXiv2026

Evidence-Grounded AI for Musculoskeletal Care

Musculoskeletal diseases are among the leading causes of disability and drive the greatest global need for rehabilitation. Because recovery, remodelling and degeneration of bones, joints and related tissues unfold over months to years, care requires longitudinal management rather than isolated decisions. Clinicians must repeatedly integrate evolving patient evidence, medical knowledge and stage-specific functional goals, yet evidence is often fragmented across visits, departments and hospital systems, disrupting continuous, individualised management. Here we report OrthoPilot, a clinical artificial intelligence (AI) system powered by a large language model (LLM) that integrates hospital data streams with authoritative external knowledge for continuous musculoskeletal care. It autonomously retrieves real-time imaging, laboratory, pathology and order data and translates evolving patient states into evidence-based decisions from admission diagnosis through rehabilitation planning. We established a specialist-validated benchmark from real-world electronic health records (EHRs) spanning 1,000 disease codes. In a full-pathway reader study against 81 orthopaedic physicians, OrthoPilot outperformed experts with 25 years of experience in diagnostic reasoning, clinical decision-making and management planning. This advantage generalised across 60 external clinical centres, where OrthoPilot surpassed all evaluated intelligent systems. In a prospective physician decision-making study of 1,870 complex cases, OrthoPilot improved full-chain management success by 10.6%. In a randomised deployment involving 8,240 inpatients, integration into routine care increased cumulative cases per bed by 9.7% and improved patient-reported access to health information. These results move clinical AI from predicting isolated events toward executing longitudinal management across complete musculoskeletal care pathways.

cs.AI↗