arXiv subjects

Haihui Ruan

Publications and source records attributed to Haihui Ruan.

7 recordsLinked to original sources

arXiv2026

A Non-Overlapping Schwarz Hybrid Finite Element-Neural Operator Framework for Solid Mechanics on Irregular Domains

Finite element (FE) methods are the benchmark for solid mechanics simulations, yet their computational cost becomes prohibitive for problems with localised nonlinearities, fine-scale features, or long-time dynamic evolution. In our earlier FE-neural operator (FE-NO) hybrid framework [1], physics-informed deep operator networks were coupled with FE solvers through overlapping domain decomposition with Dirichlet-Dirichlet interface exchange, accelerating intensive subdomains while preserving FE fidelity elsewhere. Two limitations remained: the overlapping formulation required redundant interface computations that increased inner Schwarz iteration counts, and the convolutional feature extractor restricted the NO subdomain to structured grids, precluding irregular geometries. A non-overlapping Schwarz alternating method with Neumann-Dirichlet interface exchange replaces it, transmitting traction from the NO to FE rather than displacement. This eliminates the overlap layer and reduces inner Schwarz iterations while maintaining bounded error accumulation across all tested time horizons. For arbitrarily shaped subdomains, a Point-DeepONet operates on unstructured FE point clouds without interpolation, extending it to non-convex and irregular geometries. Strain and stress operators are derived analytically from the displacement operators via kinematic equations, rather than as independent networks, reducing trainable parameter sets while enforcing mechanical consistency by construction. The framework is validated on three benchmarks: static linear elasticity, quasi-static hyperelasticity, and elastodynamics with regular and irregular geometries. These results establish a non-overlapping FE-NO coupling paradigm that is geometry-flexible, parameter-efficient, and convergence-stable, providing a pathway for hybrid physics-based and operator-learning solvers in large-scale dynamic solid mechanics.

cs.CE↗

arXiv2026

Causality-Respecting Adaptive Refinement for PINNs: Enabling Precise Interface Evolution in Phase Field Modeling

Physics-informed neural networks (PINNs) have emerged as a powerful tool for solving physical systems described by partial differential equations (PDEs). However, their accuracy in dynamical systems, particularly those involving sharp moving boundaries with complex initial morphologies, remains a challenge. This study introduces an approach combining residual-based adaptive refinement (RBAR) with causality-informed training to enhance the performance of PINNs in solving spatio-temporal PDEs. Our method employs a three-step iterative process: initial causality-based training, RBAR-guided domain refinement, and subsequent causality training on the refined mesh. Applied to the Allen--Cahn equation, a widely used model in phase field simulations, our approach demonstrates significant improvements in solution accuracy and computational efficiency over traditional PINNs. Notably, we observe an overshoot and relocate phenomenon in dynamic cases with complex morphologies, showcasing the method's adaptive error correction capabilities. This synergistic interaction between RBAR and causality training enables accurate capture of interface evolution, even in challenging scenarios where traditional PINNs fail. Our framework not only resolves the limitations of uniform refinement strategies but also provides a generalizable methodology for solving a broad range of spatio-temporal PDEs. The enhanced performance of the RBAR--causality combined framework demonstrates its strong potential for advancing PINN-based modeling of physical systems characterized by complex, evolving interfaces.

physics.comp-ph↗

arXiv2025

Time Marching Neural Operator FE Coupling: AI Accelerated Physics Modeling

Numerical solvers for PDEs often struggle to balance computational cost with accuracy, especially in multiscale and time-dependent systems. Neural operators offer a promising way to accelerate simulations, but their practical deployment is hindered by several challenges: they typically require large volumes of training data generated from high-fidelity solvers, tend to accumulate errors over time in dynamical settings, and often exhibit poor generalization in multiphysics scenarios. This work introduces a novel hybrid framework that integrates physics-informed deep operator network with FEM through domain decomposition and leverages numerical analysis for time marching. Our innovation lies in efficient coupling FE and DeepONet subdomains via a Schwarz method, expecting to solve complex and nonlinear regions by a pretrained DeepONet, while the remainder is handled by conventional FE. To address the challenges of dynamic systems, we embed a time stepping scheme directly into the DeepONet, substantially reducing long-term error propagation. Furthermore, an adaptive subdomain evolution strategy enables the ML-resolved region to expand dynamically, capturing fine-scale features without remeshing. Our framework shows accelerated convergence rates (up to 20% improvement in convergence rates compared to conventional FE coupling approaches) while preserving solution fidelity with error margins consistently below 3%. Our study shows that our proposed hybrid solver: (1) reduces computational costs by eliminating fine mesh requirements, (2) mitigates error accumulation in time-dependent simulations, and (3) enables automatic adaptation to evolving physical phenomena. This work establishes a new paradigm for coupling state of the art physics based and machine learning solvers in a unified framework, offering a robust, reliable, and scalable pathway for high fidelity multiscale simulations.

cs.LG↗

arXiv2025

Emergent facilitation by random constraints in a facilitated random walk model of glass

The physics of glass has been a significant topic of interest for decades. Dynamical facilitation is widely believed to be an important characteristic of glassy dynamics, but the precise mechanism is still under debate. We propose a lattice model of glass called the facilitated random walk (FRW). Each particle performs continuous time random walk in the presence of its own random local kinetic constraints. The particles do not interact energetically. Instead, they interact kinetically with a hopping rate resampling rule under which motions of a particle can randomly perturb the local kinetic constraints of other particles. This dynamic interaction is reversible, following a rate restoration rule. A step-by-step reversal of the particle motions exactly restore the previous constraints, modeling randomness quenched in the configuration space of glass. The model exhibits stretched exponential relaxation and dynamical heterogeneity typical of glasses. Despite the lack of explicit facilitation rule, the FRW shows facilitation behaviors closely analogous to those of the kinetically constrained models (KCM). The FRW is a coarse-grained version of the distinguishable particle lattice model (DPLM) and this exemplifies that compatible defect and atomistic models can complement each other on the study of glass.

cond-mat.stat-mech↗

arXiv2025

Precision Glass Thermoforming Assisted by Neural Networks

Many glass products require thermoformed geometry with high precision. However, the traditional approach of developing a thermoforming process through trials and errors can cause large waste of time and resources and often end up with unsuccessfulness. Hence, there is a need to develop an efficient predictive model, replacing the costly simulations or experiments, to assist the design of precision glass thermoforming. In this work, we report a surrogate model, based on a dimensionless back-propagation neural network (BPNN), that can adequately predict the form errors and thus compensate for these errors in mold design using geometric features and process parameters as inputs. Our trials with simulation and industrial data indicate that the surrogate model can predict forming errors with adequate accuracy. Although perception errors (mold designers' decisions) and mold fabrication errors make the industrial training data less reliable than simulation data, our preliminary training and testing results still achieved a reasonable consistency with industrial data, suggesting that the surrogate models are directly implementable in the glass-manufacturing industry.

cs.CE↗

arXiv2020

Ergodicity breaking of an inorganic glass in aging near ${T_g}$ probed by elasticity relaxation

We performed a series of aging experiments of an inorganic glass (As${_2}$Se${_3}$) at a temperature ${T_2}$ near the glass transition point ${T_g}$ by first relaxing it at ${T_1}$. The relaxation of Young's modulus was monitored, which was(almost if not ideally) exponential with a ${T_1}$-dependent relaxation time ${τ(T_1)}$. We demostrate the Kovacs' paradox for the first time in an inorganic glasses. Associated with the divergence of $τ$, the quasi-equilibrated Young's modulus ${E_\infty}$ does not converge either. An elastic model of relaxation time and a Mori-Tanaka analysis of ${E_\infty}$ lead to a similar estimate of the persistent memory of the history, ergodicity breaking within the accessible experimental time. Experiments with different ${T_2}$ exhibits a critical temperature ${T_p \sim T_g}$, i.e., when ${T_2 > T_p}$, both $τ$ and ${E_\infty}$ converge.

cond-mat.dis-nn↗

arXiv2020

On the mechanical beta relaxation in glass and its relation to the double-peak phenomenon in impulse excited vibration at high temperatures

A viscoelastic model is established to reveal the relation between alpha-beta relaxation of glass and the double-peak phenomenon in the experiments of impulse excited vibration. In the modelling, the normal mode analysis (NMA) of potential energy landscape (PEL) picture is employed to describe mechanical alpha and beta relaxations in a glassy material. The model indicates that a small beta relaxation can lead to an apparent double-peak phenomenon resulted from the free vibration of a glass beam when the frequency of beta relaxation peak is close to the natural frequency of specimen. The theoretical prediction is validated by the acoustic spectrum of a fluorosilicate glass beam excited by a mid-span impulse. Furthermore, the experimental results indicate a negative temperature-dependence of the frequency of beta relaxation in the fluorosilicate glass S-FSL5 which can be explained based on the physical picture of fragmented oxide-network patches in liquid-like regions.

cond-mat.dis-nn↗