arXiv subjects

Zhimin Zhang

Publications and source records attributed to Zhimin Zhang.

At least 19 recordsLinked to original sources

arXiv2026

PaddleMaterials: An End-to-End Deep Learning Toolkit for Materials Science

Machine learning supports materials design, atomistic simulation and experimental characterization, yet models and workflows remain fragmented. We present PaddleMaterials, an open-source framework integrating heterogeneous materials-learning tasks while preserving task-specific representations and scientific semantics. It unifies data processing, training, evaluation, pretrained-model management and workflows across six task classes: property prediction, structure generation, machine-learning interatomic potentials, electronic-structure fields, spectrum elucidation and microscopy image processing. Task interfaces record physical quantities, units, aggregation conventions and references, making cross-task composition verifiable. A shared compiler backend enables switching from dynamic-graph to compiled execution through one setting, using graph optimization, operator fusion and hardware-targeted code generation without changing model definitions. Across 65 model instances in 11 groups, compiled execution accelerated every instance in eight groups, with group median speedups of 11%-224% and group maximum speedups of 11%-336%. Case studies on LiMnO2 and toluene link structure generation or spectrum elucidation, interatomic-potential relaxation, property prediction and electron-density prediction, using same-geometry density functional theory (DFT) calculations as references. For LiMnO2, predicted formation energies for generated and relaxed structures differed from same-geometry PBE+U references by at most 7 meV per atom, while the computational cost of model steps was less than one-twentieth of a DFT single-point calculation. PaddleMaterials extends unified materials workflows beyond conventional property, potential and structure-generation tasks while supporting verifiable cross-task operations and compiled execution.

cs.LG↗

arXiv2026

A recovery based linear finite element method for the Monge--Ampère equation

In this paper, we study finite element approximations of a fourth-order perturbed semilinear partial differential equation that arises naturally in the computation of viscosity solutions to the fully nonlinear Monge--Ampère equation. We develop a novel recovery-based $C^0$ linear finite element method for discretizing this model problem. The key analytical tool is a Miranda--Talenti-type estimate for the recovery operator, which guides the formulation of the discrete scheme and guarantees its well-posedness. We rigorously establish convergence in the $H^2$ norm by employing a fixed-point argument. Furthermore, optimal $H^1$-error estimates are derived using a duality argument. Numerical experiments confirm the efficiency of the proposed method and validate the theoretical convergence results.

math.NA↗

arXiv2026

HierGF: Hierarchical Gaussian Fields via Geometry-perception Message Passing for Sparse-view 3D Reconstruction

Sparse view 3D reconstruction is an important and common scenario in multimedia applications, such as augmented reality/virtual reality (AR/VR) content creation, cultural heritage digitization, and certain robotic applications, where only a limited number of randomly captured views may be available. However, sparse views contain only limited 3D information, posing two major challenges:1) too few images are available for matching, making it difficult to build multi-view consistency; 2) insufficient view coverage leads to a lack of information in under-sampled regions, resulting in missing parts of object structure. Existing methods mostly still rely on limited reprojection errors and regularization terms, which are prone to overfitting to a single view and inconsistent appearances across views. In geometrically under-sampled regions, they often rely on heuristic density control, lacking reliable guidance and often resulting in blurring and structural holes.To address these issues, this paper proposes Hierarchical Gaussian Fields (HierGF), which revisits sparse-view reconstruction from a hierarchical geometry-perception perspective and converts limited observations into reliable self-generated supervision beyond fixed priors and heuristic density control. In particular, we transform coarse 3D geometric information and additional 2D generative priors into structured pseudo-supervision through a two-stage geometry-perception backbone network, thereby enhancing multi-view consistency with very few input views. In addition, we introduce a learnable confidence network to guide gradients toward cross-view consistent content, and a geometrically consistent densification module to improve the reconstruction of multi-view alignment and under-sampled regions.

cs.CV↗

arXiv2026

Natural superconvergence points for splines

This paper develops a unified theory of natural superconvergence points for polynomial spline approximations to second-order elliptic problems. Beginning with the one-dimensional case, we establish that when a point $x_0$ is a local symmetric center of the partition, the numerical error $(u-u_h)^{(s)}(x_0)$ exhibits superconvergence whenever the polynomial degree $k$ and the derivative order $s$ share the same parity. In particular, for the smoothest spline (B-spline) solution, the abundance of superconvergence points allows us to construct asymptotic expansion of the error within the element that fully characterize all superconvergence points, for both function values and derivatives. The theoretical framework is then extended to higher-dimensional settings on simplicial and tensor-product meshes, and the essential conclusions are preserved, with one-dimensional derivatives generalized to mixed derivatives. Numerical experiments demonstrate that superconvergence persists even in extremely localized symmetric regions, revealing that superconvergence points are both readily attainable and follow systematic distribution patterns.

math.NA↗

arXiv2026

Natural superconvergence points and asymptotic expansions for spline finite elements in one dimension

We study the natural superconvergence points and asymptotic expansions of one-dimensional spline finite element approximations. For a spline space of degree $k$ and any smoothness $0\leμ\le k-1$, we prove that the $s$-th derivative of the error exhibits enhanced convergence of order $O(h^{k+2-s})$ at points where $k-s$ is even, provided the mesh is symmetric within a region of size $Ch|\ln h|$ around the point. This condition is known to be optimal for the cases of low derivative order $s=0,1$; the present analysis shows that the same local condition is sufficient for all admissible $s$. Moreover, by expanding the error in Legendre polynomials, a closure theorem determines the leading-order Legendre coefficients (the asymptotic expansion of the error) by combining the Galerkin orthogonality with the superconvergence conditions. For $μ=k-1$ (B-splines) and $μ=k-2$, the Galerkin orthogonality conditions vanish and the coefficients are determined solely by the superconvergence conditions. The asymptotic expansion can be expressed through a simple antiderivative recurrence on Legendre polynomials. The resulting polynomial's zeros encode the complete set of superconvergence points for all derivative orders. Numerical experiments for selected $(k,μ)$ pairs confirm the theoretical predictions.

math.NA↗

arXiv2026

Superconvergence points of Hermite spectral interpolation

Hermite spectral method plays an important role in the numerical simulation of various partial differential equations (PDEs) on unbounded domains. In this work, we study the superconvergence properties of Hermite spectral interpolation, i.e., interpolation at the zeros of Hermite polynomials in the space spanned by Hermite functions. We identify the points at which the convergence rates of the first- and second-order derivatives of the interpolant converge faster. We further extend the analysis to the Hermite spectral collocation method in solving differential equations and identify the superconvergence points both for function and derivative values. Numerical examples are provided to confirm the analysis of superconvergence points.

math.NA↗

arXiv2026

Motion Beyond Morphology: Bootstrapping Cross-Category Motion Transfer from Abstract Motion Representations

Video motion transfer aims to animate a target object using dynamics from a reference video. Existing formulations largely rely on fixed structural correspondence, which becomes ill-defined when reference and target objects differ substantially in morphology, articulation, or deformation mechanisms. We introduce Motion Beyond Morphology, a perspective that seeks to transfer motion beyond fixed structural correspondence, by preserving dynamics that remain meaningful across different target morphologies. To realize this, we propose a two-stage framework. Stage~I learns complementary multi-granularity abstract motion views and uses them to bootstrap cross-category video pairs that preserve transferable dynamics across diverse morphologies. Stage~II internalizes this supervision into direct reference-video-conditioned generation, removing the need for explicit motion extraction at inference. We further introduce OpenVMT-Dataset and OpenVMT-Bench for training and evaluating image- and text-conditioned motion transfer across Same, Near, and Far category gaps. Extensive experiments demonstrate state-of-the-art motion fidelity and target preservation. Project page: https://miniz233.github.io/MotionBeyondMorphology/

cs.CV↗

arXiv2026

Artificial Intelligence and Innovation Ecosystem: Evolutionary Developments, Challenges, and Future Directions

The development of the Innovative Ecosystem (IE) presents a new paradigm for economic integration, collaborative advancement, and shared achievements. The rise of Artificial Intelligence (AI) has significantly accelerated the global processes of digitization, informatization, and intelligence. Exploring how AI can leverage inherent characteristics to influence the development trajectory of IE is a topic that warrants further investigation. Given AI's increasing prominence and role within IE, the paper analyzes this new form, examining both AI's unique contributions to IE and its potential challenges. Firstly, the paper synthesizes the conceptual frameworks surrounding IE, decomposing them into manifestations in physical, social, and thinking spaces. Furthermore, the concept of Artificial Intelligence IE (AIIE) is introduced from a spatial perspective, with an exploration of the characteristics AI contributes to IE. Subsequently, the paper employs an evolutionary perspective to analyze the roles provided by AI during different development periods of AIIE. The paper then verifies the feasibility, effectiveness, and rationality of the AIIE's definition and analyzes AIIE development from an evolutionary perspective using enterprise development examples. Finally, acknowledging AI's inherent limitations, the paper examines potential challenges facing AIIE in the future from four perspectives, aiming to identify new research avenues for the further development of AIIE.

cs.AI↗

arXiv2026

OmniDirector: General Multi-Shot Camera Cloning without Cross-Paired Data

Cloning camera motion from reference videos is an important task in video generation, as videos provide intuitive and precise control. Existing methods either directly use parametric representations that fail to handle multi-shot generation or synthesize cross-paired data, which suffer from data scarcity, resulting in poor performance in complicated camera motion cloning. To address these issues, we introduce a general camera motion representation that encodes cameras as grid motion videos. This camera grid represents the camera parameters visually and supports the integration of diverse trajectories for multi-shot video generation. Building upon this, we propose OmniDirector, a unified framework trained on a million-scale camera grid-video pairs that coordinates characters, actions, and cameras to provide director-level control for multimodal diffusion transformers. Furthermore, we design a novel hierarchical prompt expansion agent that harmoniously integrates different control signals by systematically describing camera motion and visual content through understanding signal relationships. Extensive experiments demonstrate the superior performance and outstanding controllability of our framework. Project page: https://ymlinfeng.github.io/OmniDirector.github.io/

cs.CV↗

arXiv2026

A Decoupled Low-Order Conforming Mixed Finite Element Method for a Three-Dimensional Fourth-Order Singularly Perturbed Problem

This paper develops a decoupled low-order conforming finite element method for a fourth-order elliptic singular perturbation problem in three dimensions. By means of a generalized Helmholtz decomposition, the problem is reduced to two second-order elliptic problems and a system of generalized singularly perturbed Stokes-type equations subject to a curl-free constraint. The former are discretized by standard linear finite elements. For the latter, we employ the MINI element and show that, after adding an $L^2$ term involving a Lagrange multiplier, the resulting discretization becomes robust with respect to the perturbation parameter. We further establish an error estimate of order $h^{1/2}$ uniform with respect to the perturbation parameter. Numerical experiments are included to support the theory.

math.NA↗

arXiv2026

Optimal convergence of local discontinuous Galerkin methods for convection-diffusion equations

The $hp$ local discontinuous Galerkin (LDG) method proposed by Castillo et al. [Math. Comp.,~71 (238): 455-478, 2002] has been shown to be an efficient approach for solving convection-diffusion equations. However, theoretical analysis indicates that, for solutions with limited spatial regularity, the method exhibits suboptimal convergence in $p$, suffering a loss of one order, comparing to numerical experiments. The purpose of this paper is to close the gap between theoretical estimates and numerical evidence. This is accomplished by establishing new approximation results for the associated Gauss-Radau projections of functions in suitable function spaces that can optimally characterize the regularity of singular solutions. We show that such a framework arises aturally and enables the study of various types of singular solutions, with full consistency between theoretical analysis and numerical results. This investigation sheds light on the resolution of the suboptimality in $p$ observed in the literature for several other types of DG schemes in different settings.

math.NA↗

arXiv2026

Element-based B-spline basis function spaces: construction and application in isogeometric analysis

This paper develops a unified theoretical framework for constructing B-spline basis function spaces with structural equivalence to finite element spaces. The theory rigorously establishes that these bases emerge as explicit linear combinations of B-spline element bases. For any prescribed smoothness requirements, this element-wise formulation enables the Hermite interpolation at nodes, which directly utilizes function values and derivatives without solving global linear systems. By focusing on explicit interpolation properties, element-wise analysis establishes optimal approximation errors, even when the space smoothness attains its theoretical maximum for the space degree. In isogeometric analysis (IgA), the construction naturally decomposes geometric mappings into element-level representations, allowing efficient computations across elements regardless of node distribution. Notably, the same Hermite interpolation framework simultaneously handles domain parameterization and IgA solutions, allowing direct imposition of boundary conditions through function and derivative matching. Numerical tests demonstrate optimal convergence rates and superconvergence properties in 2D IgA under uniform knot configurations, and improved computational efficiency in 3D IgA with non-uniform knot distributions.

math.NA↗

arXiv2025

Novel superconvergence and ultraconvergence structures for the finite volume element method

This paper develops novel natural superconvergence and ultraconvergence structures for the bi-$k$-order finite volume element (FVE) method on rectangular meshes. These structures furnish tunable and possibly asymmetric superconvergence and ultraconvergence points. We achieve one-order-higher superconvergence for both derivatives and function values, and two-orders-higher ultraconvergence for derivatives--a phenomenon that standard bi-$k$-order finite elements do not exhibit. Derivative ultraconvergence requires three conditions: a diagonal diffusion tensor, zero convection coefficients, and the FVE scheme satisfying tensorial $k$-$k$-order orthogonality (imposed via dual mesh constraints). This two-dimensional derivative ultraconvergence is not a trivial tensor-product extension of the one-dimensional phenomena; its analysis is also considerably more complex due to directional coupling. Theoretically, we introduce the asymmetric-enabled M-decompositions (AMD-Super and AMD-Ultra) to rigorously prove these phenomena. Numerical experiments confirm the theory.

math.NA↗

arXiv2025

Polynomial preserving recovery for PHT-splines

We propose a polynomial preserving recovery method for PHT-splines within isogeometric analysis to obtain more accurate gradient approximations. The method fully exploits the local interpolation properties of PHT-splines and avoids the need for information on gradient superconvergent points. By leveraging the superconvergence argument of difference quotients and the interior error estimate, we establish the superconvergence property of the recovered gradient on translation invariant meshes. As a byproduct, a recovery-based a posteriori error estimator is developed for adaptive refinement. Numerical results confirm the theoretical findings and demonstrate the effectiveness of the proposed method.

math.NA↗

arXiv2025

Behave Your Motion: Habit-preserved Cross-category Animal Motion Transfer

Animal motion embodies species-specific behavioral habits, making the transfer of motion across categories a critical yet complex task for applications in animation and virtual reality. Existing motion transfer methods, primarily focused on human motion, emphasize skeletal alignment (motion retargeting) or stylistic consistency (motion style transfer), often neglecting the preservation of distinct habitual behaviors in animals. To bridge this gap, we propose a novel habit-preserved motion transfer framework for cross-category animal motion. Built upon a generative framework, our model introduces a habit-preservation module with category-specific habit encoder, allowing it to learn motion priors that capture distinctive habitual characteristics. Furthermore, we integrate a large language model (LLM) to facilitate the motion transfer to previously unobserved species. To evaluate the effectiveness of our approach, we introduce the DeformingThings4D-skl dataset, a quadruped dataset with skeletal bindings, and conduct extensive experiments and quantitative analyses, which validate the superiority of our proposed model.

cs.CV↗

arXiv2025

Monolayer Two-dimensional Materials Database (ML2DDB) and Applications

The discovery of two-dimensional (2D) materials with tailored properties is critical to meet the increasing demands of high-performance applications across flexible electronics, optoelectronics, catalysis, and energy storage. However, current 2D material databases are constrained by limited scale and compositional diversity. In this study, we introduce a scalable active learning workflow that integrates deep neural networks with density functional theory (DFT) calculations to efficiently explore a vast set of candidate structures. These structures are generated through physics-informed elemental substitution strategies, enabling broad and systematic discovery of stable 2D materials. Through six iterative screening cycles, we established the creation of the Monolayer 2D Materials Database (ML2DDB), which contains 242,546 DFT-validated stable structures-an order-of-magnitude increase over the largest known 2D materials databases. In particular, the number of ternary and quaternary compounds showed the most significant increase. Combining this database with a generative diffusion model, we demonstrated effective structure generation under specified chemistry and symmetry constraints. This work accomplished an organically interconnected loop of 2D material data expansion and application, which provides a new paradigm for the discovery of new materials.

cond-mat.mtrl-sci↗

arXiv2025

Fast Maxwell Solvers Based on Exact Discrete Eigen-Decompositions I. Two-Dimensional Case

In this paper, we propose fast solvers for Maxwell's equations in rectangular domains. We first discretize the simplified Maxwell's eigenvalue problems by employing the lowest-order rectangular Nédélec elements and derive the discrete eigen-solutions explicitly, providing a Hodge-Helmholtz decomposition framework at the discrete level. Based on exact eigen-decompositions, we further design fast solvers for various Maxwell's source problems, guaranteeing either the divergence-free constraint or the Gauss's law at the discrete level. With the help of fast sine/cosine transforms, the computational time grows asymptotically as $\mathcal{O}(n^2\log n)$ with $n$ being the number of grids in each direction. Our fast Maxwell solvers outperform other existing Maxwell solvers in the literature and fully rival fast scalar Poisson/Helmholtz solvers based on trigonometric transforms in either efficiency, robustness, or storage complexity. It is also utilized to perform an efficient pre-conditioning for solving Maxwell's source problems with variable coefficients. Finally, numerical experiments are carried out to illustrate the effectiveness and efficiency of the proposed fast solver.

math.NA↗

arXiv2025

Spectral Method for 1-D Neutron Transport Equation

In this paper, we present an efficient fully spectral approximation scheme for exploring the one-dimensional steady-state neutron transport equation. Our methodology integrates the spectral-(Petrov-)Galerkin scheme in the spatial dimension with the Legendre-Gauss collocation scheme in the directional dimension. The directional integral in the original problem is discretized with Legendre-Gauss quadrature. We furnish a rigorous proof of the solvability of this scheme and, to our best knowledge, conduct a comprehensive error analysis for the first time. Notably, the order of convergence is optimal in the directional dimension, while in the spatial dimension, it is suboptimal and, importantly, non-improvable. Finally, we verify the computational efficiency and error characteristics of the scheme through several numerical examples.

math.NA↗