Computer Methods in Applied Mechanics and Engineering最新文献

{"title":"Continuum-kinematics-inspired peridynamics for transverse isotropy","authors":"A.M. de Villiers ,&nbsp;J. Stadler ,&nbsp;G. Limbert ,&nbsp;A.T. McBride ,&nbsp;A. Javili ,&nbsp;P. Steinmann","doi":"10.1016/j.cma.2025.117780","DOIUrl":"10.1016/j.cma.2025.117780","url":null,"abstract":"<div><div>Accounting for the combined effects of mechanical anisotropy and nonlocality is critical for capturing a wide range of material behaviour. Continuum-kinematics-inspired peridynamics (CPD) provides the essential underpinning theoretical and numerical framework to realise this objective. The formalism of rational mechanics is employed here to rigorously extend CPD to the important case of transverse isotropy at finite deformations while retaining the fundamental deformation measures of length, area and volume intrinsic to classical continuum mechanics. Details of the anisotropic contribution to the potential energy density due to length, area and volume elements are given. A series of numerical examples serve to elucidate the theory presented.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"437 ","pages":"Article 117780"},"PeriodicalIF":6.9,"publicationDate":"2025-02-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143100942","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Deep Ritz - Finite element methods: Neural network methods trained with finite elements","authors":"Georgios Grekas ,&nbsp;Charalambos G. Makridakis","doi":"10.1016/j.cma.2025.117798","DOIUrl":"10.1016/j.cma.2025.117798","url":null,"abstract":"<div><div>While much attention of neural network methods is devoted to high-dimensional PDE problems, in this work we consider methods designed to work for elliptic problems on domains <span><math><mrow><mi>Ω</mi><mo>⊂</mo><msup><mrow><mi>R</mi></mrow><mrow><mi>d</mi></mrow></msup></mrow></math></span>, <span><math><mrow><mi>d</mi><mo>=</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>,</mo><mn>3</mn></mrow></math></span> in association with more standard finite elements. We suggest to connect finite elements and neural network approximations through <em>training</em>, i.e., using finite element spaces to compute the integrals appearing in the loss functionals. This approach, retains the simplicity of classical neural network methods for PDEs, uses well established finite element tools (and software) to compute the integrals involved and it gains in efficiency and accuracy. We demonstrate that the proposed methods are stable and furthermore, we establish that the resulting approximations converge to the solutions of the PDE. Numerical results indicating the efficiency and robustness of the proposed algorithms are presented.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"437 ","pages":"Article 117798"},"PeriodicalIF":6.9,"publicationDate":"2025-02-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143100876","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"On adaptive sampling techniques for metamodels based on NURBS entities from unstructured data","authors":"M. Zani,&nbsp;E. Panettieri,&nbsp;M. Montemurro","doi":"10.1016/j.cma.2025.117781","DOIUrl":"10.1016/j.cma.2025.117781","url":null,"abstract":"<div><div>The paper investigates the influence of adaptive sampling strategies on the generation of a metamodel based on Non-Uniform Rational Basis Spline (NURBS) entities, obtained from unstructured data, with the purpose of improving accuracy while minimising computational resources. The metamodel is defined as solution of a constrained non-linear programming problem and it is solved through a three-step optimisation process based on a gradient-based algorithm. Moreover, this paper introduces a generalised formulation of the NURBS-based metamodel capable of handling unstructured sampling data, enabling simultaneous optimisation of control points and weights. Sensitivity analyses are performed to evaluate the influence of various adaptive sampling techniques, including cross-validation-based and geometry-based strategies, on the resulting metamodel, in terms of accuracy and computational costs. Analytical benchmarks functions and a complex real-world engineering problem (dealing with the non-linear thermomechanical analysis of a part produced with the fused deposition modelling technology) are used to prove the effectiveness of the NURBS-based metamodel coupled with adaptive sampling strategies in achieving high accuracy and efficiency.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"437 ","pages":"Article 117781"},"PeriodicalIF":6.9,"publicationDate":"2025-02-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143100941","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A model learning framework for inferring the dynamics of transmission rate depending on exogenous variables for epidemic forecasts","authors":"Giovanni Ziarelli,&nbsp;Stefano Pagani,&nbsp;Nicola Parolini,&nbsp;Francesco Regazzoni,&nbsp;Marco Verani","doi":"10.1016/j.cma.2025.117796","DOIUrl":"10.1016/j.cma.2025.117796","url":null,"abstract":"<div><div>In this work, we aim to formalize a novel scientific machine learning framework to reconstruct the hidden dynamics of the transmission rate, whose inaccurate extrapolation can significantly impair the quality of the epidemic forecasts, by incorporating the influence of exogenous variables (such as environmental conditions and strain-specific characteristics). We propose a hybrid model that blends a data-driven layer with a physics-based one. The data-driven layer is based on a neural ordinary differential equation that learns the dynamics of the transmission rate, conditioned on the meteorological data and wave-specific latent parameters. The physics-based layer, instead, consists of a standard <em>SEIR</em> compartmental model, wherein the transmission rate represents an input. The learning strategy follows an end-to-end approach: the loss function quantifies the mismatch between the actual numbers of infections and its numerical prediction obtained from the <em>SEIR</em> model incorporating as an input the transmission rate predicted by the neural ordinary differential equation. We apply this original approach to both a synthetic test case and a realistic test case based on meteorological data (temperature and humidity) and influenza data from Italy between 2010 and 2020. In both scenarios, we achieve low generalization error on the test set and observe strong alignment between the reconstructed model and established findings on the influence of meteorological factors on epidemic spread. Finally, we implement a data assimilation strategy to adapt the neural equation to the specific characteristics of an epidemic wave under investigation, and we conduct sensitivity tests on the network’s hyperparameters.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"437 ","pages":"Article 117796"},"PeriodicalIF":6.9,"publicationDate":"2025-02-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143100940","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A stable second-order splitting method for incompressible Navier–Stokes equations using the scalar auxiliary variable approach","authors":"Anouar Obbadi ,&nbsp;Mofdi El-Amrani ,&nbsp;Mohammed Seaid ,&nbsp;Driss Yakoubi","doi":"10.1016/j.cma.2025.117801","DOIUrl":"10.1016/j.cma.2025.117801","url":null,"abstract":"<div><div>We propose a novel second-order fractional-step method for the numerical solution of incompressible Navier–Stokes equations. This fractional-step method consists of two splitting steps and it employs the second-order implicit backward differentiation formula for the time integration. Unlike most of the projection methods for solving incompressible Navier–Stokes equations, the proposed method is free from any numerical inconsistencies generated by the treatment of boundary conditions on the pressure solution. Two pressure-correction strategies including the scalar auxiliary variable approach are proposed to enhance the accuracy of the method. A rigorous stability analysis is also carried out in this study for the considered strategies. Numerical results are presented for three benchmark problems to validate the unconditional stability and to demonstrate the performance of the proposed fractional-step method for solving unsteady incompressible viscous flows. The obtained computational results support our theoretical expectations for an unconditionally stable second-order fractional-step method for the incompressible Navier–Stokes equations.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"437 ","pages":"Article 117801"},"PeriodicalIF":6.9,"publicationDate":"2025-02-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143100937","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Gaussian process regression + deep neural network autoencoder for probabilistic surrogate modeling in nonlinear mechanics of solids","authors":"Saurabh Deshpande ,&nbsp;Hussein Rappel ,&nbsp;Mark Hobbs ,&nbsp;Stéphane P.A. Bordas ,&nbsp;Jakub Lengiewicz","doi":"10.1016/j.cma.2025.117790","DOIUrl":"10.1016/j.cma.2025.117790","url":null,"abstract":"<div><div>Many real-world applications demand accurate and fast predictions, as well as reliable uncertainty estimates. However, quantifying uncertainty on high-dimensional predictions is still a severely under-investigated problem, especially when input–output relationships are non-linear. To handle this problem, the present work introduces an innovative approach that combines autoencoder deep neural networks with the probabilistic regression capabilities of Gaussian processes. The autoencoder provides a low-dimensional representation of the solution space, while the Gaussian process is a Bayesian method that provides a probabilistic mapping between the low-dimensional inputs and outputs. We validate the proposed framework for its application to surrogate modeling of non-linear finite element simulations. Our findings highlight that the proposed framework is computationally efficient as well as accurate in predicting non-linear deformations of solid bodies subjected to external forces, all the while providing insightful uncertainty assessments.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"437 ","pages":"Article 117790"},"PeriodicalIF":6.9,"publicationDate":"2025-02-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143100938","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Variational Physics-informed Neural Operator (VINO) for solving partial differential equations","authors":"Mohammad Sadegh Eshaghi ,&nbsp;Cosmin Anitescu ,&nbsp;Manish Thombre ,&nbsp;Yizheng Wang ,&nbsp;Xiaoying Zhuang ,&nbsp;Timon Rabczuk","doi":"10.1016/j.cma.2025.117785","DOIUrl":"10.1016/j.cma.2025.117785","url":null,"abstract":"<div><div>Solving partial differential equations (PDEs) is a required step in the simulation of natural and engineering systems. The associated computational costs significantly increase when exploring various scenarios, such as changes in initial or boundary conditions or different input configurations. This study proposes the Variational Physics-Informed Neural Operator (VINO), a deep learning method designed for solving PDEs by minimizing the energy formulation of PDEs. This framework can be trained without any labeled data, resulting in improved performance and accuracy compared to existing deep learning methods and conventional PDE solvers. By discretizing the domain into elements, the variational format allows VINO to overcome the key challenge in physics-informed neural operators, namely the efficient evaluation of the governing equations for computing the loss. Comparative results demonstrate VINO’s superior performance, especially as the mesh resolution increases. As a result, this study suggests a better way to incorporate physical laws into neural operators, opening a new approach for modeling and simulating nonlinear and complex processes in science and engineering.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"437 ","pages":"Article 117785"},"PeriodicalIF":6.9,"publicationDate":"2025-02-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143100939","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Online multi-fidelity data aggregation via hierarchical neural network","authors":"Chunlong Hai ,&nbsp;Jiazhen Wang ,&nbsp;Shimin Guo ,&nbsp;Weiqi Qian ,&nbsp;Liquan Mei","doi":"10.1016/j.cma.2025.117795","DOIUrl":"10.1016/j.cma.2025.117795","url":null,"abstract":"<div><div>In many industrial applications requiring computational modeling, the acquisition of high-fidelity data is often constrained by cost and technical limitations, while low-fidelity data, though cheaper and easier to obtain, lacks the same level of accuracy. Multi-fidelity data aggregation addresses this challenge by combining both types of data to construct surrogate models, balancing modeling accuracy with data cost. Optimizing the placement and distribution of high-fidelity samples is also essential to improving model performance. In this work, we propose online multi-fidelity data aggregation via hierarchical neural network (OMA-HNN). This method comprises two key components: multi-fidelity data aggregation via hierarchical neural network (MA-HNN) and an online progressive sampling framework. MA-HNN integrates data of varying fidelities within a hierarchical network structure, employing nonlinear components to capture the differences across multi-fidelity levels. The online progressive sampling framework manages high-fidelity data acquisition through two stages: initial sampling and incremental sampling. For these stages, we develop the low-fidelity-surrogate assisted sampling (LAS) strategy for the initial phase and the model divergence-based active learning (MDAL) strategy for incremental sampling. OMA-HNN was rigorously tested on 15 numerical examples across diverse multi-fidelity scenarios and further validated through three real-world applications. The results demonstrate its effectiveness and practicality, underscoring OMA-HNN’s potential to enhance the reliability and efficiency of multi-fidelity data aggregation in industrial contexts.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"437 ","pages":"Article 117795"},"PeriodicalIF":6.9,"publicationDate":"2025-02-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143100934","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A universal surrogate modeling method based on heterogeneous graph neural network for nonlinear analysis","authors":"Yongcheng Li ,&nbsp;Changsheng Wang ,&nbsp;Wenbin Hou","doi":"10.1016/j.cma.2025.117793","DOIUrl":"10.1016/j.cma.2025.117793","url":null,"abstract":"<div><div>Nonlinear finite element analysis (FEA) is typically time-consuming, primarily due to its reliance on incremental solution schemes which require repeated stiffness matrix assembly and inversion at each step. In scenarios like structural optimization, where numerous FEA iterations are needed, deep learning-based surrogate models are usually employed as alternatives owing to their extremely high inference efficiency. However, they may exhibit weak generalization ability and produce predictions that violate established physical laws. Furthermore, their network types, such as multi-layer perceptron (MLP), limit the scalability of surrogate modeling methods, as a single model is restricted to a specific structural topology. To address these issues, we propose a universal surrogate modeling method based on heterogeneous graph neural network (HGNN) for nonlinear analysis, enhancing both scalability and generalization. Our method starts by decomposing an arbitrary engineering structure into components of different types and representing it as heterogeneous graph data, which establish a foundation for the method’s universality. Then, each increment step in the nonlinear FEA is used to extract a new sample, achieving significant data augmentation without additional computation. To further improve prediction accuracy, we leverage a physical loss derived from the nonlinear equations of each increment step to direct the model’s training process. Numerical experiments on the car body frame and car roof achieved prediction accuracies of 99.45% and 99.66%, respectively, demonstrating our method’s feasibility and efficacy.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"437 ","pages":"Article 117793"},"PeriodicalIF":6.9,"publicationDate":"2025-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143100933","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"History-Matching of imbibition flow in fractured porous media Using Physics-Informed Neural Networks (PINNs)","authors":"Jassem Abbasi ,&nbsp;Ben Moseley ,&nbsp;Takeshi Kurotori ,&nbsp;Ameya D. Jagtap ,&nbsp;Anthony R. Kovscek ,&nbsp;Aksel Hiorth ,&nbsp;Pål Østebø Andersen","doi":"10.1016/j.cma.2025.117784","DOIUrl":"10.1016/j.cma.2025.117784","url":null,"abstract":"<div><div>In this work, we propose a workflow based on physics-informed neural networks (PINNs) to model multiphase fluid flow in fractured porous media. After validating the workflow in forward and inverse modeling of a synthetic problem of flow in fractured porous media, we applied it to a real experimental dataset in which brine is injected at a constant pressure drop into a CO<span><math><msub><mrow></mrow><mrow><mn>2</mn></mrow></msub></math></span> saturated naturally fractured shale core plug. The exact spatial positions of natural fractures and the dynamic in-situ distribution of fluids were imaged using a CT-scan setup. To model the targeted system, we followed a domain decomposition approach for matrix and fractures and a multi-network architecture for the separate calculation of water saturation and pressure. The flow equations in the matrix, fractures and interplay between them were solved during training. Prior to fully-coupled simulations, we suggested pre-training the model. This aided in a more efficient and successful training of the coupled system. Both for the synthetic and experimental inverse problems, we determined flow parameters within the matrix and the fractures. Multiple random initializations of network and system parameters were performed to assess the uncertainty and uniqueness of the resulting calculations. The results confirmed the precision of the inverse calculated parameters in retrieving the main flow characteristics of the system. The consideration of matrix-fracture interactions is commonly overlooked in existing workflows. Accounting for them led to several orders of magnitude variations in the calculated flow properties compared to not accounting for them. The proposed PINNs-based workflow offer a reliable and computationally efficient solution for inverse modeling of multiphase flow in fractured porous media, achieved through history-matching noisy and multi-fidelity experimental measurements.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"437 ","pages":"Article 117784"},"PeriodicalIF":6.9,"publicationDate":"2025-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143100935","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}