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Hao Wu

Publications and source records attributed to Hao Wu.

At least 217 records · Page 12Linked to original sources
arXiv2026

A Geometry-Aware Operator Learning Framework for Interface Problems on Varying Domains

Solving Partial Differential Equation (PDE) interface problems on varying domains is a critical task in design and optimization, yet it remains computationally prohibitive for traditional solvers. Although operator learning has shown promise on fixed geometries, its potential for geometry-dependent interface problems has been largely unexplored. To bridge this gap, we propose an extension-based neural operator framework applicable to general linear interface problems. A key innovation of our method is the integration of the Tailored Finite Point Method (TFPM) with our base network, which reduces memory consumption and effectively alleviates the curse of dimensionality. On the theoretical front, we establish the continuity of the Helmholtz operator with respect to domain perturbations and provide rigorous error estimates for the proposed encodings. Comprehensive numerical experiments demonstrate that our framework achieves state-of-the-art accuracy and robustness. Consequently, this work provides a powerful, data-efficient tool for varying-domain simulations, offering new possibilities for real-time shape optimization.

math.NA↗
arXiv2026

Stop Wandering: Efficient Vision-Language Navigation via Metacognitive Reasoning

Training-free Vision-Language Navigation (VLN) agents powered by foundation models can follow instructions and explore 3D environments. However, existing approaches rely on greedy frontier selection and passive spatial memory, leading to inefficient behaviors such as local oscillation and redundant revisiting. We argue that this stems from a lack of metacognitive capabilities: the agent cannot monitor its exploration progress, diagnose strategy failures, or adapt accordingly. To address this, we propose MetaNav, a metacognitive navigation agent integrating spatial memory, history-aware planning, and reflective correction. Spatial memory builds a persistent 3D semantic map. History-aware planning penalizes revisiting to improve efficiency. Reflective correction detects stagnation and uses an LLM to generate corrective rules that guide future frontier selection. Experiments on GOAT-Bench, HM3D-OVON, and A-EQA show that MetaNav achieves state-of-the-art performance while reducing VLM queries by 20.7%, demonstrating that metacognitive reasoning significantly improves robustness and efficiency.

cs.RO↗
arXiv2026

HabitatAgent: An End-to-End Multi-Agent System for Housing Consultation

Housing selection is a high-stakes and largely irreversible decision problem. We study housing consultation as a decision-support interface for housing selection. Existing housing platforms and many LLM-based assistants often reduce this process to ranking or recommendation, resulting in opaque reasoning, brittle multi-constraint handling, and limited guarantees on factuality. We present HabitatAgent, the first LLM-powered multi-agent architecture for end-to-end housing consultation. HabitatAgent comprises four specialized agent roles: Memory, Retrieval, Generation, and Validation. The Memory Agent maintains multi-layer user memory through internal stages for constraint extraction, memory fusion, and verification-gated updates; the Retrieval Agent performs hybrid vector--graph retrieval (GraphRAG); the Generation Agent produces evidence-referenced recommendations and explanations; and the Validation Agent applies multi-tier verification and targeted remediation. Together, these agents provide an auditable and reliable workflow for end-to-end housing consultation. We evaluate HabitatAgent on 100 real user consultation scenarios (300 multi-turn question--answer pairs) under an end-to-end correctness protocol. A strong single-stage baseline (Dense+Rerank) achieves 75% accuracy, while HabitatAgent reaches 95%.

cs.LG↗
arXiv2026

Two-Step Decoding of Binary $2\times2$ Sum-Rank-Metric Codes

We address an open problem posed by Chen-Cheng-Qi (IEEE Trans.\ Inf.\ Theory, 2025): can the decoding of binary sum-rank-metric codes $\SR(C_1,C_2)$ with $2\times2$ matrix blocks be reduced entirely to decoding the constituent Hamming-metric codes $C_1$ and $C_2$ without the additional requirement $d_1\ge\tfrac{2}{3}d_{\mathrm{sr}}$ used in their fast decoder? We answer this in the affirmative by exhibiting a simple two-step procedure: first uniquely decode $C_2$, then apply a single error-erasure decoding for $C_1$. This shows that the restrictive hypothesis $d_1\ge\tfrac{2}{3}d_{\mathrm{sr}}$ is theoretically unnecessary. The resulting decoder achieves unique decoding up to $\lfloor (d_{\mathrm{sr}}-1)/2\rfloor$ with overall cost $T_2+T_1$, where $T_2$ and $T_1$ are the complexities of the Hamming decoders for $C_2$ and $C_1$, respectively. We further show that this reduction is asymptotically optimal in a black-box model, as any sum-rank decoder must inherently decode the constituent Hamming codes. For BCH or Goppa instantiations over $\F_4$, the decoder runs in $O(\ell^2)$ time.

cs.IT↗
arXiv2026

$Pin^{-}(2)$ Bauer-Furuta invariants

Adapting Bauer and Furuta's constructions of the refinement of the Seiberg-Witten invariants, we establish the analogous stable cohomotopy refinement of the $Pin^{-}(2)$ monopole invariants proposed by Nakamura \cite{nakamura2015pin}, and give the corresponding connected sum formula.

math.DG↗
arXiv2026

Editable-DeepSC: Reliable Cross-Modal Semantic Communications for Facial Editing

Interactive computer vision (CV) plays a crucial role in various real-world applications, whose performance is highly dependent on communication networks. Nonetheless, the data-oriented characteristics of conventional communications often do not align with the special needs of interactive CV tasks. To alleviate this issue, the recently emerged semantic communications only transmit task-related semantic information and exhibit a promising landscape to address this problem. However, the communication challenges associated with Semantic Facial Editing, one of the most important interactive CV applications on social media, still remain largely unexplored. In this paper, we fill this gap by proposing Editable-DeepSC, a novel cross-modal semantic communication approach for facial editing. Firstly, we theoretically discuss different transmission schemes that separately handle communications and editings, and emphasize the necessity of Joint Editing-Channel Coding (JECC) via iterative attributes matching, which integrates editings into the communication chain to preserve more semantic mutual information. To compactly represent the high-dimensional data, we leverage inversion methods via pre-trained StyleGAN priors for semantic coding. To tackle the dynamic channel noise conditions, we propose SNR-aware channel coding via model fine-tuning. Extensive experiments indicate that Editable-DeepSC can achieve superior editings while significantly saving the transmission bandwidth, even under high-resolution and out-of-distribution (OOD) settings.

cs.IT↗
arXiv2026

Latent representation learning based model correction and uncertainty quantification for PDEs

Model correction is essential for reliable PDE learning when the governing physics is misspecified due to simplified assumptions or limited observations. In the machine learning literature, existing correction methods typically operate in parameter space, where uncertainty is often quantified via sampling or ensemble-based methods, which can be prohibitive and motivates more efficient representation-level alternatives. To this end, we develop a latent-space model-correction framework by extending our previously proposed LVM-GP solver, which couples latent-variable model with Gaussian processes (GPs) for uncertainty-aware PDE learning. Our architecture employs a shared confidence-aware encoder and two probabilistic decoders, with the solution decoder predicting the solution distribution and the correction decoder inferring a discrepancy term to compensate for model-form errors. The encoder constructs a stochastic latent representation by balancing deterministic features with a GP prior through a learnable confidence function. Conditioned on this shared latent representation, the two decoders jointly quantify uncertainty in both the solution and the correction under soft physics constraints with noisy data. An auxiliary latent-space regularization is introduced to control the learned representation and enhance robustness. This design enables joint uncertainty quantification of both the solution and the correction within a single training procedure, without parameter sampling or repeated retraining. Numerical experiments show accuracy comparable to Ensemble PINNs and B-PINNs, with improved computational efficiency and robustness to misspecified physics.

math.NA↗
arXiv2026

DSO: Dual-Scale Neural Operators for Stable Long-term Fluid Dynamics Forecasting

Long-term fluid dynamics forecasting is a critically important problem in science and engineering. While neural operators have emerged as a promising paradigm for modeling systems governed by partial differential equations (PDEs), they often struggle with long-term stability and precision. We identify two fundamental failure modes in existing architectures: (1) local detail blurring, where fine-scale structures such as vortex cores and sharp gradients are progressively smoothed, and (2) global trend deviation, where the overall motion trajectory drifts from the ground truth during extended rollouts. We argue that these failures arise because existing neural operators treat local and global information processing uniformly, despite their inherently different evolution characteristics in physical systems. To bridge this gap, we propose the Dual-Scale Neural Operator (DSO), which explicitly decouples information processing into two complementary modules: depthwise separable convolutions for fine-grained local feature extraction and an MLP-Mixer for long-range global aggregation. Through numerical experiments on vortex dynamics, we demonstrate that nearby perturbations primarily affect local vortex structure while distant perturbations influence global motion trends, providing empirical validation for our design choice. Extensive experiments on turbulent flow benchmarks show that DSO achieves state-of-the-art accuracy while maintaining robust long-term stability, reducing prediction error by over 88% compared to existing neural operators.

cs.LG↗
arXiv2026

HortiMulti: A Multi-Sensor Dataset for Localisation and Mapping in Horticultural Polytunnels

Agricultural robotics is gaining increasing relevance in both research and real-world deployment. As these systems are expected to operate autonomously in more complex tasks, the availability of representative real-world datasets becomes essential. While domains such as urban and forestry robotics benefit from large and established benchmarks, horticultural environments remain comparatively under-explored despite the economic significance of this sector. To address this gap, we present HortiMulti, a multimodal, cross-season dataset collected in commercial strawberry and raspberry polytunnels across an entire growing season, capturing substantial appearance variation, dynamic foliage, specular reflections from plastic covers, severe perceptual aliasing, and GNSS-unreliable conditions, all of which directly degrade existing localisation and perception algorithms. The sensor suite includes two 3D LiDARs, four RGB cameras, an IMU, GNSS, and wheel odometry. Ground truth trajectories are derived from a combination of Total Station surveying, AprilTag fiducial markers, and LiDAR-inertial odometry, spanning dense, sparse, and marker-free coverage to support evaluation under both controlled and realistic conditions. We release time-synchronised raw measurements, calibration files, reference trajectories, and baseline benchmarks for visual, LiDAR, and multi-sensor SLAM, with results confirming that current state-of-the-art methods remain inadequate for reliable polytunnel deployment, establishing HortiMulti as a one-stop resource for developing and testing robotic perception systems in horticulture environments.

cs.RO↗
arXiv2026

Enhancing and Reporting Robustness Boundary of Neural Code Models for Intelligent Code Understanding

With the development of deep learning, Neural Code Models (NCMs) such as CodeBERT and CodeLlama are widely used for code understanding tasks, including defect detection and code classification. However, recent studies have revealed that NCMs are vulnerable to adversarial examples, inputs with subtle perturbations that induce incorrect predictions while remaining difficult to detect. Existing defenses address this issue via data augmentation to empirically improve robustness, but they are costly, offer no theoretical robustness guarantees, and typically require white-box access to model internals, such as gradients. To address the above challenges, we propose ENBECOME, a novel black-box training-free and lightweight adversarial defense. ENBECOME is designed to both enhance empirical robustness and report certified robustness boundaries for NCMs. ENBECOME operates solely during inference, introducing random, semantics-preserving perturbations to input code snippets to smooth the NCM's decision boundaries. This smoothing enables ENBECOME to formally certify a robustness radius within which adversarial examples can never induce misclassification, a property known as certified robustness. We conduct comprehensive experiments across multiple NCM architectures and tasks. Results show that ENBECOME significantly reduces attack success rates while maintaining high accuracy. For example, in defect detection, it reduces the average ASR from 42.43% to 9.74% with only a 0.29% drop in accuracy. Results show that ENBECOME significantly reduces attack success rates while maintaining high accuracy. For example, in defect detection, it reduces the average ASR from 42.43% to 9.74% with only a 0.29% drop in accuracy. Furthermore, ENBECOME achieves an average certified robustness radius of 1.63, meaning that adversarial modifications to no more than 1.63 identifiers are provably ineffective.

cs.SE↗
arXiv2026

The Fate of the Milky Way--Andromeda System: To Merge or Not?

It has long been predicted that the Milky Way (MW) will eventually merge with Andromeda (M31), a view reinforced by \textit{HST} measurements indicating a small M31 transverse velocity. However, using updated \textit{Gaia}-based proper motions (PMs) and including the dynamical influence of the Large Magellanic Cloud (LMC) and M33, Sawala et al. reported an MW--M31 merger probability of $\sim$50\% within 10 Gyr, leaving the fate of the Local Group (LG) uncertain. Adopting their semi-analytic framework, we revisit this problem with the latest and most precise \textit{Gaia}-based PMs for M31 and M33, corrected for systematic offsets in \textit{Gaia} astrometry. In our fiducial model, the MW--M31 merger probability rises to 90\%, with a median merger time of $6.5_{-1.5}^{+1.3}$ Gyr, broadly restoring the classical picture. A sensitivity analysis shows that the merger probability depends strongly on the adopted M31 PM through two channels: a direct effect via the radial-tangential balance of the MW-M31 orbit, and a satellite-mediated effect, where the M31 PM fixes the orbital plane and determines how satellite-induced barycentric reflex motions project onto it, either promoting or suppressing a merger. Given this sensitivity, current measurements, while favoring a high merger probability, remain inconclusive, spanning from 64.7\% to 100\% across the 2$σ$ PM region. Future PM measurements with uncertainty of $\lesssim2\,\upmu\mathrm{as\,yr^{-1}}$ will be required to reach a firm conclusion, i.e., to constrain the probability range within 10\% at the 2$σ$ level.

astro-ph.GA↗
arXiv2026

3DCity-LLM: Empowering Multi-modality Large Language Models for 3D City-scale Perception and Understanding

While multi-modality large language models excel in object-centric or indoor scenarios, scaling them to 3D city-scale environments remains a formidable challenge. To bridge this gap, we propose 3DCity-LLM, a unified framework designed for 3D city-scale vision-language perception and understanding. 3DCity-LLM employs a coarse-to-fine feature encoding strategy comprising three parallel branches for target object, inter-object relationship, and global scene. To facilitate large-scale training, we introduce 3DCity-LLM-1.2M dataset that comprises approximately 1.2 million high-quality samples across seven representative task categories, ranging from fine-grained object analysis to multi-faceted scene planning. This strictly quality-controlled dataset integrates explicit 3D numerical information and diverse user-oriented simulations, enriching the question-answering diversity and realism of urban scenarios. Furthermore, we apply a multi-dimensional protocol based on text-similarity metrics and LLM-based semantic assessment to ensure faithful and comprehensive evaluations for all methods. Extensive experiments on two benchmarks demonstrate that 3DCity-LLM significantly outperforms existing state-of-the-art methods, offering a promising and meaningful direction for advancing spatial reasoning and urban intelligence. The source code and dataset are available at https://github.com/SYSU-3DSTAILab/3D-City-LLM.

cs.CV↗
arXiv2026

The Cahn--Hilliard--Darcy--Forchheimer system with surfactant: Existence and long-time behavior of global weak solutions

We consider a diffuse-interface model for two-phase incompressible viscous flows with a soluble surfactant in a bounded porous medium. This hydrodynamic system consists of a Darcy--Forchheimer equation for the seepage velocity $\boldsymbol{u}$ coupled with two Cahn--Hilliard equations involving Flory--Huggins type singular potentials, one for the phase-field variable $ϕ$, the difference in volume fractions of the two fluids, and the other for the surfactant concentration $ψ$. We study the initial boundary value problem in two or three dimensions, with impermeability boundary conditions for $\boldsymbol{u}$ and homogeneous Neumann boundary conditions for $(ϕ, ψ)$ and their associated chemical potentials. First, we establish the existence of global weak solutions via an implicit-explicit time-discretization scheme based on the energy dissipation law. Furthermore, applying the seminal results of the first and third authors (arXiv:2510.17296), we prove that every weak solution satisfying an energy inequality converges to a single equilibrium as time tends to infinity. In sharp contrast with the available literature on similar models, in this case weak solutions are enough to guarantee the uniqueness of asymptotic limits, without the necessity of any further eventual regularization.

math.AP↗
arXiv2026

Asymptotic Results for Spectrally Positive Compound Poisson Processes

Finite excursions away from zero of a spectrally positive compound Poisson process with a negative drift can always be decomposed into two parts lying above and below zero, respectively. This paper is concerned with the asymptotic relationships among the lengths and heights of these two parts. Our results state that both their lengths and heights are asymptotically strongly dependent and exhibit a scale symmetry.

math.PR↗
arXiv2026

OMNIFLOW: A Physics-Grounded Multimodal Agent for Generalized Scientific Reasoning

Large Language Models (LLMs) have demonstrated exceptional logical reasoning capabilities but frequently struggle with the continuous spatiotemporal dynamics governed by Partial Differential Equations (PDEs), often resulting in non-physical hallucinations. Existing approaches typically resort to costly, domain-specific fine-tuning, which severely limits cross-domain generalization and interpretability. To bridge this gap, we propose OMNIFLOW, a neuro-symbolic architecture designed to ground frozen multimodal LLMs in fundamental physical laws without requiring domain-specific parameter updates. OMNIFLOW introduces a novel \textit{Semantic-Symbolic Alignment} mechanism that projects high-dimensional flow tensors into topological linguistic descriptors, enabling the model to perceive physical structures rather than raw pixel values. Furthermore, we construct a Physics-Guided Chain-of-Thought (PG-CoT) workflow that orchestrates reasoning through dynamic constraint injection (e.g., mass conservation) and iterative reflexive verification. We evaluate OMNIFLOW on a comprehensive benchmark spanning microscopic turbulence, theoretical Navier-Stokes equations, and macroscopic global weather forecasting. Empirical results demonstrate that OMNIFLOW significantly outperforms traditional deep learning baselines in zero-shot generalization and few-shot adaptation tasks. Crucially, it offers transparent, physically consistent reasoning reports, marking a paradigm shift from black-box fitting to interpretable scientific reasoning.

cs.LG↗
arXiv2026

Conflict-Free Policy Languages for Probabilistic ML Predicates: A Framework and Case Study with the Semantic Router DSL

Conflict detection in policy languages is a solved problem -- as long as every rule condition is a crisp Boolean predicate. BDDs, SMT solvers, and NetKAT all exploit that assumption. But a growing class of routing and access-control systems base their decisions on probabilistic ML signals: embedding similarities, domain classifiers, complexity estimators. Two such signals, declared over categories the author intended to be disjoint, can both clear their thresholds on the same query and silently route it to the wrong model. Nothing in the compiler warns about this. We characterize the problem as a three-level decidability hierarchy -- crisp conflicts are decidable via SAT, embedding conflicts reduce to spherical cap intersection, and classifier conflicts are undecidable without distributional knowledge -- and show that for the embedding case, which dominates in practice, replacing independent thresholding with a temperature-scaled softmax partitions the embedding space into Voronoi regions where co-firing is impossible. No model retraining is needed. We implement the detection and prevention mechanisms in the Semantic Router DSL, a production routing language for LLM inference, and discuss how the same ideas apply to semantic RBAC and API gateway policy.

cs.LG↗
arXiv2026

Fast and Optimal Differentially Private Frequent-Substring Mining

Given a dataset of $n$ user-contributed strings, each of length at most $\ell$, a key problem is how to identify all frequent substrings while preserving each user's privacy. Recent work by Bernardini et al. (PODS'25) introduced a $\varepsilon$-differentially private algorithm achieving near-optimal error, but at the prohibitive cost of $O(n^2\ell^4)$ space and processing time. In this work, we present a new $\varepsilon$-differentially private algorithm that retains the same near-optimal error guarantees while reducing space complexity to $O(n \ell+ |Σ| )$ and time complexity to $O(n \ell\log |Σ| + |Σ| )$, for input alphabet $Σ$. Our approach builds on a top-down exploration of candidate substrings but introduces two new innovations: (i) a refined candidate-generation strategy that leverages the structural properties of frequent prefixes and suffixes, and (ii) pruning of the search space guided by frequency relations. These techniques eliminate the quadratic blow-ups inherent in prior work, enabling scalable frequent substring mining under differential privacy.

cs.DS↗
arXiv2026

Interface Engineered Moiré Graphene Superlattices: Breaking the Auger Carrier Multiplication Limit for Infrared Single-Photon Detection

Hot electrons undergo Auger scattering during their relaxation process has a multiplication effect,which can generate more electrons above the Fermi level, thus improving the efficiency of photoelectric signal conversion.However,the photo-current gain brought by the Auger carrier multiplication is generally limited with a value less than 5,due to the rapid recombination of photo-generated charge-carriers and the inherently low light absorption of two-dimensional materials.Herein,by twisting graphene to an interlayer angle of 10 o ,we report a layer-dependent electronic correlations leading to an efficient carrier multiplication gain of 10 3 .This is primarily offered by the additional localized density-of-states at interface of the bi-layer 10 o ,moire graphene,and the enhanced interlayer coupling of electron waves in a five-layer moire graphene superlattice structure.Therefore,we can harvest the hot electrons during their energy relaxation through a thermalized optical phonon bottleneck effect.It is this effect that promotes the accumulated hot electrons to achieve a maximum Auger scattering rate ~ 10 10 *ps -1 *cm -2 .Furthermore,the ballistic transport of these hot electrons and Schottky barrier from a 90 nm thick silicon-on-insulator (SOI) silicon effectively block the thermal noise,thus leading to a highly sensitive near-infrared detection characteristic.At a low incident light power of ~ 10 -13 W/cm 2 ,the resulting signal-to-noise ratio is more than 100 dB.The strengthened electromagnetic interaction from highly thermalized optical phonon in stacked moire graphene is utilized in this work.The hot electron multiplication suggests the applicability of Van der Waals moire superlattice architecture for harvesting charge carriers,thus paving the pathway to design infrared single-photon avalanche detectors.

physics.app-ph↗