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Jin Zhao

Publications and source records attributed to Jin Zhao.

At least 19 recordsLinked to original sources
arXiv2026

First-Order Optimization under Uniform Nondegeneracy: Geometry, Computation, and Information

Strongly convex minimization and its natural indefinite extension to strongly convex--strongly concave minimax problems combine quantitative control of curvature with a prescribed curvature orientation. We disentangle these two roles by retaining uniform nondegeneracy alone: curvature remains uniformly separated from zero but may have either sign, with no prescribed positive--negative splitting. Surprisingly, a large part of the familiar theory nevertheless re-emerges. We first derive an intrinsic formulation through first-order secant inequalities, making the gradient on $\mathbb{R}^d$ a global bi-Lipschitz homeomorphism and yielding a unique stationary point. We then pair signed Moreau envelopes to construct a smooth scalar merit that recovers the missing descent geometry at both zeroth and first order, and the resulting paired proximal descent method achieves global linear convergence with dimension-free first-order oracle complexity. Meanwhile, we show that this tractability can break down on restricted domains: merely assuming the existence of a stationary point in the domain may lead to the curse of dimensionality, even with access to an infinite-order oracle. To overcome this information barrier, we introduce certified feasibility, an observable localization condition that enables feasible continuation. Together, these results establish a first-order optimization theory under uniform nondegeneracy that spans geometry, computation, and information.

math.OC↗
arXiv2026

Mesh-Uniform Power Stability of Two-Relaxation-Time Vector Lattice Boltzmann Schemes with Reversible Boundaries

We consider the collision-transport operator for vector-valued two-relaxation-time lattice Boltzmann schemes linearized about a uniform rest state. Assume that the equilibrium blocks are positive definite and that the link-even and link-odd relaxation parameters satisfy s_+ + s_- = 2 and 0 < s_- < 2. If the homogeneous transport is unitary in the equilibrium metric and reversible under velocity exchange, then the powers of the amplification operator are bounded uniformly with respect to the number and arrangement of lattice nodes. The admissible transports include periodic transport, vector halfway bounce-back, coordinate-aligned specular reflection, tangential orthogonal involutions, and compatible multi-channel scattering. The proof reduces the population equation to a two-step macroscopic recurrence generated by a contraction. An inclusion of the numerical range in an ellipse, combined with the Crouzeix-Palencia theorem, yields a dimension-independent estimate for the companion operator and hence the population bound. For a three-coefficient off-midpoint boundary interpolation, we give an exact rational D2N5 example whose finite-domain amplification matrix has a real eigenvalue larger than one, although the interpolation coefficients and bulk parameters are admissible. Thus coefficient convexity alone does not ensure stability for this boundary family.

math.NA↗
arXiv2026

Evo-GTransNet for Parabolic PDEs: A Fixed-Feature Galerkin Method of Lines with Quadrature-Mass Orthonormalization

In this paper, we develop an evolutionary generalized transferable neural network (Evo-GTransNet) solver for parabolic partial differential equations, formulated as a retained-space fixed-feature Galerkin method of lines. A GTransNet provides the prescribed spatial dictionary, while only the retained output coefficients evolve, thereby avoiding nonlinear training during time integration. To address severe mass-matrix ill-conditioning, we apply a quadrature-weighted truncated singular value decomposition (SVD) to select the numerically resolved trial space, followed by a separate rescaling that makes its basis orthonormal with respect to the assembly-quadrature mass inner product. Rank truncation modifies the approximation space, whereas the subsequent orthonormalization changes only its coordinate representation and preserves the retained discrete functions in exact arithmetic. The resulting semidiscrete coefficient system has an identity mass matrix, and we establish a semidiscrete energy law for symmetric linear parabolic problems. With the implicit midpoint scheme for time discretization, we further prove the contractivity of the method and derive a conditional fully discrete error estimate in which the error is controlled by the retained-space approximation error and the consistency defects. Numerical experiments demonstrate second-order temporal convergence using repeated feature samples together with separate assembly and validation quadratures, and quantify the accuracy of the retained space in the presence of severe raw-mass ill-conditioning. For the high-frequency and multiscale benchmark problems considered here, GTransNet achieves the smallest mean validation errors among the tested fixed-feature dictionaries at the same nominal output dimension.

math.NA↗
arXiv2026

Convergence analysis of a MAC scheme for the barotropic Euler system

We study a Marker-and-Cell (MAC) scheme for the barotropic Euler system. First, we apply the recently developed Lax-type convergence theorem to show the convergence of the MAC scheme to i) a dissipative weak solution unconditionally and ii) a strong solution as long as it exists. Second, We derive relative energy error estimates up to the lifespan of a strong solution, without assuming uniform boundedness of the numerical sequence. Additionally, assuming the boundedness of the numerical solutions, we obtain the optimal relative energy rate of 1, corresponding to a convergence rate of 1/2 for the numerical solutions. Finally, we corroborate our theoretical results by numerical experiments.

math.NA↗
arXiv2026

Guided Flow Matching for Forward and Inverse PDE Problems with Sparse Observations: Algorithm and Theory

Reconstructing PDE solutions from sparse observations is a core challenge in scientific computing. We present FM4PDE, a flow-matching generative framework that learns the joint distribution of PDE coefficients (or initial states) and solutions (or final states), enabling both forward simulation and inverse recovery with limited paired data. At inference, sampling is guided by a composite loss that enforces agreement with sparse measurements and reduces the PDE residual; we support deterministic, stochastic, and hybrid samplers. We provide error guarantees for these guided procedures. For the deterministic optimizer, a coercivity condition ensures trajectory boundedness and a phase-wise contraction yields logarithmic complexity in the target accuracy. For the stochastic sampler, we introduce adaptive guidance and assume dissipativity of the velocity field to obtain uniform moment bounds independent of the noise-floor parameter. This leads to polynomial-time error bounds, and a matching lower bound shows constant guidance induces an unavoidable positive bias, motivating adaptivity. A hybrid deterministic-stochastic analysis is also provided. Experiments on static and time-dependent benchmark PDEs demonstrate competitive accuracy and faster inference than diffusion-based generative models.

stat.ML↗
arXiv2026

From Accounting to Coordination: A Virtual Water-Aware Electricity-Computation-Water Nexus Framework for Data Center Dispatch

The expansion of data centers (DCs) drives a sustained increase in electricity demand and associated water withdrawals at generation sites. These withdrawals occur at generation sites and are virtually allocated to demand based on network power flows. Consequently, the actual water footprint of a specific load varies dynamically with generation dispatch and network conditions. Existing approaches typically rely on static statistical accounting to quantify these water footprints. However, such static methods fail to capture how dispatch optimization and workload relocation dynamically affect water withdrawals. As a result, static statistical accounting approaches remain decoupled from the optimization process, rendering them incapable of guiding workload relocation or power dispatch to mitigate water stress. To address this limitation, this paper develops an operational electricity-computation-water (ECW) nexus framework that internalizes virtual water impacts directly into power system dispatch. The framework represents dispatch optimization as a differentiable optimization layer embedded within a deep learning architecture, enabling efficient end-to-end learning of coordination policies while preserving operational feasibility. Combined with fixed-point coordination, the framework enforces consistency between virtual water attribution and physical generation-side withdrawals. Case studies on the IEEE 30-bus and 118-bus test systems demonstrate reliable convergence, exact power-water consistency, and reductions of approximately 3-5% in generation-related freshwater withdrawals under water-constrained conditions.

cs.AI↗
arXiv2026

Shifted Matrix-Sign Reflectors for Prescribed-Index Eigenspace Reflection

Spectral projectors and the reflectors derived from them are basic objects in numerical linear algebra. This paper studies the prescribed-index reflector I-2P_k, where P_k is the spectral projector associated with the first k eigenvectors of a symmetric matrix. If a shift s lies in the target spectral gap, then this reflector is exactly the shifted matrix sign sign(H-sI). The exact identity is elementary, but its algorithmic consequences are not: all admissible shifts give the same exact reflector, while finite-step sign filters can have very different errors. We analyze odd sign-preserving spectral filters, prove local inheritance and discrete stability for the induced reflector iterations, derive a gap-dependent Newton-Schulz operator bound, and give deterministic admissibility certificates for inexact and reused shifts. The analysis identifies the shifted spectral margin as the quantity controlling finite-step reflector accuracy and explains why the midpoint shift is the natural default. Numerical experiments separate the matrix-function issues from the outer saddle-search dynamics: controlled spectra verify the margin predictions, low-dimensional tests distinguish shifted signs from raw signs, target-index scans probe non-small k, and Allen-Cahn and dense timing tests identify the regimes in which full-matrix sign filters are useful and the stiff regimes in which stronger sign engines are needed.

math.NA↗
arXiv2026

UAV-based Energy-Efficient Data Collection in Smart Grids with ISAC QoS Guarantees

Dynamic line rating (DLR) is a methodology that requires timely monitoring data to determine the real-time ampacity of power lines. However, DLR monitoring devices (MD) are vulnerable to connectivity disruptions, leading to missing or delayed data. Although unmanned aerial vehicles (UAV) can enable resilient data collection from MD, their limited onboard energy challenges timely monitoring over extended transmission corridors with flight hazards. This paper proposes a cooperative UAV-based data collection framework with integrated sensing and communication (ISAC) to support timely DLR updates. In this framework, ISAC is employed to maintain the sensing and communication quality required for safe and cooperative UAV data collection. Accordingly, a joint energy minimization problem is formulated over UAV trajectories and collection scheduling under ISAC constraints. To solve it, a hybrid algorithm combining deep reinforcement learning (DRL) and semidefinite relaxation (SDR) is proposed, where DRL optimizes the trajectory and collection scheduling, while SDR is used to handle the non-convex ISAC constraints. Simulation results show that the proposed scheme reduces energy consumption by up to 34.6% compared with offline benchmarks and by about 2.2% compared with the separated sensing-and-communication baseline, while satisfying the minute-level timescale requirement of DLR.

eess.SP↗
arXiv2026

Hubbard-$U$-corrected electron-phonon interactions in strongly correlated materials via the finite-displacement method

Although the density functional theory plus Hubbard $U$ correction method (DFT+$U$) is broadly used to study electronic structure of strongly correlated materials, the extension of this method to electron-phonon $g$ matrices has received limited attention. Here, we implement an algorithm that integrates DFT+$U$ method with the finite-displacement method for the calculations of phonons and electron-phonon $g$ matrices. The Hubbard $U$ corrections are applied not only to electronic and phonon structures, but, more importantly, also to electron-phonon $g$ matrices. We demonstrate our algorithm in two prototypical correlated materials: infinite-layer nickelates LaNiO$_2$ and ruthenium dioxide RuO$_2$. We find that: i) While the Hubbard $U$ corrections weakly increase the electron-phonon interaction of 20% hole-doped LaNiO$_2$, its total electron-phonon coupling remains small and is insufficient to account for the observed superconducting transition temperature of about 10-30 K. Our results contrast with the recent work showing that the full GW corrections yield an elevated electron-phonon coupling of 20% hole-doped LaNiO$_2$ five times larger than its DFT value. We attribute this discrepancy to the differences in the Fermi surface topology between DFT+$U$ and GW methods. ii) The inclusion of Hubbard $U$ corrections eliminates the imaginary phonon modes of RuO$_2$ under strain on the TiO$_2$ substrate and substantially reduces the electron-phonon coupling. Our results alleviate the discrepancy between the reported large theoretical electron-phonon coupling and the low superconducting transition temperature observed experimentally. Our work provides an algorithm that fully includes the Hubbard $U$ corrections on electron-phonon properties of correlated materials, and highlights the importance of Fermi surface shape and correlation effects on phonon spectrum and electron-phonon $g$ matrices.

cond-mat.str-el↗
arXiv2026

Evaluating Answer Leakage Robustness of LLM Tutors against Adversarial Student Attacks

Large Language Models (LLMs) are increasingly used in education, yet their default helpfulness often conflicts with pedagogical principles. Prior work evaluates pedagogical quality via answer leakage-the disclosure of complete solutions instead of scaffolding-but typically assumes well-intentioned learners, leaving tutor robustness under student misuse largely unexplored. In this paper, we study scenarios where students behave adversarially and aim to obtain the correct answer from the tutor. We evaluate a broad set of LLM-based tutor models, including different model families, pedagogically aligned models, and a multi-agent design, under a range of adversarial student attacks. We adapt six groups of adversarial and persuasive techniques to the educational setting and use them to probe how likely a tutor is to reveal the final answer. We evaluate answer leakage robustness using different types of in-context adversarial student agents, finding that they often fail to carry out effective attacks. We therefore introduce an adversarial student agent that we fine-tune to jailbreak LLM-based tutors, which we propose as the core of a standardized benchmark for evaluating tutor robustness. Finally, we present simple but effective defense strategies that reduce answer leakage and strengthen the robustness of LLM-based tutors in adversarial scenarios.

cs.CR↗
arXiv2026

Developing and characterizing a new-generation regolith simulant "IGCAS-AST01" for the Tianwen-2 target asteroid (469219) Kamo'oalewa

China plans to return samples from the near-Earth asteroid (469219) Kamo'oalewa, which we previously identified as an LL-chondrite-compositional, highly space-weathered object with fine-grained regolith. In this study, we developed 10 mL of Kamo'oalewa regolith simulant, designated "IGCAS-AST01", by irradiating LL5/6 chondrite (Kheneg Ljou^ad) powder with a high-energy pulsed laser. We then analyzed the composition, grain size distribution, density, porosity, visible to near-infrared reflectance spectrum, thermal emission spectrum, thermal diffusivity, specific heat capacity, and microstructural features of both the fresh (unirradiated) powder and IGCAS-AST01. IGCAS-AST01 is composed of 57.8 vol.% olivine, 19.9 vol.% orthopyroxene, 5.6 vol.% diopside, 12.2 vol.% plagioclase, 2.6 vol.% troilite, and minor amounts of other phases. It has a mean size of 26.99 um, a median size of 23.19 um, a density of 700 kg m^-3, and a porosity of 79.1%. Additionally, IGCAS-AST01 exhibits a low reflectance of 0.1 at 0.55 um and an extremely steep spectral slope. In the temperature range of 253.15-473.15 K, its thermal diffusivity and specific heat capacity range from 3.6-4.7 x 10^-6 m^2 s^-1 and 718.43-890.20 J kg^-1 K^-1, respectively. Furthermore, thick amorphous rims and abundant nanophase metallic iron particles are observed in olivine and pyroxene grains of IGCAS-AST01. These results could support the Tianwen-2 mission's payload calibration, sampling operations, on-orbit scientific data interpretation, and future sample analysis.

astro-ph.EP↗
arXiv2026

Shape, regolith size and thickness, SMFe^0 content, and spectral type of Tianwen-2 target asteroid (469219) Kamo'oalewa

China's Tianwen-2 spacecraft will return samples from the near-Earth asteroid (469219) Kamo'oalewa. We previously reported that Kamo'oalewa develops an LL-chondrite-compositional, highly space-weathered surface. This study aims to estimate Kamo'oalewa's shape, regolith grain size and thickness, sub-micrometer iron (SMFe0) content, and spectral type. Using the lightcurve data and the Cellinoid model, we modeled Kamo'oalewa's shape, rotation period, and pole orientation. We then estimated its global distribution of regolith critical size using the balance method of gravity, cohesive force, and centrifugal force. Furthermore, in the temperature range of 253.15 to 473.15 K, we measured the thermal parameters of laser-irradiated LL chondrite powder that best matches Kamo'oalewa's spectrum, estimating Kamo'oalewa's thermal inertia and skin depth (lower limit of regolith thickness). Using the radiative transfer mixing model, we also estimated the content of SMFe0 in Kamo'oalewa's regolith. Finally, using the MIT online spectral classification tool for the laser-irradiated LL chondrite powder, we obtained a virtual spectral type of Kamo'oalewa. Our model gives a size of 68 m x 46 m x 39 m, a rotation period of 27.66 minutes, and a pole orientation of 134.7 degrees longitude and -11.4 degrees latitude for Kamo'oalewa. Regolith grains with a size <2 cm can remain stable over 93.8% of the global surface area of Kamo'oalewa. Laser-irradiated LL chondrite powder shows a low thermal inertia (95.5 to 135.1 J m^-2 K^-1 s^-1/2), corresponding to a thermal skin depth of 3 to 3.5 mm on Kamo'oalewa. An SMFe0 content of 0.29 +- 0.05 wt.% is required to match Kamo'oalewa's spectrum. The virtual spectral type of Kamo'oalewa is given as "Sqw".

astro-ph.EP↗
arXiv2026

Computing Saddle Points in Stiff Problems via a Preconditioned High-index Saddle Dynamics Method

High-index saddle dynamics (HiSD) is an effective approach for computing saddle points of a prescribed Morse index and constructing solution landscapes for complex nonlinear systems. However, for problems with ill-conditioned Hessians arising from fine discretizations or stiff potentials, the efficiency of standard HiSD deteriorates as its convergence rate worsens with the spectral condition number $\kappa$. To address this issue, we propose a preconditioned HiSD (p-HiSD) framework that reformulates the continuous dynamics within a Riemannian metric induced by a symmetric positive definite preconditioner $M$. By generalizing orthogonal reflections and unstable-subspace tracking to the $M$-inner product, the proposed scheme modifies the geometry of the saddle-search dynamics while remaining computationally efficient. Rigorous theoretical analysis confirms that the equilibria and their Morse indices are invariant under this metric. Furthermore, we establish the local exponential stability of the continuous dynamics and prove a discrete linear convergence rate governed by the preconditioned condition number $\kappa_M$. Consequently, the iteration complexity is sharply reduced from $O(\kappa\log(1/\epsilon))$ to $O(\kappa_M\log(1/\epsilon))$. We validate the method on nine numerical tests spanning finite-dimensional model problems, stiff lattice systems, and PDE discretizations. The results demonstrate that p-HiSD resolves stiffness-induced convergence failures, permits substantially larger step sizes, and significantly reduces iteration counts.

math.NA↗
arXiv2026

TED: Training-Free Experience Distillation for Multimodal Reasoning

Knowledge distillation is typically realized by transferring a teacher model's knowledge into a student's parameters through supervised or reinforcement-based optimization. While effective, such approaches require repeated parameter updates and large-scale training data, limiting their applicability in resource-constrained environments. In this work, we propose TED, a training-free, context-based distillation framework that shifts the update target of distillation from model parameters to an in-context experience injected into the student's prompt. For each input, the student generates multiple reasoning trajectories, while a teacher independently produces its own solution. The teacher then compares the student trajectories with its reasoning and the ground-truth answer, extracting generalized experiences that capture effective reasoning patterns. These experiences are continuously refined and updated over time. A key challenge of context-based distillation is unbounded experience growth and noise accumulation. TED addresses this with an experience compression mechanism that tracks usage statistics and selectively merges, rewrites, or removes low-utility experiences. Experiments on multimodal reasoning benchmarks MathVision and VisualPuzzles show that TED consistently improves performance. On MathVision, TED raises the performance of Qwen3-VL-8B from 0.627 to 0.702, and on VisualPuzzles from 0.517 to 0.561 with just 100 training samples. Under this low-data, no-update setting, TED achieves performance competitive with fully trained parameter-based distillation while reducing training cost by over 5x, demonstrating that meaningful knowledge transfer can be achieved through contextual experience.

cs.LG↗
arXiv2026

High-Throughput In-Situ Fabrication of Fibrous Membranes Enables Scalable Passive Radiative Cooling

Deploying fibrous membranes for passive daytime radiative cooling (PDRC) on large and irregular surfaces is highly desirable but remains challenging, owing to the slow deposition rates and the need for electrically conductive substrates in conventional electrospinning. Here, we demonstrate a high-throughput in-situ strategy for fabricating nanocomposite PDRC fibrous membranes via solution blow spinning. This method achieves deposition rates 8-12 times faster than electrospinning and can be applied directly onto nonplanar, nonconductive objects. The resulting membranes, composed of styrene-ethylene-butylene-styrene (SEBS) fibers embedded with Y2O3 nanoparticles, achieve sub-ambient cooling of up to 7.0 {\deg}C outdoors, effectively delaying ice melting. Moreover, they are fully recyclable through simple cleaning, dissolution, and reprocessing. This scalable and sustainable fabrication route provides a versatile and practical platform for integrating PDRC fibrous membranes across diverse surfaces, paving the way toward real-world thermal management applications.

physics.optics↗
arXiv2026

SaddleScape V1.0: A Python Package for Constructing Solution Landscapes via High-index Saddle Dynamics

We present SaddleScape V1.0, a Python software package designed for the exploration and construction of solution landscapes in complex systems. The package implements the High-index Saddle Dynamics (HiSD) framework and its variants, including the Generalized HiSD for non-gradient systems and the Accelerated HiSD. SaddleScape V1.0 enables the systematic identification of critical points, including both local minima and high-index saddle points, by dynamically updating both the state estimate and an associated subspace characterizing the saddle's local manifold. It supports both gradient systems, defined by energy functions/functionals, and general non-gradient autonomous dynamical systems. Key features include automatic differentiation for symbolic inputs, numerical approximation techniques for Hessian-vector products, diverse eigenvalue solvers, and algorithms for constructing solution landscapes. The software offers a user-friendly interface with flexible parameter configuration, tools for trajectory and landscape visualization, and data export capabilities. By providing an efficient and accessible implementation of advanced saddle dynamics, SaddleScape V1.0 facilitates the construction of solution landscapes, empowering researchers in various scientific disciplines to gain deeper insights into the hierarchical structure of complex systems. The source code is available at the repository https://github.com/HiSDpackage/saddlescape. The package's introductory website is available at https://hisdpackage.github.io/saddlescape.

math.NA↗
arXiv2025

MAD-NG: Meta-Auto-Decoder Neural Galerkin Method for Solving Parametric Partial Differential Equations

Parametric partial differential equations (PDEs) are fundamental for modeling a wide range of physical and engineering systems influenced by uncertain or varying parameters. Traditional neural network-based solvers, such as Physics-Informed Neural Networks (PINNs) and Deep Galerkin Methods, often face challenges in generalization and long-time prediction efficiency due to their dependence on full space-time approximations. To address these issues, we propose a novel and scalable framework that significantly enhances the Neural Galerkin Method (NGM) by incorporating the Meta-Auto-Decoder (MAD) paradigm. Our approach leverages space-time decoupling to enable more stable and efficient time integration, while meta-learning-driven adaptation allows rapid generalization to unseen parameter configurations with minimal retraining. Furthermore, randomized sparse updates effectively reduce computational costs without compromising accuracy. Together, these advancements enable our method to achieve physically consistent, long-horizon predictions for complex parameterized evolution equations with significantly lower computational overhead. Numerical experiments on benchmark problems demonstrate that our methods performs comparatively well in terms of accuracy, robustness, and adaptability.

cs.LG↗
arXiv2025

Permutation-Equivariant Learning for Dynamic Security Assessment of Power System Frequency Response

This paper presents a hybrid model-AI framework for real-time dynamic security assessment of frequency stability in power systems. The proposed method rapidly estimates key frequency parameters under a dynamic set of disturbances, which are continuously updated based on operating conditions and unit commitment. To achieve this, the framework builds on a modal-based formulation of the system frequency response (SFR), which leverages the system's eigenstructure to predict key frequency stability metrics. A Deep Sets-inspired neural network is employed to estimate the complex modal coefficients required by the modal-based SFR approach, formulated as a permutation-equivariant learning problem. This enables fast and accurate prediction of the frequency nadir and its timing across different operating conditions and disturbances. The framework achieves scalability by reusing precomputed modal structures and updating only the disturbance-specific coefficients. It demonstrates strong generalization capabilities without requiring an extensive set of operating scenarios during training or the widespread deployment of phasor measurement units (PMUs). The method is validated on the IEEE 39-bus and 118-bus systems, showing superior accuracy, robustness, and computational efficiency compared to purely data-driven approaches.

eess.SY↗