arXiv subjects

Xiaoying Zhuang

Publications and source records attributed to Xiaoying Zhuang.

At least 19 recordsLinked to original sources

arXiv2026

Mechanism-resolved phase-field fracture of composite shells with a certified admissible constitutive operator

Phase-field models of fracture in fibre-reinforced shells are usually formulated against a single closed-form stored energy, so that the stress, consistent tangent and plane-stress condensation are derived and verified for that expression alone. Here the constitutive law enters instead as a replaceable operator. The Green-Lagrange strain of a geometrically exact Reissner-Mindlin shell is pulled back through the Cholesky factor of the reference metric and resolved on four mutually orthogonal invariants with an exact closure identity, making the separation into fibre, inter-fibre and interaction channels a change of basis rather than a modelling assumption. On a curved midsurface, the metric, Cholesky factor and fibre direction vary through the thickness through the shifter I - zeta b, and the invariants inherit that dependence. The tension-compression split, channel degradation, plane-stress condensation, consistent tangent and finite-element assembly are all expressed in the channel potentials and their derivatives, allowing either closed-form or learned operators. The fibre-transverse interaction energy is stored once and degraded by the product of the fields whose mechanisms it couples. Six conditions define admissible operators; the two linear invariants are proved convex in the deformation gradient, the geometric tangent is shown independent of the material tangent, and the plane-stress condensation is regular wherever the residual stiffness is positive. A three-tier protocol certifies the algebra, solver state and admission of a state as training data. Numerical studies on notched IM7/8552 shells verify the discretisation in thin and curved regimes and show that fibre orientation governs the damage envelope and load capacity, while curvature drives a through-thickness fracture asymmetry that a single midsurface field cannot represent.

physics.comp-ph↗

arXiv2026

Constitutive-Set Mechanics: variational mechanics on an admissible set of constitutive laws

A structural simulation needs a constitutive law, and experiments rarely determine one uniquely: several laws may fit the same data and satisfy the same physical constraints, yet differ where the structure is loaded in ways the tests never were. Constitutive-Set Mechanics (CSM) keeps all of those laws. It replaces the single law in the variational formulation by the admissible set, and lets the mechanics itself decide which members of the set affect the structural prediction. The framework rests on one observation: a finite element assembly consults the law only at the strains the structure reaches, so the incremental energy depends on the law through a weighted record of those strains, the occupation measure of the state. The energy of a state under the set is a support function on that measure, and the equilibrium solve one performs anyway supplies the information needed to bound the worst case. Equilibrium states become certificates on the robust response, rigorous on the upper side for any mechanics solver and two-sided under global minimisation; the certificate has at most one more state than the number of constitutive directions the structure interrogates; a coherence theorem identifies when the pointwise-worst material is one no single material can be; and constitutive inference acts on the same support function. The method is demonstrated on linear elasticity, a data-constrained constitutive function, phase-field fracture, an assembled finite-strain composite shell, and a membrane characterised by one-mode tests alone. On the shell the structure interrogates four of 226 constitutive directions; on the membrane the certified worst-case energy exceeds the reference more than fourfold, and the experiment that most contracts the certified prediction is not the one where the constitutive uncertainty is largest.

physics.comp-ph↗

arXiv2026

The role of weak interfaces in the tensile deformation and fracture of particle-filled polymers studied by phase-field model

Weak particle-matrix interfaces play a critical role in the tensile fracture of particle-filled polymer composites, but how they govern progressive debonding, fracture localization, and the resulting changes in macroscopic mechanical properties remains insufficiently understood. In this study, a cohesive-zone phase-field model incorporating a hyperelastic polymer matrix and a smeared interface is employed to investigate the coupled evolution of interfacial debonding and matrix fracture in particle-filled polymer composites. The model is calibrated against and compared with uniaxial tensile responses of particle-filled polyurethane composites and then used to study how interfacial strength, interfacial fracture energy, and matrix fracture properties affect the macroscopic stress-strain response and damage evolution. The results show that weak interfaces can induce an intermediate softening regime in the stress-strain response, characterized by a reduced effective tangent stiffness and associated with distributed interfacial damage. Interfacial strength mainly controls the initiation of debonding, whereas interfacial fracture energy affects whether debonding can develop progressively in a distributed manner or rapidly localizes into a dominant crack band. Comparisons with well-bonded reference systems further demonstrate that weak interfaces may reduce the maximum stress but increase the strain at break by promoting distributed debonding around particles and delaying the formation of a dominant crack band. These findings clarify the dual role of weak interfaces and provide a mechanistic understanding of interface-controlled tensile failure in particle-filled polymer composites.

cond-mat.mtrl-sci↗

arXiv2026

Plasolver: Physics-Informed Neural Operators for Elastoplasticity

Elastoplastic analysis is computationally demanding because its nonlinear, path-dependent constitutive behavior requires incremental loading and repeated iterative solutions. To address this challenge, we propose Plasolver, a physics-informed neural operator framework that combines the efficiency of operator learning with the accuracy and robustness of classical numerical solvers. Plasolver consists of a physics-informed pretraining stage and an optional warm-start stage. During pretraining, the neural operator is trained solely by minimizing the incremental potential energy of elastoplasticity formulated by Simo, without requiring any labeled solution data. It operates directly on unstructured point clouds by encoding spatial coordinates, loading histories, and material properties as unified point-wise prompts. This formulation provides dual invariance to spatial and loading-path discretizations, enabling consistent predictions across different spatial resolutions and different numbers of increments representing the same loading trajectory. The pretrained Plasolver achieves relative errors on the order of 1\% while providing approximately two orders of magnitude acceleration over conventional finite element simulations. In the warm-start stage, the pretrained prediction is supplied as the initial solution to a classical iterative solver, preserving its numerical accuracy, robustness, and convergence properties while substantially accelerating convergence. Numerical results show that Plasolver reduces the required number of iterations by approximately 50\% compared with conventional zero-initialized solvers and converges to solutions at any prescribed tolerance. Plasolver thus provides an efficient, accurate, and discretization-invariant computational framework for nonlinear, path-dependent elastoplastic problems.

physics.comp-ph↗

arXiv2026

Neural Operators for Immersed-Boundary Soft Swimmers Locomotion

High-fidelity immersed-boundary simulation resolves the coupled motion of a deforming swimmer and its surrounding flow, but the resulting cost limits repeated evaluations for engineering design, parameter studies, and control. We develop neural-operator surrogates for temporal prediction of the hydrodynamic fields generated by planar and volumetric eel swimmers. The surrogates are trained on regular-grid fields exported from adaptive fluid--structure simulations and are conditioned on swimmer geometry and Reynolds number. The planar model jointly predicts two velocity components, scalar vorticity, and pressure. On five held-out high-Reynolds-number trajectories, its full-domain global relative L^2 error is 3.51 %. The volumetric formulation uses three target-specific models with a common multichannel input: one model predicts three-dimensional velocity, one predicts vorticity, and one predicts pressure. Their full-domain global relative L^2 errors on five held-out within-range trajectories are 3.44 %, 5.58 %, and 19.2 %. Together, the results demonstrate the feasibility of field-resolved neural surrogates for moving-boundary swimmer flows while identifying pressure accuracy and physical consistency as priorities for further development.

cs.LG↗

arXiv2026

FEVessel: Mesh-Independent Analysis of 3D Pressure Vessels with the Label-Free Pretrained Finite Element Method

Pressure vessel analysis in the chemical, nuclear, and new-energy industries requires solving the same elasticity problem across many materials, geometries, and loads, where mesh quality and repeated solving govern both accuracy and cost. The finite element method (FEM) cannot amortise this repeated cost and fails on degenerate meshes, while the neural operators meant to replace it still need labelled data that FEM must generate. This paper proposes FEVessel, an adaptation of the Pretrained Finite Element Method (PFEM) to three-dimensional (3D) pressure vessels, and validates four capabilities across the two limitations above. FEVessel i) encodes each vessel as a point cloud with coordinate, material, and load channels, ii) pretrains a Transolver operator on the total potential energy instead of FEM labels, and iii) warm-starts iterative solvers with its prediction. A single model generalises across material, geometry, and boundary conditions at a $1.35\%$ relative displacement error, and its $2.07\%$ strain error is about $4.7$ times lower than that of a supervised Fourier neural operator ($9.72\%$), whose structured grid cannot preserve the through-thickness strain. Its warm start cuts algebraic multigrid iterations from $195$ to $18$, a $9.2\times$ end-to-end wall-clock speedup at the $10^{-3}$ engineering tolerance. The model transfers across mesh resolutions without retraining, holding about $3\%$ error at only $30\%$ of the training point density. On inverted and sliver meshes where FEM fails, the error remains below $3.66\%$. To our knowledge, this is the first systematic study of mesh-independent solution on industrially relevant 3D pressure vessels with degenerate meshes. Because training needs no labels, FEVessel works exactly where FEM cannot supply any, removing manual mesh repair from the analysis pipeline.

math.NA↗

arXiv2026

GA-VINO: A Geometry-Aware Variational Physics-informed Neural Operator for Mindlin-Reissner Plates

Plate and shell structures are widely used in engineering fields. Rapid response prediction for such structures under complex geometries, heterogeneous materials, and varying loads is important for engineering design, but conventional numerical methods usually require repeated modeling and solution when the physical configuration changes. To address this issue, this study proposes a geometry-aware variational physics-informed neural operator (GA-VINO) for Mindlin-Reissner plates. GA-VINO represents the plate geometry using boundary point clouds and incorporates a material encoder, a load encoder, and a scalar-parameter branch to handle spatially random material fields, spatially varying pressure loads, and sample-level uniform parameters. Through multi-branch point cloud encoding and cross-attention, GA-VINO fuses geometric, material, loading, and query point information, and predicts the transverse deflection and rotations at arbitrary query locations. Unlike conventional data-driven neural operators, GA-VINO requires no labeled solution data during training. Instead, it minimizes a variational physics-informed loss constructed from the discretized total potential energy of the Mindlin-Reissner plate. Compared with grid-based neural operators, GA-VINO directly processes irregular point clouds and allows different physical fields to be discretized on different point sets, avoiding forced interpolation onto a common grid. The method is validated on multiple examples involving different geometries, material fields, and load distributions. The results show that GA-VINO achieves promising accuracy in deflection, rotation, gradient-sensitive, and energy-based metrics, completes full-field inference for new samples within milliseconds, and exhibits promising cross-geometry generalization capability.

cs.AI↗

arXiv2026

Dmsh: A Multi-Agent Reinforcement Learning Framework for All-Quad Mesh Generation

Generating high-quality meshes for arbitrary geometries remains a fundamental bottleneck in computational engineering, often demanding heuristic tuning and semi-manual workflows. In this paper, we introduce Dmsh, a first fully automated reinforcement learning pipeline that unifies geometric decomposition and quadrilateral mesh generation within a single learning-based framework. Dmsh decomposes the problem through three coordinated agents handling topology simplification, geometric regularization, and mesh generation. The meshing process is formulated as a Markov Decision Process and solved using a parametric Soft Actor-Critic architecture with decoupled critics, enabling efficient exploration of a hybrid discrete-continuous action space. A curriculum learning strategy ensures scalability from simple domains to highly complex geometries, suppressing seed variance. By design, the recursive decomposition enables parallel meshing of subregions, yielding globally conforming all-quadrilateral meshes without post hoc correction. Across a wide range of benchmarks, Dmsh consistently outperforms existing methods in automation, robustness, and mesh quality, establishing a new paradigm for learning-based mesh generation.

math.NA↗

arXiv2026

NOWS: Neural Operator Warm Starts for Accelerating Iterative Solvers

Partial differential equations (PDEs) underpin quantitative descriptions across the physical sciences and engineering, yet high-fidelity simulation remains a major computational bottleneck for many-query, real-time, and design tasks. Data-driven surrogates can be strikingly fast but are often unreliable when applied outside their training distribution. Here we introduce Neural Operator Warm Starts (NOWS), a hybrid strategy that harnesses learned solution operators to accelerate classical iterative solvers by producing high-quality initial guesses for Krylov methods such as conjugate gradient and GMRES. NOWS leaves existing discretizations and solver infrastructures intact, integrating seamlessly with finite-difference, finite-element, isogeometric analysis, finite volume method, etc. Across our benchmarks, the learned initialization consistently reduces iteration counts and end-to-end runtime, resulting in a reduction of the computational time of up to 90 %, while preserving the stability and convergence guarantees of the underlying numerical algorithms. By combining the rapid inference of neural operators with the rigor of traditional solvers, NOWS provides a practical and trustworthy approach to accelerate high-fidelity PDE simulations.

cs.LG↗

arXiv2026

Replay-Based Continual Learning for Physics-Informed Neural Operators

Neural operators generally demonstrate strong predictive performance on in-distribution (ID) problems. However, a critical limitation of existing methods is their significant performance degradation when encountering out-of-distribution (OOD) data. To address this issue, this work introduces continual learning into physics-informed neural operators, with particular emphasis on neural operators built upon the Transolver architecture, and proposes a simple yet effective replay-based continual learning strategy. The proposed method is fully physics-informed and does not require labeled data, relying solely on input fields together with physical constraints for training. When new OOD data become available, a small number of past data are incorporated through a distillation-based constraint to preserve previously acquired knowledge and alleviate catastrophic forgetting. Meanwhile, a transfer learning LoRA is employed to enable rapid adaptation to the new data. The proposed framework is systematically validated on three representative physical problems, including the Darcy flow problem in fluid mechanics, a two-dimensional hyperelastic brain tumor problem in biomechanics, and a three-dimensional linear elastic Triply Periodic Minimal Surfaces problem in solid mechanics. The results demonstrate that the proposed method effectively mitigates catastrophic forgetting on previously learned data while maintaining fast adaptability to new data. Compared with conventional joint training strategies, the proposed method significantly improves training efficiency while reducing additional memory usage and computational cost.

cs.LG↗

arXiv2026

Artificial intelligence for partial differential equations in computational mechanics: A review

In recent years, Artificial intelligence (AI) has become ubiquitous, empowering various fields, especially integrating artificial intelligence and traditional science (AI for Science: Artificial intelligence for science), which has attracted widespread attention. In AI for Science, using artificial intelligence algorithms to solve partial differential equations (AI for PDEs: Artificial intelligence for partial differential equations) has become a focal point in computational mechanics. The core of AI for PDEs is the fusion of data and partial differential equations (PDEs), which can solve almost any PDEs. Therefore, this article provides a comprehensive review of the research on AI for PDEs, summarizing the existing algorithms and theories. The article discusses the applications of AI for PDEs in computational mechanics, including solid mechanics, fluid mechanics, and biomechanics. The existing AI for PDEs algorithms include those based on Physics-Informed Neural Networks (PINNs), Deep Energy Methods (DEM), Operator Learning, and Physics-Informed Neural Operator (PINO). AI for PDEs represents a new method of scientific simulation that provides approximate solutions to specific problems using large amounts of data, then fine-tuning according to specific physical laws, avoiding the need to compute from scratch like traditional algorithms. Thus, AI for PDEs is the prototype for future foundation models in computational mechanics, capable of significantly accelerating traditional numerical algorithms.

eess.SY↗

arXiv2026

Towards Unified AI-Driven Fracture Mechanics: The Extended Deep Energy Method (XDEM)

Physics-Informed Neural Networks (PINNs) have recently emerged as powerful tools for solving partial differential equations (PDEs), with the Deep Energy Method (DEM) proving especially effective in fracture mechanics due to its energy-based formulation. Despite these advances, existing DEM approaches require dense collocation near cracks, face stability challenges, and typically treat discrete and continuous fracture models separately. To overcome these limitations, we introduce the Extended Deep Energy Method (XDEM), a unified deep learning framework that incorporates both displacement discontinuities and crack-tip asymptotics in the discrete setting, while flexibly coupling displacement and phase fields in the continuous setting. This integration enables accurate fracture predictions using uniformly distributed, relatively sparse collocation points. Validation across benchmark problems including stress intensity factor evaluation, straight and kinked crack growth, and complex crack initiation demonstrates that XDEM consistently outperforms standard DEM in accuracy and efficiency. By bridging discrete and phase-field models within a single framework, XDEM establishes a robust foundation for applying AI to fracture mechanics and opens new avenues for predictive modeling in engineering and materials science.

physics.comp-ph↗

arXiv2026

Pretrain Finite Element Method: A Pretraining and Warm-start Framework for PDEs via Physics-Informed Neural Operators

We propose a Pretrained Finite Element Method (PFEM),a physics driven framework that bridges the efficiency of neural operator learning with the accuracy and robustness of classical finite element methods (FEM). PFEM consists of a physics informed pretraining stage and an optional finetuning stage. In the pretraining stage, a neural operator based on the Transolver architecture is trained solely from governing partial differential equations, without relying on labeled solution data. The model operates directly on unstructured point clouds, jointly encoding geometric information, material properties, and boundary conditions, and produces physically consistent initial solutions with extremely high computational efficiency. PDE constraints are enforced through explicit finite element, based differentiation, avoiding the overhead associated with automatic differentiation. In the fine-tuning stage, the pretrained prediction is used as an initial guess for conventional FEM solvers, preserving their accuracy, convergence guarantees, and extrapolation capability while substantially reducing the number of iterations required to reach a prescribed tolerance. PFEM is validated on a broad range of benchmark problems, including linear elasticity and nonlinear hyperelasticity with complex geometries, heterogeneous materials, and arbitrary boundary conditions. Numerical results demonstrate strong generalization in the pretraining stage with relative errors on the order of 1\%, and speedups of up to one order of magnitude in the fine-tuning stage compared to FEM with zero initial guesses.

math.NA↗

arXiv2026

A Computational Model for Flexoelectricity-Driven Contact Electrification

Recent theoretical studies show that nanoscale contact on dielectric substrates can induce flexoelectric polarization large enough to drive electron transfer. This has been supported by experimental evidence, indicating that contact electrification is inherently a coupled electromechanical phenomenon. In this work, we develop a computational model for flexoelectricity-driven contact electrification that integrates finite-deformation flexoelectricity with contact mechanics and physically motivated charge transfer. A tunneling transparency function is introduced to regulate the interfacial channel based on the WKB approximation, capturing the irreversible charge trapping during unloading. Three contact scenarios are investigated with specific hypotheses for charge transfer: unbiased metal-dielectric contact driven by surface polarization, biased contact restricted to carriers of a single polarity, and dielectric-dielectric contact where surface states with finite capacity limit the transferable charge. The model is compared with atomic force microscopy measurements on PMMA and PDAP substrates under both biased and unbiased conditions.For contact between identical dielectric materials, we show that geometric asymmetry in surface curvature is sufficient to induce charge separation, with polarity reversal occurring at a critical surface wavenumber. Three-dimensional simulations on random rough surfaces reproduce the mosaic charge distributions observed experimentally, confirming that contact-induced local strain gradient heterogeneity can generate spatially non-uniform charge patterns without introducing any material inhomogeneity.

physics.app-ph↗

arXiv2026

Deep Energy Method with Large Language Model assistance: an open-source Streamlit-based platform for solving variational PDEs

Physics-informed neural networks (PINNs) in energy form, also known as the deep energy method (DEM), offer advantages over strong-form PINNs such as lower-order derivatives and fewer hyperparameters, yet dedicated and user-friendly software for energy-form PINNs remains scarce. To address this gap, we present \textbf{LM-DEM} (Large-Model-assisted Deep Energy Method), an open-source, Streamlit-based platform for solving variational partial differential equations (PDEs) in computational mechanics. LM-DEM integrates large language models (LLMs) for geometry modeling: users can generate Gmsh-compatible geometries directly from natural language descriptions or images, significantly reducing the burden of traditional geometry preprocessing. The solution process is driven by the deep energy method, while finite element solutions can be obtained in parallel. The framework supports built-in problems including Poisson, screened Poisson, linear elasticity, and hyperelasticity in two and three dimensions, as well as user-defined energy functionals analogous to the \texttt{UMAT} interface in Abaqus. The source code is available at https://github.com/yizheng-wang/LMDEM, and a web-based version is accessible at https://ai4m.llmdem.com. LM-DEM aims to lower the barrier for practitioners and beginners to adopt energy-form PINNs for variational PDE problems.

math.NA↗

arXiv2026

Physics-Informed Kolmogorov-Arnold Networks for multi-material elasticity problems in electronic packaging

This paper proposes a Physics-Informed Kolmogorov-Arnold Network for analyzing elasticity problems in multi-material electronic packaging structures. The method replaces traditional Multi-Layer Perceptrons with Kolmogorov-Arnold Networks within an energy-based Physics-Informed Neural Network framework. By constructing admissible displacement fields satisfying essential boundary conditions and optimizing network parameters through numerical integration, the proposed method effectively handles material property discontinuities. Unlike traditional methods that require domain decomposition and interface constraints for multi-material problems, Kolmogorov-Arnold Networks' trainable B-spline activation functions provide inherent piecewise characteristics. This capability stems from B-splines' local support, which enables effective approximation of discontinuities despite their individual smoothness. Consequently, this approach enables accurate approximation across the entire domain using a single network and simplifying the computational framework. Numerical experiments demonstrate that the proposed method achieves excellent accuracy and robustness in multi-material elasticity problems, validating its practical potential for electronic packaging analysis. Source codes are available at https://github.com/yanpeng-gong/PIKAN-MultiMaterial.

math.NA↗

arXiv2025

Phase-field modeling of multicomponent vesicles in viscoelastic fluid

Multicomponent vesicles suspended in viscoelastic fluids are crucial for understanding a variety of physiological processes. In this work, we develop a continuum surface force (CSF) phase-field model to investigate the hydrodynamics of inextensible multicomponent vesicles in viscoelastic fluid flows with inertial forces. Our model couples a fluid field comprising both Newtonian and Oldroyd-B fluids, a surface concentration field representing the multicomponent distribution on the vesicle membrane, and a phase-field variable governing the membrane evolution. The viscoelasticity effect of extra stress is well incorporated into the full Navier-Stokes equations in the fluid field. The surface concentration field is determined by Cahn-Hilliard equations, while the membrane evolution is governed by a nonlinear advection-diffusion equation. The membrane is coupled to the surrounding fluid through the continuum surface force (CSF) framework. To ensure stable numerical solutions of the highly nonlinear multi-field model, we employ a residual-based variational multiscale (RBVMS) method for the Navier-Stokes equations, a Streamline-Upwind Petrov-Galerkin (SUPG) method for the Oldroyd-B equations, and a standard Galerkin finite element framework for the remaining equations. The system of PDEs is solved using an implicit, monolithic scheme based on the generalized-$α$ time integration method. To enhance spatial accuracy, we employ isogeometric analysis (IGA). We present a series of two-dimensional numerical examples in shear and Poiseuille flows to elucidate the influence of membrane composition and fluid viscoelasticity on the hydrodynamics of multicomponent vesicles.

physics.flu-dyn↗

arXiv2025

A coupled finite element-virtual element method for thermomechanical analysis of electronic packaging structures

This study presents a finite element and virtual element (FE-VE) coupled method for thermomechanical analysis in electronic packaging structures. The approach partitions computational domains strategically, employing FEM for regular geometries to maximize computational efficiency and VEM for complex shapes to enhance geometric flexibility. Interface compatibility is maintained through coincident nodal correspondence, ensuring solution continuity across domain boundaries while reducing meshing complexity and computational overhead. Validation through electronic packaging applications demonstrates reasonable agreement with reference solutions and acceptable convergence characteristics across varying mesh densities. The method effectively captures thermal distributions and stress concentrations in multi-material systems, establishing a practical computational framework for electronic packaging analysis involving complex geometries. Source codes are available at https://github.com/yanpeng-gong/FeVeCoupled-ElectronicPackaging.

math.NA↗