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Jin Zhao

Publications and source records attributed to Jin Zhao.

At least 19 recordsLinked to original sources
arXiv2026

Quadrature Perturbations and High-Order Time Discretization for Prescribed-Feature Evolutionary GTransNet Galerkin Systems

In this paper we study quadrature perturbations and high-order time discretization for a prescribed-feature evolutionary generalized transferable neural network (Evo-GTransNet) Galerkin method for linear self-adjoint parabolic equations. Assembly quadrature, together with truncated singular value decomposition, is used to select a numerically resolved trial space and obtain coordinates with an identity mass matrix. Since this normalization depends on the assembly quadrature, the retained functions are also evaluated using a separate comparison quadrature, which is finer in the numerical experiments. For the two resulting semidiscrete systems, we derive an exact equation for the difference between their trajectories and an energy estimate that separates errors arising from the effective operator, load vector, and initial projection. The estimate is conditional on the trial space selected by the assembly quadrature. The retained rank, discarded mass, cross mass, and principal angles are used to assess this selection step. Refining the comparison quadrature yields stable retained spaces for the reported configurations, whereas deliberate underintegration leads to much larger perturbations. On the fixed retained systems, the temporal convergence of implicit midpoint, BDF, Radau IIA, and Gauss--Legendre methods is consistent with their classical orders over the resolved refinement ranges. The experiments distinguish the retained-coordinate error from the total solution error; the latter is measured against the PDE solution in the $L^2$ norm, with the error integrals evaluated by sufficiently fine quadrature. They also illustrate the importance of suitable starting values for BDF3 and show how the performance of IMEX-BDF schemes depends on the operator splitting and time step size.

math.NA↗
arXiv2026

Fast and Memory Efficient Offload Training Framework with Hybrid XPU Computation

With the ever-growing size of deep learning models, GPU memory is prone to being insufficient during training. A prominent approach is ZeRO-Offload, which moves the optimizer states to CPU memory and performs parameter update using CPU. However, the deficiencies of ZeRO-Offload include low GPU utilization, imperfect overlapping of communication and computation, and inflexible offloading. In this paper, we leverage Direct Host Access (DHA) on the GPU that can compute data in CPU memory, forming a novel hybrid on-GPU and DHA. We design and implement MemFerry consisting of an execution scheduler and a shadow model. The scheduler strategically chooses layers of parameters for DHA computation and transmits the remaining parameters to GPU memory simultaneously to shorten forward propagation time, and further loads DHA parameters to GPU memory to reduce backward propagation time. The shadow model presents a unified memory abstraction for the parameter partitions stored separately in GPU and CPU memories. To further reduce GPU memory usage, we present MemFerry along with its dynamic programming algorithm that offloads gradients to CPU memory via DHA. We further extend MemFerry to emerging scale-up domains with ScaleUp-MemFerry, which exploits otherwise underutilized accelerator interconnect bandwidth to assist host-to-accelerator data movement through adaptive multi-path transfer. Our experiments show that \system trains up to $1.68\times$ faster and MemFerry can train $1.52\times$ larger model compared to ZeRO-Offload on a single GPU, and increase training speed by at least $28.1\%$ when scaling to data parallelism on 8 GPUs. We further extend the design to a Huawei CloudMatrix384 scale-Up node with up to 8 NPUs, and our ScaleUp-MemFerry reduces the end-to-end iteration time by up to $20.7\%$ over DeepSpeed.

cs.DC↗
arXiv2026

Descent--Ascent Structure of Uniform Nondegeneracy

Classical models such as smooth strongly convex minimization and strongly convex--strongly concave optimization combine two types of curvature information: curvature remains uniformly separated from zero, and its positive and negative orientations are prescribed in advance. Uniform nondegeneracy disentangles these roles, retaining the separation from zero while allowing the curvature orientation to vary across the domain. We identify a family of descent--ascent inequalities (DAI) that characterizes uniform nondegeneracy and naturally gives rise to Alternating Descent Ascent (ADA), a simple explicit method that alternates full-gradient descent and ascent. ADA converges globally and linearly to the unique stationary point from arbitrary initialization, with dimension-free first-order complexity. The framework recovers the smooth strongly convex setting as a limit and encompasses the strongly convex--strongly concave and linearly constrained settings, highlighting uniform nondegeneracy as a common first-order structure across various classical regimes.

math.OC↗
arXiv2026

Restoring without Forgetting: Filter-Level Continual Image Restoration via Parameter-Space Integrated Gradients

Adapting image restoration models to a stream of new tasks without revisiting past data remains challenging due to catastrophic forgetting. In this work, we propose Restoring without Forgetting (RwF), a filter-level continual adaptation framework for image restoration built upon a critical observation: task-specific knowledge is centered in a small subset of filters and can be separated from those reconstructing general content. RwF first performs parameter-space integrated gradients attribution to localize degradation-critical filters in a coarse-to-fine manner. It then adapts to new tasks by generating task-specific filters from a filter bank using compact factorized low-rank transformations, further augmented with cross-task attention and prototypical contrastive learning, and lastly assembles them back only at localized positions. Experiments on six restoration tasks show that RwF effectively avoids forgetting and achieves competitive restoration quality against all-in-one methods that have full data access, and outperforms LoRA-style adaptation with $\sim$10$\times$ fewer additional parameters. Code is available at https://github.com/funkdub/Restoring-without-Forgetting.

cs.CV↗
arXiv2026

A Lattice Boltzmann Method with Adaptive Relaxation Parameter and Lax--Friedrichs-Type Equilibrium for Hyperbolic Systems

In this paper, a lattice Boltzmann method with an adaptive relaxation parameter and a Lax--Friedrichs-type equilibrium is proposed for hyperbolic systems with source terms. The equilibrium distribution recovers the conservative variables and physical fluxes while incorporating dissipation determined by characteristic-speed bounds. To balance accuracy and robustness, the relaxation parameter is selected from a local smoothness indicator based on characteristic projections. In smooth regions, the parameter approaches the low-dissipation limit, retaining second-order accuracy; near discontinuities, it is automatically reduced to introduce localized dissipation and suppress nonphysical oscillations. The stabilization acts directly through the local collision step and preserves the standard collide-and-stream structure, without a posteriori recomputation or interface-based limiting. Maxwell iteration establishes second-order consistency in smooth regions, and a weighted $L^2$-stability estimate is proved for linear hyperbolic systems with periodic boundary conditions under a standard CFL condition. Numerical experiments for scalar advection, Euler, shallow-water, and reactive Euler equations demonstrate the expected accuracy for smooth solutions and robust resolution of challenging one- and two-dimensional discontinuous problems, including wet--dry fronts and reactive discontinuities. A large-scale simulation of a 2D cellular detonation further demonstrates the capability of the method to resolve long-time multidimensional shock--reaction interactions.

math.NA↗
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

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

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

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 $κ$. 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 $κ_M$. Consequently, the iteration complexity is sharply reduced from $O(κ\log(1/ε))$ to $O(κ_M\log(1/ε))$. 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

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

Amoeba: Runtime Tensor Parallel Transformation for LLM Inference Services

In Large Language Model (LLM) inference services, it is challenging to make a parallelism strategy configuration, to efficiently process the requests of variance context lengths. Requests of long context require high degree of parallelism to provide more memory for Key-Value (KV) Cache, while requests of short context prefer low degree of parallelism to increase concurrency, thus improving throughput. To maintain high throughput while supporting large context lengths on demand, we propose Amoeba, a runtime Tensor Parallel (TP) transformation for online LLM inference services, which adaptively adjusts the TP of running instances to align with the dynamics of incoming requests. Evaluations using real-world traces show that Amoeba improves throughput by 1.75x-6.57x compared to state-of-the-art solutions.

cs.DC↗
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↗