Computer Methods in Applied Mechanics and Engineering最新文献

{"title":"A hybrid polynomial chaos expansion – Gaussian process regression method for Bayesian uncertainty quantification and sensitivity analysis","authors":"Paolo Manfredi","doi":"10.1016/j.cma.2024.117693","DOIUrl":"10.1016/j.cma.2024.117693","url":null,"abstract":"<div><div>This paper introduces a novel hybrid method for uncertainty quantification (UQ) combining the benefits of polynomial chaos expansion (PCE) and Gaussian process regression (GPR). The proposed method features a GPR formulation that leverages special implicit kernels involving an infinite sequence of some of the orthogonal polynomials from the Wiener-Askey scheme. These kernels enable the closed-form calculation of PCE coefficients by analytical integration of the GPR posterior, thereby leading to a Bayesian estimation in terms of both expected value and covariance matrix. Notably, the Bayesian definition allows associating confidence information to the computed coefficients, which is then propagated to the classical closed-form estimates associated to PCEs, i.e., first- and second-order moments and Sobol’ sensitivity indices. The advocated method helps mitigate some long-standing shortcomings of PCEs in terms of training efficiency and scalability to higher dimensions, while providing an accurate quantification of the intrinsic model uncertainty. Moreover, it allows for a nonparametric computation of PCE coefficients, since the basis functions do not need to be selected a priori. A simple and effective multi-output formulation, involving the tuning of a single set of hyperparameters, is also discussed. The hybrid PCE-GPR method is extensively illustrated and validated based on both synthetic examples and high-dimensional application test cases in the field of electrical engineering, for which it is shown to substantially outperform state-of-the-art PCE methods such as least-angle regression, orthogonal matching pursuit, subspace pursuit, and Bayesian compressive sensing.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"436 ","pages":"Article 117693"},"PeriodicalIF":6.9,"publicationDate":"2025-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142918017","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":"Deep learning for inverse material characterization","authors":"Yousef Ghaffari Motlagh ,&nbsp;Farshid Fathi ,&nbsp;John C. Brigham ,&nbsp;Peter K. Jimack","doi":"10.1016/j.cma.2024.117650","DOIUrl":"10.1016/j.cma.2024.117650","url":null,"abstract":"<div><div>This paper presents an approach for computationally efficient inverse material characterization using Physics-Informed Neural Networks (PINNs) based on partial-field response measurements. PINNs reconstruct the full spatial distribution of the system’s response from the measured portion of the response field and estimate the spatial distribution of unknown material properties. The primary computational expense in this approach is the one-time generation of potential responses for the PINNs, resulting in significant computational efficiency. Furthermore, this study utilizes PINNs to train a model based on the underlying physics described by differential equations, and to quantify <em>aleatoric</em> uncertainty arising from noisy data. We demonstrate several one-dimensional and two-dimensional examples where the elastic modulus distribution is characterized based on static partial-field displacement response measurements. The inversion procedure efficiently provides accurate estimates of material property distributions, showcasing the potential of PINNs in practical applications.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"436 ","pages":"Article 117650"},"PeriodicalIF":6.9,"publicationDate":"2025-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142918016","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":"Adaptive Kriging-assisted multi-fidelity subset simulation for reliability analysis","authors":"Hongzhe Dai ,&nbsp;Dashuai Li ,&nbsp;Michael Beer","doi":"10.1016/j.cma.2024.117705","DOIUrl":"10.1016/j.cma.2024.117705","url":null,"abstract":"<div><div>Accurate estimation of rare event probabilities with reasonable computational demands is crucial in reliability analysis. However, with increasing complexity of engineering problems, traditional methods are facing rising challenges in terms of computational efficiency and accuracy. In this work, an effective multi-fidelity framework is provided for assessing rare event probabilities. We firstly define the multi-fidelity failure domains by introducing a series of intermediate failure events associated with performance functions at various fidelity levels. Subset simulation is then employed to decompose the rare event probability into a series of conditional probabilities associated with these multi-fidelity failure domains. In this context, we demonstrate that the estimation accuracy of failure probability only depends on that of the conditional probability of a critical failure domain, rather than on those of the rest of multi-fidelity failure domains. With aid of this fact, the rest of failure domains is approximated by a series of Kriging models constructed with the computationally cheap low-fidelity performance functions. Thus, the computational demand for estimating the conditional probabilities of the rest failure domains is significantly decreased in reliability analysis. Since these approximated failure domains, which gradually approach the critical failure domain, allow for sufficiently sampling deep into the critical one, the Kriging model of the high-fidelity performance function can be accurately constructed with the sufficient number of candidate samples. As a result, the conditional probability of the critical failure domain, and thus the rare event probability, are finally estimated with high precision. Three illustrative examples, including a concrete arch dam subject to both hydrostatic and sediment accumulation loads, are investigated to validate the proposed method.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"436 ","pages":"Article 117705"},"PeriodicalIF":6.9,"publicationDate":"2025-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142918012","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":"Constrained or unconstrained? Neural-network-based equation discovery from data","authors":"Grant Norman ,&nbsp;Jacqueline Wentz ,&nbsp;Hemanth Kolla ,&nbsp;Kurt Maute ,&nbsp;Alireza Doostan","doi":"10.1016/j.cma.2024.117684","DOIUrl":"10.1016/j.cma.2024.117684","url":null,"abstract":"<div><div>Throughout many fields, practitioners often rely on differential equations to model systems. Yet, for many applications, the theoretical derivation of such equations and/or the accurate resolution of their solutions may be intractable. Instead, recently developed methods, including those based on parameter estimation, operator subset selection, and neural networks, allow for the data-driven discovery of both ordinary and partial differential equations (PDEs), on a spectrum of interpretability. The success of these strategies is often contingent upon the correct identification of representative equations from noisy observations of state variables and, as importantly and intertwined with that, the mathematical strategies utilized to enforce those equations. Specifically, the latter has been commonly addressed via unconstrained optimization strategies. Representing the PDE as a neural network, we propose to discover the PDE (or the associated operator) by solving a constrained optimization problem and using an intermediate state representation similar to a physics-informed neural network (PINN). The objective function of this constrained optimization problem promotes matching the data, while the constraints require that the discovered PDE is satisfied at a number of spatial collocation points. We present a penalty method and a widely used trust-region barrier method to solve this constrained optimization problem, and we compare these methods on numerical examples. Our results on several example problems demonstrate that the latter constrained method outperforms the penalty method, particularly for higher noise levels or fewer collocation points. This work motivates further exploration into using sophisticated constrained optimization methods in scientific machine learning, as opposed to their commonly used, penalty-method or unconstrained counterparts. For both of these methods, we solve these discovered neural network PDEs with classical methods, such as finite difference methods, as opposed to PINNs-type methods relying on automatic differentiation. We briefly highlight how simultaneously fitting the data while discovering the PDE improves the robustness to noise and other small, yet crucial, implementation details.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"436 ","pages":"Article 117684"},"PeriodicalIF":6.9,"publicationDate":"2025-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142918015","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":"Non-overlapping, Schwarz-type domain decomposition method for physics and equality constrained artificial neural networks","authors":"Qifeng Hu,&nbsp;Shamsulhaq Basir,&nbsp;Inanc Senocak","doi":"10.1016/j.cma.2024.117706","DOIUrl":"10.1016/j.cma.2024.117706","url":null,"abstract":"<div><div>We present a non-overlapping, Schwarz-type domain decomposition method with a generalized interface condition, designed for physics-informed machine learning of partial differential equations (PDEs) in both forward and inverse contexts. Our approach employs physics and equality-constrained artificial neural networks (PECANN) within each subdomain. Unlike the original PECANN method, which relies solely on initial and boundary conditions to constrain PDEs, our method uses both boundary conditions and the governing PDE to constrain a unique interface loss function for each subdomain. This modification improves the learning of subdomain-specific interface parameters while reducing communication overhead by delaying information exchange between neighboring subdomains. To address the constrained optimization in each subdomain, we apply an augmented Lagrangian method with a conditionally adaptive update strategy, transforming the problem into an unconstrained dual optimization. A distinct advantage of our domain decomposition method is its ability to learn solutions to both Poisson’s and Helmholtz equations, even in cases with high-wavenumber and complex-valued solutions. Through numerical experiments with up to 64 subdomains, we demonstrate that our method consistently generalizes well as the number of subdomains increases.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"436 ","pages":"Article 117706"},"PeriodicalIF":6.9,"publicationDate":"2024-12-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142918018","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":"Concurrent topology optimization of two-scale structures with minimum width control in microscale by using a M-VCUT level set based model of microstructures","authors":"Minjie Shao,&nbsp;Zhuo Huang,&nbsp;Tielin Shi,&nbsp;Qi Xia","doi":"10.1016/j.cma.2024.117697","DOIUrl":"10.1016/j.cma.2024.117697","url":null,"abstract":"<div><div>A method is proposed to control the minimum width in microscale for concurrent topology optimization of two-scale structures by using a M-VCUT level set model of microstructures. The key idea is to construct a data-driven model of microstructures that satisfies the requirement of minimum width in an off-line phase. Especially, a topology variable is assigned to each virtual microstructure to eliminate it if it is inefficient. During the on-line phase of concurrent topology optimization, a simple numerical relationship between the design variables and the effective mechanical properties of microstructure is used for efficient finite element analysis in the macroscale. The results of several numerical examples prove that the proposed method is effective.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"436 ","pages":"Article 117697"},"PeriodicalIF":6.9,"publicationDate":"2024-12-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142918075","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 time step-size computing arc-length method for the phase-field hydraulic fracture model","authors":"Ritukesh Bharali ,&nbsp;Frans P. van der Meer ,&nbsp;Fredrik Larsson ,&nbsp;Ralf Jänicke","doi":"10.1016/j.cma.2024.117687","DOIUrl":"10.1016/j.cma.2024.117687","url":null,"abstract":"<div><div>The phase-field hydraulic fracture model entails a non-convex energy functional. This renders a poor convergence behaviour for monolithic solution techniques, such as the Newton–Raphson method. Consequently, researchers have adopted alternative solution techniques such as the staggered solution technique and the Newton–Raphson method with convexification via extrapolation of the phase-field. Both methods are robust. However, the former is computationally expensive and in the latter, the extrapolation itself is questionable w.r.t regularity in time. In this work, a novel dissipation-based arc-length method is proposed as a robust and computationally efficient monolithic solution technique for the phase-field hydraulic fracture model. Similar to brittle fracture in force driven mechanical problems, constant flux driven hydraulic fracture processes are also unstable. Furthermore, due to the constant flux loading in hydraulic fracturing problems, scaling of the external force is not possible. Instead, the time step-size is considered as the additional unknown, augmenting the arc-length constraint equation. The robustness and computational efficiency of the proposed arc-length method is demonstrated using numerical experiments, where comparisons are made with the staggered solver as well as the quasi-Newton BFGS method.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"436 ","pages":"Article 117687"},"PeriodicalIF":6.9,"publicationDate":"2024-12-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142918019","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":"Riemannian geometry based peridynamics computational homogenization method for cellular metamaterials","authors":"Kumari Neelam Ranjana,&nbsp;Sajal,&nbsp;Pranesh Roy","doi":"10.1016/j.cma.2024.117714","DOIUrl":"10.1016/j.cma.2024.117714","url":null,"abstract":"<div><div>A novel Riemannian geometry-based two-scale computational homogenization technique is developed in peridynamics (PD) framework for cellular metamaterials. The idea here is to envision two infinitesimally close material points in reference configuration of a macroscopic body which are finite distance apart in microstructure. Due to the presence of holes or defects in the microstructure, the shortest path between these two points is not a straight line, but a geodesic curve. This clearly shows that the infinitesimal distance between these two points in the macrostructure cannot be calculated using Euclidean geometry. Proposing the inherent geometry of the macrostructure to be Riemannian with an associated symmetric metric tensor, a search horizon-based procedure is designed to calculate the components of the metric tensor. Borrowing ideas from the graph theory of computer science, we propose a novel approach based on Dijkstra's algorithm to calculate the shortest distance between two particles in a discretized PD domain by considering the PD domain to be an undirected weighted graph. A two-scale PD based computational homogenization method is proposed, and calculation procedure of the effective material properties is outlined. The response of macrostructure for static and dynamic load cases is obtained using the Newton-Raphson and the predictor-corrector methods, respectively. First, the solution of the PD model is validated with analytical solution, finite element analysis result obtained using ANSYS®, and experimental results. The response of macrostructures obtained using the proposed homogenization method in PD framework is validated with finite element method solution. Thereafter, macrostructures with different configurations with and without cracks are analyzed under static and dynamic loading. The effect of different search horizons, which leads to different metric tensor coefficients, is also investigated by comparing the response of macrostructures. Dynamic crack propagation simulations demonstrate the importance of considering Riemannian geometry in macrostructure.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"436 ","pages":"Article 117714"},"PeriodicalIF":6.9,"publicationDate":"2024-12-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142918020","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":"Combination of intrusive POD-based reduced-order models and augmented Riemann solvers applied to unsteady 2D shallow water equations","authors":"P. Solán-Fustero ,&nbsp;J.L. Gracia ,&nbsp;A. Navas-Montilla ,&nbsp;P. García-Navarro","doi":"10.1016/j.cma.2024.117702","DOIUrl":"10.1016/j.cma.2024.117702","url":null,"abstract":"<div><div>The shallow water equations (SWEs) can be used to model the spatio-temporal evolution of free surface flows. The numerical resolution of realistic problems based on the 2D SWEs by means of augmented Roe-based (ARoe) methods requires the inclusion of certain numerical corrections to avoid non-physical results in presence of irregular topography and wet dry fronts. Besides that, their complex and transient nature involves high computational costs. In this direction, intrusive reduced-order models (ROMs) based on the proper orthogonal decomposition (POD) are presented as alternative to speed up computational calculations without compromising the accuracy of the solutions. The main objective of this article is to study whether the inclusion of numerical corrections in the ROM strategy of the 2D SWEs for non trivial situations is necessary to obtain accurate solutions or not, and, if necessary, to present their reduced version. In addition to this, it is proposed to solve problems with Dirichlet-type boundary conditions (BCs) by means of ROMs using a technique whereby the BCs are directly integrated into the on-line phase of ROM solving. The efficiency of the ARoe-based ROM has been tested with respect to the full-order model by comparing their computational cost and the accuracy of their solutions in different numerical cases.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"436 ","pages":"Article 117702"},"PeriodicalIF":6.9,"publicationDate":"2024-12-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142918053","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":"Efficient fully discrete and decoupled scheme with unconditional energy stability and second-order accuracy for micropolar Navier–Stokes equations","authors":"Guo-Dong Zhang ,&nbsp;Yunqing Huang ,&nbsp;Xiaoming He ,&nbsp;Xiaofeng Yang","doi":"10.1016/j.cma.2024.117692","DOIUrl":"10.1016/j.cma.2024.117692","url":null,"abstract":"<div><div>This article focuses on the numerical approximation of the micropolar Navier–Stokes (MNS) system for micropolar fluids, which consists of the Navier–Stokes equations and the angular momentum equations. A significant challenge in developing efficient numerical algorithms for this model is the complex coupling structure, involving both linear and nonlinear couplings. In particular, the linear coupling between flow velocity and angular velocity requires innovative methods for effective decoupling. Recognizing that the terms associated with this linear coupling constitute a diffusion term in the form of a complete square, we introduce a new nonlocal auxiliary variable and construct an ordinary differential equation with an ingenious structure. Reformulating the MNS system into an equivalent form allows us to decouple the linear coupling through explicit discretization. This novel method integrates the zero-energy-contribution decoupling method for handling nonlinear couplings, the second-order projection method for hydrodynamics, and the spatial finite element method, resulting in a fully discrete scheme that is unconditionally energy stable, fully decoupled, linear, and second-order accurate in time. Moreover, the proposed scheme is highly efficient, as only a few independent linear elliptic problems with constant coefficients need to be solved at each time step. The unconditional energy stability and well-posedness of the scheme are also established. Numerical simulations, including 2D/3D driven cavity flows and stirring of a passive scalar, are implemented to verify the stability and accuracy of the scheme, with the numerical results exhibiting interesting phenomena in micropolar fluids.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"436 ","pages":"Article 117692"},"PeriodicalIF":6.9,"publicationDate":"2024-12-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142918025","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}