arXiv subjects

Xiaoli Li

Publications and source records attributed to Xiaoli Li.

At least 19 recordsLinked to original sources

arXiv2026

A linear mass-lumped finite element method for the Landau-Lifshitz-Gilbert equation: unconditional energy dissipation and length preservation

We develop a linear, unconditionally energy-dissipative, mass-lumped finite element method for the highly nonlinear Landau--Lifshitz--Gilbert (LLG) equation on quasi-uniform triangular meshes. The method is built on a projection strategy for enforcing the nonconvex pointwise constraint $|\mathbf{m}| = 1$, whose simultaneous preservation with unconditional energy stability remains challenging for standard finite element discretizations. The key innovation is a unified hybrid finite element-finite difference framework that underlies both the design and the analysis of the proposed method. In the scheme construction, we exploit the weak formulation and nodal structure of mass-lumped finite element method, while incorporating suitable interpolation operators and a node-wise length-preserving mechanism inspired by finite difference discretizations. This combination yields a linear scheme that preserves the node-wise unit-length constraint and satisfies a discrete energy dissipation law. The same hybrid framework also plays a central role in the error analysis, where the weak formulation and quasi-uniform mesh structure of finite elements are combined with interpolation-based and nodewise finite difference method to control the strongly nonlinear damping term and to establish an optimal-order error estimate. More importantly, the proposed method provides a unified framework that systematically integrates the geometric flexibility of finite element method with the pointwise constraint-preserving property of finite difference method, and thus offers a general strategy for designing and analyzing structure-preserving discretizations of constrained dissipative systems. Numerical experiments, including a classical blow-up simulation, confirm the predicted accuracy, energy dissipation, and robustness of the method.

math.NA↗

arXiv2026

RobustMAD: Evaluating Real-World Robustness of Multimodal Small Language Models for Deployable Anomaly Detection Assistants

Multimodal industrial anomaly inspection assistants are a critical component of next-generation smart factories, enabling interactive vision-language-based querying. However, multimodal large language models remain impractical for on-site deployment due to prohibitive computational demands and privacy risks from cloud-based inference. Compact multimodal small language models (MSLMs) offer a deployable alternative, yet progress is constrained by the lack of comprehensive robustness analyses and meaningfully challenging benchmarks that reflect real-world industrial conditions. To address this gap, we develop RobustMAD, the first deployment-motivated benchmark, designed to comprehensively evaluate model robustness through diverse open-ended queries spanning object understanding, anomaly detection, unanswerable problems, and visual quality degradations. Contrary to conventional assumptions, top-performing MSLMs exhibit promising capabilities, surprisingly outperforming even the larger GPT-5 Nano. However, they still fall short of safety-critical requirements, and RobustMAD reveals critical robustness gaps that pose operational risks. In particular, three recurring failure modes emerge: (i) fragile multimodal grounding under fine-grained distinctions or degraded visual conditions, (ii) insufficiently comprehensive responses, and (iii) weak logical grounding on unanswerable or ill-posed queries, leading to hallucinated outputs. Grounded in these insights, we provide actionable guidance for the design of next-generation multimodal industrial inspection assistants that leverage their promising competence. Code is available at https://github.com/en-research/RobustMAD.

cs.LG↗

arXiv2026

A new class of efficient linear higher-order schemes for the Landau-Lifshitz-Gilbert equation with reduced restriction on the damping parameter

Classical high-order backward differentiation formula (BDF) methods for the Landau-Lifshitz-Gilbert (LLG) equation often suffer from restrictive stability constraints, requiring small time steps and imposing stringent lower bounds on the damping parameter. These limitations become particularly severe for schemes of order higher than three. In this paper, we develop a class of high-order generalized BDF (GBDF) schemes for the LLG equation, including both semi-implicit and fully explicit treatments of the gyromagnetic term. The proposed schemes significantly improve stability properties and substantially relax the damping parameter constraints, but introduce essential difficulty in its analysis compared to the classical BDF schemes. We construct a novel multiplier which enables us to carry out a energy-based error analysis. This approach yields optimal-order error estimates under considerably weaker assumptions on the damping parameter than those required for classical BDF schemes. Numerical experiments are presented to confirm the theoretical results, and demonstrate that the proposed GBDF schemes achieve higher accuracy, enhanced stability, and much wider admissible damping regimes compared to classical high-order BDF methods.

math.NA↗

arXiv2026

InA-Probe: Instruction-Aware Active Probing for Time Series Forecasting with LLMs

Large Language Models (LLMs) have recently demonstrated impressive potential for time series forecasting. However, existing methods predominantly rely on passive modality alignment or static task reprogramming, which often fail to capture fine-grained, non-stationary temporal patterns or to adapt to nuanced task intents. In this paper, we propose Instruction-aware Active Probing (InA-Probe), which shifts the paradigm from passive alignment toward an active, instruction-driven probing mechanism. Specifically, we design a Multi-Level Instruction Injection mechanism that enriches the model with both global task objectives and fine-grained, patch-level semantic priors. Building on this, an Adaptive Query Generation module produces sample-specific probes that are dynamically modulated by the temporal context. These probes are then refined through a dual-stage attention process: they first internalize task-specific intents via Instruction-Aware Self-Attention, and subsequently interrogate the projected temporal representations through Temporal Cross-Attention to extract salient patterns. Comprehensive experiments on seven real-world benchmarks show that InA-Probe consistently outperforms state-of-the-art deep learning and LLM-based baselines, excelling in both one-for-all generalization and zero-shot transfer while reducing forecasting error by up to 37\% in challenging cross-domain scenarios. Ablation studies further confirm that the synergy between adaptive querying and fine-grained instructions is key to unlocking the reasoning power of LLMs for complex time series.

cs.AI↗

arXiv2026

Physically-Constrained Mamba-SDE for Remaining Useful Life Prediction under Irregular Observations

Accurate Remaining Useful Life prediction is critical for industrial predictive maintenance. However, real-world deployment is challenging due to the irregular nature of sensor observations, characterized by asynchronous sampling, burst missingness, and temporal jitter. Compounding this issue, purely data-driven models often generate physically implausible degradation trajectories that violate the irreversible nature of damage accumulation. To address this, we propose PC-MambaSDE, a unified continuous-time framework for robust RUL prediction under irregular observations. Specifically, we design a Mask-Aware Continuous Mamba Encoder that explicitly leverages observation masks to extract context-rich control signals. Furthermore, we introduce a Physics-Guided Latent SDE with parametrically rectified hybrid drift, superimposing a global physical bias to enforce monotonic degradation even amid severe observation gaps. Additionally, we formulate RUL prediction as a boundary value problem via a Terminal Degradation Penalty, which decouples a Health Index dimension and applies a penalty loss to guide trajectories toward the failure state. Theoretically, we prove that our variational objective is mathematically equivalent to minimizing the KL divergence via Girsanov's theorem, and we guarantee the global asymptotic stability of the learned dynamics through Lyapunov analysis. To enable rigorous evaluation, we develop a Hybrid Irregularity Generation Scheme that simulates realistic industrial imperfections. Extensive experiments on public benchmarks demonstrate that PC-MambaSDE significantly outperforms state-of-the-art methods, particularly under extreme observation scarcity, validating the efficacy of embedding physical priors into continuous-time latent dynamics.

cs.AI↗

arXiv2026

A unified framework of fully decoupled, bound-preserving and energy-dissipative schemes for two-phase flow in porous media

Developing high-order numerical schemes for two-phase flow in porous media that preserve key physical properties remains a significant challenge in numerical analysis. In this article, we propose a general framework to construct fully discrete first- and second-order numerical schemes for thermodynamically consistent model of incompressible and immiscible two-phase flow in porous media. The proposed schemes are rigorously proved to ensure five fundamental properties: (i) unique solvability; (ii) full decoupling; (iii) bound preservation for both phases; (iv) original energy dissipation; (v) local mass conservation for both phases. The key to ensure the unique solvability lies in guaranteeing the strict convexity of the discrete energy functionals associated with the constructed schemes. Departing from the coupled solution approach for the pressure and saturation variables, the proposed approach breaks traditional paradigm by subtracting the two-phase mass conservation equations to derive a fully decoupled system. In addition, the bound-preserving property for both phases is established by leveraging the singular nature of the logarithmic term around the limit values of $0$ and $1$. A rigorous error estimate for the first-order scheme, in the $\ell^{\infty}(0,T; H_h^{-1} (\Omega)) \cap \ell^{2}(0,T; \ell^2(\Omega))$ norm for the saturations of two phases, is established. Finally, various numerical examples are presented to verify the theoretical results and demonstrate the efficiency of the proposed schemes.

math.NA↗

arXiv2026

Foundation Model Guided Dual-Branch Co-Adaptation for Source-Free EEG Decoding

Source-free domain adaptation (SFDA) provides a practical solution to cross-subject EEG decoding by adapting source-pretrained models to unlabeled target domains without accessing source data. However, existing SFDA methods rely solely on the limited internal knowledge of source-pretrained models, leading to inferior cross-domain generalization and unreliable pseudo-labels. Although EEG Foundation Models (FMs) pretrained on large-scale data exhibit strong generalizability, their potential in SFDA remains largely unexplored. To this end, we propose FUSED, a Foundation-guided Source-free EEG Decoding framework that integrates a large-scale FM with a compact Specialist Model (SM) via dual-branch co-adaptation. Specifically, we introduce a Co-adaptation mechanism equipping both branches with linear and prototype views, enabling cross-branch pseudo-label generation. Additionally, we design a Consensus Filtering Mechanism that exploits the FM's inherent stability to identify high-quality samples, along with a Two-Stage Pseudo-Label Refinement scheme to suppress error accumulation through cross-branch arbitration. Finally, we calibrate the FM's decision boundaries via mutual information maximization with the SM, followed by knowledge distillation from FM to SM, forming a principled calibrate-then-distill pipeline. To our knowledge, FUSED is the first work to leverage EEG FMs within the SFDA framework for cross-subject EEG decoding. Extensive experiments across three EEG paradigms, including motor imagery, emotion recognition, and SSVEP, demonstrate consistent state-of-the-art performance, validating the effectiveness of foundation-guided synergy for robust and privacy-preserving EEG decoding.

eess.SP↗

arXiv2026

HiRAS: A Hierarchical Multi-Agent Framework for Paper-to-Code Generation and Execution

Recent advances in large language models have highlighted their potential to automate computational research, particularly reproducing experimental results. However, existing approaches still use fixed sequential agent pipelines with weak global coordination, which limits their robustness and overall performance. In this work, we propose Hierarchical Research Agent System (HiRAS), a hierarchical multi-agent framework for end-to-end experiment reproduction that employs supervisory manager agents to coordinate specialised agents across fine-grained stages. We also identify limitations in the reference-free evaluation of the Paper2Code benchmark and introduce Paper2Code-Extra (P2C-Ex), a refined protocol that incorporates repository-level information and better aligns with the original reference-based metric. We conduct extensive evaluation, validating the effectiveness and robustness of our proposed methods, and observing improvements, including >10\% relative performance gain beyond the previous state-of-the-art using open-source backbone models and significantly reduced hallucination in evaluation. Our work is available on GitHub: https://github.com/KOU-199024/HiRAS.

cs.CL↗

arXiv2026

A comparison of methods for Poisson regression in the presence of background

This paper provides a statistical analysis of three common methods of regression for Poisson data in the presence of Poisson background, namely the joint fit with two parametric models for the source and the background, the use of a non-parametric model for the background known as the wstat method, and the regression with a fixed background. The non-parametric background method, which is a popular method for spectral data, is found to be significantly biased, especially in the low-count and background-dominated regimes. Similar conclusions apply to the fixed-background regression. The joint-fit method, on the other hand, simultaneously affords reliable hypothesis testing by means of the usual Cash statistic and unbiased reconstruction of source parameters. We also investigate the effect of non-parametric regression on the number of effective degrees of freedom by means of the Efron degree of freedom function. We find that the wstat method adds a significantly larger number of degrees of freedom, compared to the number of free parameters in the source model. The other two methods have a number of degrees of freedom consistent with the number of adjustable parameters, at least for the simple models investigated in this paper.

stat.ME↗

arXiv2026

IMPACT: Influence Modeling for Open-Set Time Series Anomaly Detection

Open-set anomaly detection (OSAD) is an emerging paradigm designed to utilize limited labeled data from anomaly classes seen in training to identify both seen and unseen anomalies during testing. Current approaches rely on simple augmentation methods to generate pseudo anomalies that replicate unseen anomalies. Despite being promising in image data, these methods are found to be ineffective in time series data due to the failure to preserve its sequential nature, resulting in trivial or unrealistic anomaly patterns. They are further plagued when the training data is contaminated with unlabeled anomalies. This work introduces $\textbf{IMPACT}$, a novel framework that leverages $\underline{\textbf{i}}$nfluence $\underline{\textbf{m}}$odeling for o$\underline{\textbf{p}}$en-set time series $\underline{\textbf{a}}$nomaly dete$\underline{\textbf{ct}}$ion, to tackle these challenges. The key insight is to $\textbf{i)}$ learn an influence function that can accurately estimate the impact of individual training samples on the modeling, and then $\textbf{ii)}$ leverage these influence scores to generate semantically divergent yet realistic unseen anomalies for time series while repurposing high-influential samples as supervised anomalies for anomaly decontamination. Extensive experiments show that IMPACT significantly outperforms existing state-of-the-art methods, showing superior accuracy under varying OSAD settings and contamination rates. Code is available at https://github.com/mala-lab/IMPACT.

cs.LG↗

arXiv2026

AnalogAgent: Self-Improving Analog Circuit Design Automation with LLM Agents

Recent advances in large language models (LLMs) suggest strong potential for automating analog circuit design. Yet most LLM-based approaches rely on a single-model loop of generation, diagnosis, and correction, which favors succinct summaries over domain-specific insight and suffers from context attrition that erases critical technical details. To address these limitations, we propose AnalogAgent, a training-free agentic framework that integrates an LLM-based multi-agent system (MAS) with self-evolving memory (SEM) for analog circuit design automation. AnalogAgent coordinates a Code Generator, Design Optimizer, and Knowledge Curator to distill execution feedback into an adaptive playbook in SEM and retrieve targeted guidance for subsequent generation, enabling cross-task transfer without additional expert feedback, databases, or libraries. Across established benchmarks, AnalogAgent achieves 92% Pass@1 with Gemini and 97.4% Pass@1 with GPT-5. Moreover, with compact models (e.g., Qwen-8B), it yields a +48.8% average Pass@1 gain across tasks and reaches 72.1% Pass@1 overall, indicating that AnalogAgent substantially strengthens open-weight models for high-quality analog circuit design automation.

cs.AI↗

arXiv2026

Evidential Domain Adaptation for Remaining Useful Life Prediction with Incomplete Degradation

Accurate Remaining Useful Life (RUL) prediction without labeled target domain data is a critical challenge, and domain adaptation (DA) has been widely adopted to address it by transferring knowledge from a labeled source domain to an unlabeled target domain. Despite its success, existing DA methods struggle significantly when faced with incomplete degradation trajectories in the target domain, particularly due to the absence of late degradation stages. This missing data introduces a key extrapolation challenge. When applied to such incomplete RUL prediction tasks, current DA methods encounter two primary limitations. First, most DA approaches primarily focus on global alignment, which can misaligns late degradation stage in the source domain with early degradation stage in the target domain. Second, due to varying operating conditions in RUL prediction, degradation patterns may differ even within the same degradation stage, resulting in different learned features. As a result, even if degradation stages are partially aligned, simple feature matching cannot fully align two domains. To overcome these limitations, we propose a novel evidential adaptation approach called EviAdapt, which leverages evidential learning to enhance domain adaptation. The method first segments the source and target domain data into distinct degradation stages based on degradation rate, enabling stage-wise alignment that ensures samples from corresponding stages are accurately matched. To address the second limitation, we introduce an evidential uncertainty alignment technique that estimates uncertainty using evidential learning and aligns the uncertainty across matched stages.

cs.LG↗

arXiv2026

A unified framework of energy-stable splitting exponential integrators for damped Hamiltonian systems

In this work, we study long-time numerical integration of Hamiltonian systems subject to linear perturbations. By introducing an energy-induced metric, we establish a straightforward, coordinate-free criterion for dissipativity that ensures the decay of the physical energy for a wide class of linearly perturbed Hamiltonian systems. Since the conservative and dissipative effects cannot always be merged into a single gradient-structured dissipation and classical energy-stable methods developed for gradient flows can not directly extend to this setting, we propose a unified framework of two efficient and energy-stable splitting exponential integrators (SEI) to separately handle the dissipative and conservative parts: SEISAV (SEI based on the scalar auxiliary variable) and SEILM (SEI based on Lagrange multiplier). The SEISAV scheme composes the exact damping subflow with an exponential integrator based on the SAV update for the Hamiltonian subflow and requires solving only a one-dimensional linear algebraic equation at each time step. We prove the unconditional discrete decay for a modified energy that mirrors the continuous energy-dissipation mechanism. To enforce decay of the original energy rather than a modified one, we further develop SEILM by incorporating a Lagrange-multiplier formulation within the splitting exponential framework, leading to only a nonlinear algebraic equation at each time step. Numerical experiments on representative linearly damped Hamiltonian models confirm the predicted convergence rates, energy stability, and competitive efficiency relative to state-of-the-art schemes, indicating that the proposed framework provides a simple and robust approach for simulating linearly perturbed Hamiltonian dynamics.

math.NA↗

arXiv2026

Document Reconstruction Unlocks Scalable Long-Context RLVR

Reinforcement Learning with Verifiable Rewards~(RLVR) has become a prominent paradigm to enhance the capabilities (i.e.\ long-context) of Large Language Models~(LLMs). However, it often relies on gold-standard answers or explicit evaluation rubrics provided by powerful teacher models or human experts, which are costly and time-consuming. In this work, we investigate unsupervised approaches to enhance the long-context capabilities of LLMs, eliminating the need for heavy human annotations or teacher models' supervision. Specifically, we first replace a few paragraphs with special placeholders in a long document. LLMs are trained through reinforcement learning to reconstruct the document by correctly identifying and sequencing missing paragraphs from a set of candidate options. This training paradigm enables the model to capture global narrative coherence, significantly boosting long-context performance. We validate the effectiveness of our method on two widely used benchmarks, RULER and LongBench~v2. While acquiring noticeable gains on RULER, it can also achieve a reasonable improvement on LongBench~v2 without any manually curated long-context QA data. Furthermore, we conduct extensive ablation studies to analyze the impact of reward design, data curation strategies, training schemes, and data scaling effects on model performance. We publicly release our code, data, and models.

cs.CL↗

arXiv2026

Stability and error analysis of fully discrete original energy-dissipative and length-preserving scheme for the Landau-Lifshitz-Gilbert equation

The Landau-Lifshitz-Gilbert (LLG) equation, regarded as a gradient flow with manifold constraint, is the fundamental model describing magnetization dynamics in ferromagnetic materials. It is well known that the normalized tangent plane method is able to simultaneously achieve the non-convex manifold constraint and original energy dissipation. However, the associated computational cost of this numerical approach is exceedingly high. By contrast, the projection method is more straightforward to implement, while it often compromises the inherent energy dissipative property of the continuous model, and the error analysis turns out to be even more challenging. In this work, we first construct a linear and fully discrete finite difference numerical scheme, based on the projection method for the LLG equation, which is capable of simultaneously preserving the non-convex manifold constraint $|\mathbf{m}| = 1$ and an unconditional original energy dissipation. In the error analysis, the classical theoretical technique becomes ineffective, due to the presence of the nonlinear Laplacian term, which in turn poses a significant challenge. To overcome this subtle difficulty, we carefully rewrite the numerical method in an equivalent weak form, in which a point-wise length preserving feature of the numerical solution plays an essential role. As a result of these estimates in the reformulated weak form, an optimal convergence rate could be theoretically established. In our knowledge, this numerical method is the first linear algorithm that preserves the following combined theoretical properties: (i) point-wise length preservation, (ii) unconditional original energy dissipation, (iii) a theoretical justification of convergence analysis and optimal rate error estimate.

math.NA↗

arXiv2026

Novel linear, decoupled, and energy dissipative schemes for the Navier-Stokes-Darcy model and extension to related two-phase flow

We construct efficient original-energy-dissipative schemes for the Navier-Stokes-Darcy model and related two-phase flows using a prediction-correction framework. A new relaxation technique is incorporated in the correction step to guarantee dissipation of the original energy, thereby ensuring unconditional boundedness of the numerical solutions for velocity and hydraulic head in the $l^{\infty}(L^2)$ and $l^2(H^1)$ norms. At each time step, the schemes require solving only a sequence of linear equations with constant coefficients. We rigorously prove that the schemes dissipate the original energy and, as an example, carry out a rigorous error analysis of the first-order scheme for the Navier-Stokes-Darcy model. Finally, a series of benchmark numerical experiments are conducted to demonstrate the accuracy, stability, and effectiveness of the proposed methods.

math.NA↗

arXiv2026

Passive Daytime Radiative Cooling Enabled by Bio-Derived Ceramic-Polymer Coatings on Rapid-Curing Fiberglass Casts

Passive daytime radiative cooling (PDRC) provides an energy-free approach to suppress surface temperatures by reflecting solar irradiation while emitting thermal radiation through the mid-infrared atmospheric window. Despite rapid progress in optical performance, most PDRC systems remain limited by rigid, fragile, or planar substrates, restricting their use on flexible, curved, or wearable surfaces. Here, we report a biocompatible and structurally robust PDRC system integrated onto a commercial rapid-curing fiberglass cast, a conformal substrate widely used in orthopedic and industrial applications. The cooling architecture adopts a bilayer polymer design consisting of a polyvinyl alcohol (PVA) adhesion layer and a polymethyl methacrylate (PMMA) protective layer, both embedded with calcium pyrophosphate (CPP) ceramic particles derived from processed animal bone waste. The bio-derived CPP simultaneously enables broadband solar scattering and high mid-infrared emittance, while offering sustainability and biocompatibility advantages. The resulting composite exhibits over 90% solar reflectance and achieves up to 15 C sub-ambient cooling under direct outdoor sunlight.

physics.optics↗

arXiv2026

Beyond Factual Accuracy: Evaluating Global Reasoning Integrity in RAG Systems with LogicScore

Current evaluation methods for Retrieval Augmented Generation (RAG) suffer from \textit{factual myopia}: they relentlessly emphasize factual accuracy yet neglect global logical integrity in long-form answer generation. This drives models to force unnatural connections, producing factually grounded yet logically incoherent responses with unaddressed gaps, ambiguous links, or redundant premises. To mitigate this, we present \textsc{LogicScore}, shifting from local, fact-by-fact assessment to rigorous global reasoning scrutiny. Grounded in Horn Rules, our approach integrates a backward verification mechanism to systematically evaluate three key reasoning dimensions: \textit{Completeness} (logically sound deduction), \textit{Essentiality} (non-redundancy), and \textit{Determinateness} (consistent answer entailment). Extensive experiments across three multi-hop QA datasets (HotpotQA, MusiQue, and 2WikiMultiHopQA) and over 20 LLMs (including GPT-5, Gemini-3-Pro, LLaMA3, and task-specific tuned models) reveal a critical capability gap: leading models often achieve high factual accuracy (e.g., 92.85\% precision for Gemini-3 Pro) but struggle with global reasoning quality (e.g., 35.11\% Essentiality for Gemini-3 Pro). Our work establishes a robust standard for logical evaluation, highlighting the need to prioritize reasoning coherence alongside factual grounding in LLM development.

cs.CL↗