arXiv subjects

Yan Jiang

Publications and source records attributed to Yan Jiang.

At least 19 recordsLinked to original sources

arXiv2026

Energy Stability and Error Estimates for a Globally Divergence-Free DG Method of Arbitrary Order

We propose and analyze an arbitrary-order globally divergence-free (GDF) discontinuous Galerkin (DG) method for the two-dimensional linear magnetic induction equation on unstructured triangular meshes. To the best of our knowledge, this is the first work to provide a rigorous energy-based analysis of high-order GDF-DG methods. First, we incorporate the edge normal-trace evolution into a closed, strictly local semidiscrete operator acting on the elementwise magnetic field alone. Then, we introduce two local modifications to the continuous electric field: a weighted patch moment correction that enforces local polynomial orthogonality and a vertex-patch stabilization that damps the remaining high-order modes. On shape-regular, quasi-uniform periodic triangulations, we prove semidiscrete energy stability with a sufficiently large mesh-independent penalty and establish a priori error estimates for smooth solutions. Numerical experiments support the analysis.

math.NA↗

arXiv2026

High-Order Fully Discrete Entropy-Stable DG Methods with Compact Explicit Single-Step Time Discretizations

We develop a unified framework for high-order, fully discrete entropy-stable discontinuous Galerkin (DG) methods with compact explicit single-step time discretizations. At the end of each time step, the preliminary DG polynomial is scaled toward its cell average to enforce a strong cell entropy inequality while preserving conservation. This correction is feasible if and only if the updated cell average satisfies a weak cell entropy inequality, which standard third-order strong-stability-preserving Runge--Kutta DG updates can violate at arbitrarily small positive CFL numbers. For compact single-step schemes, including compact Runge--Kutta, Lax--Wendroff, and ADER-DG methods, we derive an explicit interval of feasible numerical entropy fluxes at each interface and prove that it is nonempty under a CFL condition. Projecting a compatible high-order target flux onto this interval guarantees the weak cell entropy inequality and preserves single-step high-order accuracy on smooth solutions, including near nondegenerate extrema. The limiter also enforces multiple entropy inequalities simultaneously. We also establish a Lax--Wendroff-type theorem. Numerical experiments for scalar conservation laws and the compressible Euler equations demonstrate high-order accuracy, multi-entropy control, and robustness for strong shocks.

math.NA↗

arXiv2026

DIME: Scaling Facial Representation Learning via Differential Masked Autoencoding

Scaling up data and model capacity has driven substantial progress in visual representation learning. However, conventional pretext tasks exhibit diminishing returns on fine-grained facial analysis. We attribute this to a scaling bottleneck: these tasks model each image's appearance and are dominated by identity, pose, and illumination, so subtle within-identity facial differences contribute little to the training signal. We introduce DIME, a differential masked autoencoder for large-scale facial representation learning. DIME builds on a simple observation: two images of the same person share identity-specific appearance, so their difference exposes facial changes. DIME reconstructs both masked images in an identity-matched pair and, through an Explicit Differential Direction Supervision (EDDS) objective, aligns the direction of their reconstructed difference with the true difference, while source isolation makes each reconstruction depend only on its own image. Shared appearance cancels in this difference, and because EDDS ignores magnitude, subtle facial changes count as much as large pose or illumination changes. DIME uses identity labels only to form pretraining pairs, requires no dense annotations, and learns dense facial representations with emergent part-level semantics. We pretrain DIME on 20 million high-resolution facial images consolidated from existing face datasets. DIME's AU detection performance continues to improve as pretraining data scales from 6M to 20M images, with its BP4D F1 increasing by 5.9 points, while MAE gains only 0.5 points on the same subsets. DIME also outperforms specialized facial methods on AU detection, AU intensity estimation, cross-domain anti-spoofing, landmark localization, head pose estimation, face parsing, and face generation.

cs.CV↗

arXiv2026

Fourier--Laplace Injectivity for Oblique and Polygonal Cylinders in Passive Inverse Problems

We study Fourier--Laplace transforms on null phases arising in passive inverse problems. Densities with codimension-one dependence in oblique cylinders are first considered. Integration in the distinguished direction reduces the data to an entire transform on a real-analytic maximally totally real submanifold. Holomorphic uniqueness then gives injectivity. A fixed transverse polytope swept along a polygonal curve, forming a polygonal cylinder, is next considered. The density is assumed to be polynomial in the material transverse variables on each swept piece. A weighted Brion--Barvinok expansion separates the vertex terms and the successive pieces. The same representation gives a finite-dimensional Lipschitz estimate when the polynomial degree is fixed. We apply these transform results to passive wave and heat equations in arbitrary dimension. The initial state is zero outside the observation domain. Equality of the Laplace-domain boundary data determines the quantity of the initial data divided by the speed squared in the acoustic model and the quantity of the initial data divided by the coefficient of thermal conductivity in the parabolic model. The question of what remains true when only weighted generalized boundary data on a finite interval $[0,T]$ are available is then studied. These data determine the harmonic moments of the quotient up to the weighted terminal residual. This identity gives a Hölder estimate in an oblique cylinder and a Lipschitz estimate in a polygonal cylinder. Finally, a continuous generating curve is approximated by a polygonal curve and a continuous material density by piecewise transverse polynomials. The resulting reconstruction estimate separates measurement noise, density approximation error, geometric error, and the condition number of the finite sampling matrix.

math.AP↗

arXiv2026

Determining Schrodinger Potentials on Riemannian Manifolds

We prove that the Dirichlet-to-Neumann map uniquely determines a smooth real Schrödinger potential on any prescribed compact connected smooth Riemannian manifold of dimension at least three with nonempty smooth boundary. The proof combines local continuation of Green kernels with uniform estimates for the associated integral representations on shrinking spheres. These estimates yield local recovery of the potential, and a continuation argument extends this recovery throughout the manifold.

math.AP↗

arXiv2026

Readout Blindness: VLM Scores Miss the Spatial Direction Their Frozen Encoders Retain

CLIP-like vision-language models remain a cornerstone of multimodal systems, yet their scores stay near chance on directed spatial relations, such as whether one object is left of another. We call this failure readout blindness and analyze, theoretically and empirically, why deployed scores miss the direction: when scoring rules treat the subject and object symmetrically, direction cancels regardless of encoder training. Guided by this analysis, we introduce Antisymmetric Displacement Readout (ADR), which aligns caption words with image patches in the frozen features and scores each relation by the signed displacement between matched object centroids. Notably, ADR succeeds without additional training or learned parameters, thereby demonstrating that directional information remains in the frozen encoder. However, text and world priors can inflate accuracy, so we further introduce prior deflation, which measures the benefit of the image-text pairing as the grounded gain over a null that pairs each item with an unrelated image. Extensive experiments across encoder families show that ADR substantially improves over deployed scores, which remain near chance on most direction-balanced sets even for fine-tuned encoders. Compared with more complex readouts, ADR outperforms the evaluated MLLM likelihood readouts and is competitive with their chat inference at a small fraction of the computation. These results support our claim that directional information can be recovered from frozen features by an appropriate readout. Our implementation and evaluation kit will be publicly available.

cs.CV↗

arXiv2026

Determining $W^{1,n}$ conductivities in Calderón's problem for $n\geq4$

We establish a global uniqueness result at the critical Sobolev regularity for the isotropic Calderón problem in all dimensions $n\ge 4$. More precisely, for every $n\ge4$ and every bounded Lipschitz domain $Ω\subset\mathbb{R}^n$, any real-valued, uniformly elliptic scalar conductivity $γ\in W^{1,n}(Ω)$ is uniquely determined by its full Dirichlet-to-Neumann map. This settles a long-standing open problem in the field. To prove uniqueness at this endpoint, we develop an averaged trace norm method, which combines complex geometrical optics with trace norm estimates averaged over wave orientations.

math.AP↗

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

An energy-based discontinuous Galerkin method for wave equations on complex geometric domains

This paper develops a high-order cut energy-based discontinuous Galerkin (CutEDG) method for second-order acoustic wave equations on complex domains and across stationary material interfaces. The method employs unfitted Carte- sian meshes and addresses the small-cut-cell problem by introducing ghost-penalty stabilization directly into the local bilinear forms defining the EDG energy, while leaving the original spatial coupling and numerical-flux structure unchanged. We establish semidiscrete energy stability and a priori error estimates showing that high-order accuracy is retained. The formulation is further extended to interface problems with discontinuous wave speeds. Numerical experiments confirm the pre- dicted convergence rates and demonstrate robustness with respect to arbitrarily small cut cells. In particular, the explicit time-step restriction is governed by the background mesh size rather than the smallest physical cut cell, and the stabilized energy Gram matrices exhibit cut-independent conditioning.

math.NA↗

arXiv2026

From Laboratory to Real World: A New Benchmark Towards Privacy-Preserved Visible-Infrared Person Re-Identification

Aiming to match pedestrian images captured under varying lighting conditions, visible-infrared person re-identification (VI-ReID) has drawn intensive research attention and achieved promising results. However, in real-world surveillance contexts, data is distributed across multiple devices/entities, raising privacy and ownership concerns that make existing centralized training impractical for VI-ReID. To tackle these challenges, we propose L2RW, a benchmark that brings VI-ReID closer to real-world applications. The rationale of L2RW is that integrating decentralized training into VI-ReID can address privacy concerns in scenarios with limited data-sharing regulation. Specifically, we design protocols and corresponding algorithms for different privacy sensitivity levels. In our new benchmark, we ensure the model training is done in the conditions that: 1) data from each camera remains completely isolated, or 2) different data entities (e.g., data controllers of a certain region) can selectively share the data. In this way, we simulate scenarios with strict privacy constraints which is closer to real-world conditions. Intensive experiments with various server-side federated algorithms are conducted, showing the feasibility of decentralized VI-ReID training. Notably, when evaluated in unseen domains (i.e., new data entities), our L2RW, trained with isolated data (privacy-preserved), achieves performance comparable to SOTAs trained with shared data (privacy-unrestricted). We hope this work offers a novel research entry for deploying VI-ReID that fits real-world scenarios and can benefit the community.

cs.CV↗

arXiv2026

Quasianalyticity and geometric rigidity in anisotropic Calderón's problem

The anisotropic Calderón problem of determining a smooth Riemannian metric from boundary measurements, up to a boundary-fixing diffeomorphism, remains open in dimensions $n\ge3$~\cite{uhlmann2009electrical}. We establish unique identifiability results in two complementary regimes. In the first, the identity principle for quasianalytic functions propagates boundary information and yields unique identifiability on compact manifolds without a prescribed product structure, including a partial-data 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 unique identifiability 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 when no global product structure is prescribed, while symmetry or one-sided order replaces that continuation at $C^\infty$ regularity.

math.AP↗

arXiv2026

Optimal Allocation of Grid-Forming Frequency Shaping Control

Various inverter-based control strategies have been proposed to improve frequency security for power systems with high renewable penetration. Among them, the grid-forming frequency shaping control is particularly promising due to its ability to shape the post-contingency aggregate system frequency dynamics into first-order with prescribed rate of change of frequency (RoCoF) and steady-state frequency deviation. Moreover, the shaped aggregate dynamics depends on the harmonic sum of all inverter transfer functions rather than on their distribution. In light of this, here we explore how to allocate shaping control resources to minimize the transient control effort needed to achieve ideal coherent dynamics. We formulate it as a constrained optimization problem by tackling two main difficulties. First, we make the squared $\mathcal{H}_2$ norm legitimate quantification of transient control cost under step power imbalances through a system transformation. Second, we simplify the $s$-domain constraint for Nadir elimination into a standard constraint that is easy to implement in optimization. The resulting non-convex optimization problem can be solved by existing successive convexification method. The effectiveness of the allocation has been verified on the modified Icelandic Power Network test case.

eess.SY↗

arXiv2026

On an inverse boundary problem in elastodynamics

We study the simultaneous identification of the Lamé parameters $λ$ and $μ$ in three-dimensional static isotropic elasticity. For smooth coefficients, we establish uniqueness from the full Dirichlet-to-Neumann map when $μ$ is axisymmetric, admits a multiplicative or additive separation on a product domain, or is quasianalytic in one fixed direction. These results require neither smallness of $\nablaμ$ nor real analyticity of the coefficients, and impose no corresponding structural condition on $λ$. In the axisymmetric and separated cases, partial boundary data suffice to determine $μ$.

math.AP↗

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

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

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

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↗