Pub Date : 2025-01-30DOI: 10.1016/j.cma.2025.117754
Ngoc Cuong Nguyen
We present a generative reduced basis (RB) approach for the rapid and reliable solution of parametrized linear partial differential equations. Central to this approach is the construction of generative RB spaces that provide rapidly convergent approximations of the solution manifold. We propose a generative snapshot method to generate significantly larger sets of snapshots from a small initial set of solution snapshots. This method leverages multivariate nonlinear transformations to enrich the RB spaces, thereby enabling a more accurate approximation of the solution manifold than commonly used dimensionality reduction techniques such as proper orthogonal decomposition and greedy sampling. We employ the generative RB spaces to construct reduced order models and compute a posteriori error estimates. The error estimates allow us to efficiently explore the parameter space and select parameter points that improve the efficiency and accuracy of the reduced order model. Through numerical experiments, we demonstrate that the generative RB method not only improves the accuracy of the reduced order model but also provides tight error estimates.
{"title":"Generative reduced basis method","authors":"Ngoc Cuong Nguyen","doi":"10.1016/j.cma.2025.117754","DOIUrl":"10.1016/j.cma.2025.117754","url":null,"abstract":"<div><div>We present a generative reduced basis (RB) approach for the rapid and reliable solution of parametrized linear partial differential equations. Central to this approach is the construction of generative RB spaces that provide rapidly convergent approximations of the solution manifold. We propose a generative snapshot method to generate significantly larger sets of snapshots from a small initial set of solution snapshots. This method leverages multivariate nonlinear transformations to enrich the RB spaces, thereby enabling a more accurate approximation of the solution manifold than commonly used dimensionality reduction techniques such as proper orthogonal decomposition and greedy sampling. We employ the generative RB spaces to construct reduced order models and compute <em>a posteriori</em> error estimates. The error estimates allow us to efficiently explore the parameter space and select parameter points that improve the efficiency and accuracy of the reduced order model. Through numerical experiments, we demonstrate that the generative RB method not only improves the accuracy of the reduced order model but also provides tight error estimates.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"437 ","pages":"Article 117754"},"PeriodicalIF":6.9,"publicationDate":"2025-01-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143071654","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}
Pub Date : 2025-01-30DOI: 10.1016/j.cma.2025.117788
C. Caballero-Cárdenas , I. Gómez-Bueno , A. Del Grosso , J. Koellermeier , T. Morales de Luna
When dealing with shallow water simulations, the velocity profile is often assumed to be constant along the vertical axis. However, since in many applications this is not the case, modeling errors can be significant. Hence, in this work, we deal with the Shallow Water Linearized Moment Equations (SWLME), in which the velocity is no longer constant in the vertical direction, where a polynomial expansion around the mean value is considered. The linearized version implies neglecting the non-linear terms of the basis coefficients in the higher order equations. As a result, the model is always hyperbolic and the stationary solutions can be more easily computed. Then, our objective is to propose an efficient, accurate and robust numerical scheme for the SWLME model, specially adapted for low Froude number situations. Hence, we describe a semi-implicit second order exactly fully well-balanced method. More specifically, a splitting is performed to separate acoustic and material phenomena. The acoustic waves are treated in an implicit manner to gain in efficiency when dealing with subsonic flow regimes, whereas the second order of accuracy is achieved thanks to a polynomial reconstruction and Strang-splitting method. We also exploit a reconstruction operator to achieve the fully well-balanced character of the method. Extensive numerical tests demonstrate the well-balanced properties and large speed-up compared to traditional methods.
{"title":"A semi-implicit exactly fully well-balanced relaxation scheme for the Shallow Water Linearized Moment Equations","authors":"C. Caballero-Cárdenas , I. Gómez-Bueno , A. Del Grosso , J. Koellermeier , T. Morales de Luna","doi":"10.1016/j.cma.2025.117788","DOIUrl":"10.1016/j.cma.2025.117788","url":null,"abstract":"<div><div>When dealing with shallow water simulations, the velocity profile is often assumed to be constant along the vertical axis. However, since in many applications this is not the case, modeling errors can be significant. Hence, in this work, we deal with the Shallow Water Linearized Moment Equations (SWLME), in which the velocity is no longer constant in the vertical direction, where a polynomial expansion around the mean value is considered. The linearized version implies neglecting the non-linear terms of the basis coefficients in the higher order equations. As a result, the model is always hyperbolic and the stationary solutions can be more easily computed. Then, our objective is to propose an efficient, accurate and robust numerical scheme for the SWLME model, specially adapted for low Froude number situations. Hence, we describe a semi-implicit second order exactly fully well-balanced method. More specifically, a splitting is performed to separate acoustic and material phenomena. The acoustic waves are treated in an implicit manner to gain in efficiency when dealing with subsonic flow regimes, whereas the second order of accuracy is achieved thanks to a polynomial reconstruction and Strang-splitting method. We also exploit a reconstruction operator to achieve the fully well-balanced character of the method. Extensive numerical tests demonstrate the well-balanced properties and large speed-up compared to traditional methods.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"437 ","pages":"Article 117788"},"PeriodicalIF":6.9,"publicationDate":"2025-01-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143071611","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}
Pub Date : 2025-01-30DOI: 10.1016/j.cma.2025.117773
Nataly A. Manque , Jan Liedmann , Franz-Joseph Barthold , Marcos A. Valdebenito , Matthias G.R. Faes
Geometric uncertainty poses a significant challenge in many engineering sub-disciplines ranging from structural design to manufacturing processes, often attributed to the underlying manufacturing technology and operating conditions. When combined with geometric complexity, this phenomenon can result in substantial disparities between numerical predictions and the actual behavior of mechanical systems. One of the underlying causes lies in the initial design phase, where insufficient information impedes the development of robust numerical models due to epistemic uncertainty in system dimensions. In such cases, set-based methods, like intervals, prove useful for characterizing these uncertainties by employing lower and upper bounds to define uncertain input parameters. Nevertheless, employing interval methods for treating geometric uncertainties can become computationally demanding, especially when traditional methods like finite element analysis (FEA) are utilized to represent the system. This is due to the necessity of performing iterative analyses for different realizations of geometry within the bounds of uncertain parameters, requiring the repeated execution of the meshing process and thereby escalating the numerical effort. Moreover, the process of remeshing introduces a second challenge by disrupting the continuity of the underlying optimization problem inherent in interval analysis, further complicating the computational procedure. In this work, the potential of Isogeometric Analysis (IGA) for quantifying geometric uncertainties characterized by intervals is explored. IGA utilizes the same basis functions, Non-Uniform Rational B-Splines (NURBS), employed in Computer-Aided Design (CAD) to approximate solution fields in numerical analysis. This integration enhances the accurate description of complex shapes and interfaces while maintaining geometric fidelity throughout the simulation process. The primary advantage of employing IGA for uncertainty quantification lies in its ability to control the system’s geometry through the position of control points, which define the shape of NURBS. Consequently, alterations in the model’s geometry can be achieved by varying the position of these control points, thereby bypassing the numerical costs associated with remeshing when performing uncertainty quantification considering intervals. To propagate geometric uncertainties, a gradient-based optimization (GBO) algorithm is applied to determine the lower and upper bounds of the system response. The corresponding sensitivities are computed from the IGA model with a variational approach. Two case studies involving linear systems with uncertain geometric parameters demonstrate that the proposed strategy accurately estimates uncertain stress triaxiality.
{"title":"Interval Isogeometric Analysis for coping with geometric uncertainty","authors":"Nataly A. Manque , Jan Liedmann , Franz-Joseph Barthold , Marcos A. Valdebenito , Matthias G.R. Faes","doi":"10.1016/j.cma.2025.117773","DOIUrl":"10.1016/j.cma.2025.117773","url":null,"abstract":"<div><div>Geometric uncertainty poses a significant challenge in many engineering sub-disciplines ranging from structural design to manufacturing processes, often attributed to the underlying manufacturing technology and operating conditions. When combined with geometric complexity, this phenomenon can result in substantial disparities between numerical predictions and the actual behavior of mechanical systems. One of the underlying causes lies in the initial design phase, where insufficient information impedes the development of robust numerical models due to epistemic uncertainty in system dimensions. In such cases, set-based methods, like intervals, prove useful for characterizing these uncertainties by employing lower and upper bounds to define uncertain input parameters. Nevertheless, employing interval methods for treating geometric uncertainties can become computationally demanding, especially when traditional methods like finite element analysis (FEA) are utilized to represent the system. This is due to the necessity of performing iterative analyses for different realizations of geometry within the bounds of uncertain parameters, requiring the repeated execution of the meshing process and thereby escalating the numerical effort. Moreover, the process of remeshing introduces a second challenge by disrupting the continuity of the underlying optimization problem inherent in interval analysis, further complicating the computational procedure. In this work, the potential of Isogeometric Analysis (IGA) for quantifying geometric uncertainties characterized by intervals is explored. IGA utilizes the same basis functions, Non-Uniform Rational B-Splines (NURBS), employed in Computer-Aided Design (CAD) to approximate solution fields in numerical analysis. This integration enhances the accurate description of complex shapes and interfaces while maintaining geometric fidelity throughout the simulation process. The primary advantage of employing IGA for uncertainty quantification lies in its ability to control the system’s geometry through the position of control points, which define the shape of NURBS. Consequently, alterations in the model’s geometry can be achieved by varying the position of these control points, thereby bypassing the numerical costs associated with remeshing when performing uncertainty quantification considering intervals. To propagate geometric uncertainties, a gradient-based optimization (GBO) algorithm is applied to determine the lower and upper bounds of the system response. The corresponding sensitivities are computed from the IGA model with a variational approach. Two case studies involving linear systems with uncertain geometric parameters demonstrate that the proposed strategy accurately estimates uncertain stress triaxiality.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"437 ","pages":"Article 117773"},"PeriodicalIF":6.9,"publicationDate":"2025-01-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143071613","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}
Pub Date : 2025-01-30DOI: 10.1016/j.cma.2025.117787
Jinshuai Bai , Zhongya Lin , Yizheng Wang , Jiancong Wen , Yinghua Liu , Timon Rabczuk , YuanTong Gu , Xi-Qiao Feng
Numerical methods for contact mechanics are of great importance in engineering applications, enabling the prediction and analysis of complex surface interactions under various conditions. In this work, we propose an energy-based physics-informed neural network (PINN) framework for solving frictionless contact problems under large deformation. Inspired by microscopic Lennard-Jones potential, a surface contact energy is used to describe the contact phenomena. To ensure the robustness of the proposed PINN framework, relaxation, gradual loading and output scaling techniques are introduced. In the numerical examples, the well-known Hertz contact benchmark problem is conducted, demonstrating the effectiveness and robustness of the proposed PINN framework. Moreover, challenging contact problems with the consideration of geometrical and material nonlinearities are tested. It has been shown that the proposed PINN framework provides a reliable and powerful tool for nonlinear contact mechanics. More importantly, the proposed PINN framework exhibits competitive computational efficiency to the commercial FEM software when dealing with those complex contact problems. The codes used in this manuscript are available at https://github.com/JinshuaiBai/energy_PINN_Contact.
{"title":"Energy-based physics-informed neural network for frictionless contact problems under large deformation","authors":"Jinshuai Bai , Zhongya Lin , Yizheng Wang , Jiancong Wen , Yinghua Liu , Timon Rabczuk , YuanTong Gu , Xi-Qiao Feng","doi":"10.1016/j.cma.2025.117787","DOIUrl":"10.1016/j.cma.2025.117787","url":null,"abstract":"<div><div>Numerical methods for contact mechanics are of great importance in engineering applications, enabling the prediction and analysis of complex surface interactions under various conditions. In this work, we propose an energy-based physics-informed neural network (PINN) framework for solving frictionless contact problems under large deformation. Inspired by microscopic Lennard-Jones potential, a surface contact energy is used to describe the contact phenomena. To ensure the robustness of the proposed PINN framework, relaxation, gradual loading and output scaling techniques are introduced. In the numerical examples, the well-known Hertz contact benchmark problem is conducted, demonstrating the effectiveness and robustness of the proposed PINN framework. Moreover, challenging contact problems with the consideration of geometrical and material nonlinearities are tested. It has been shown that the proposed PINN framework provides a reliable and powerful tool for nonlinear contact mechanics. More importantly, the proposed PINN framework exhibits competitive computational efficiency to the commercial FEM software when dealing with those complex contact problems. The codes used in this manuscript are available at <span><span>https://github.com/JinshuaiBai/energy_PINN_Contact</span><svg><path></path></svg></span>.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"437 ","pages":"Article 117787"},"PeriodicalIF":6.9,"publicationDate":"2025-01-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143071653","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}
Pub Date : 2025-01-29DOI: 10.1016/j.cma.2025.117782
Rami Cassia, Rich Kerswell
Machine learning techniques are being used as an alternative to traditional numerical discretization methods for solving hyperbolic partial differential equations (PDEs) relevant to fluid flow. Whilst numerical methods are higher fidelity, they are computationally expensive. Machine learning methods on the other hand are lower fidelity but can provide significant speed-ups. The emergence of physics-informed neural networks (PINNs) in fluid dynamics has allowed scientists to directly use PDEs for evaluating loss functions. The downfall of this approach is that the differential form of systems is invalid at regions of shock inherent in hyperbolic PDEs such as the compressible Euler equations. To circumvent this problem we propose the Godunov loss function: a loss based on the finite volume method (FVM) that crucially incorporates the flux of Godunov-type methods. These Godunov-type methods are also known as approximate Riemann solvers and evaluate intercell fluxes in an entropy-satisfying and non-oscillatory manner, yielding more physically accurate shocks. Our approach leads to superior performance compared to standard PINNs that use regularized PDE-based losses as well as FVM-based losses, as tested on the 2D Riemann problem in the context of time-stepping and super-resolution reconstruction.
{"title":"Godunov loss functions for modelling of hyperbolic conservation laws","authors":"Rami Cassia, Rich Kerswell","doi":"10.1016/j.cma.2025.117782","DOIUrl":"10.1016/j.cma.2025.117782","url":null,"abstract":"<div><div>Machine learning techniques are being used as an alternative to traditional numerical discretization methods for solving hyperbolic partial differential equations (PDEs) relevant to fluid flow. Whilst numerical methods are higher fidelity, they are computationally expensive. Machine learning methods on the other hand are lower fidelity but can provide significant speed-ups. The emergence of physics-informed neural networks (PINNs) in fluid dynamics has allowed scientists to directly use PDEs for evaluating loss functions. The downfall of this approach is that the differential form of systems is invalid at regions of shock inherent in hyperbolic PDEs such as the compressible Euler equations. To circumvent this problem we propose the Godunov loss function: a loss based on the finite volume method (FVM) that crucially incorporates the flux of Godunov-type methods. These Godunov-type methods are also known as approximate Riemann solvers and evaluate intercell fluxes in an entropy-satisfying and non-oscillatory manner, yielding more physically accurate shocks. Our approach leads to superior performance compared to standard PINNs that use regularized PDE-based losses as well as FVM-based losses, as tested on the 2D Riemann problem in the context of time-stepping and super-resolution reconstruction.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"437 ","pages":"Article 117782"},"PeriodicalIF":6.9,"publicationDate":"2025-01-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143071655","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}
Pub Date : 2025-01-29DOI: 10.1016/j.cma.2025.117779
Stephan Wulfinghoff
In computational homogenization, the microscopic problem is regularly solved via Galerkin-projection methods to speed up the computation. By evaluating the involved integrals by hyper-reduction techniques, a very high efficiency can be achieved. Here, a novel hyper-reduction method is proposed and applied to magnetostatics. The method combines the ideas of microstructural clustering with the empirical identification/correction of a reduced set of integration points, not being taken from the set of finite element integration points. The results show that the macroscopic response (2D) is hardly distinguishable from the finite element results already for 12 integration points at a phase contrast of 1000 for a porous microstructure. The online costs (but also the offline costs) are thus found to be particularly low. Further, a two-scale example is discussed and the code is made available online.
{"title":"Empirically corrected cluster cubature (E3C)","authors":"Stephan Wulfinghoff","doi":"10.1016/j.cma.2025.117779","DOIUrl":"10.1016/j.cma.2025.117779","url":null,"abstract":"<div><div>In computational homogenization, the microscopic problem is regularly solved via Galerkin-projection methods to speed up the computation. By evaluating the involved integrals by hyper-reduction techniques, a very high efficiency can be achieved. Here, a novel hyper-reduction method is proposed and applied to magnetostatics. The method combines the ideas of microstructural clustering with the empirical identification/correction of a reduced set of integration points, <em>not</em> being taken from the set of finite element integration points. The results show that the macroscopic response (2D) is hardly distinguishable from the finite element results already for 12 integration points at a phase contrast of <span><math><mo>∼</mo></math></span>1000 for a porous microstructure. The online costs (but also the offline costs) are thus found to be particularly low. Further, a two-scale example is discussed and the code is made available online.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"437 ","pages":"Article 117779"},"PeriodicalIF":6.9,"publicationDate":"2025-01-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143071661","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}
Pub Date : 2025-01-29DOI: 10.1016/j.cma.2025.117761
Shengjun Liu, Hanchao Liu, Ting Zhang, Xinru Liu
Geometric partial differential equations (geometric PDEs) are defined on manifolds in Riemannian space, specifically tailored for modeling the temporal evolution of surfaces in natural sciences and engineering. For varying initial surfaces (initial conditions), traditional numerical methods require re-solving the equation even for the same geometric PDE, which significantly hinders the efficiency of simulations. The efficient predictive capabilities of neural networks (NNs) makes them a powerful tool for solving differential equations. The solution of geometric PDEs governs the continuous evolution of the surface over time, making it challenging for most NNs to handle solution prediction for geometric PDEs with varying initial surfaces. We propose a novel neural operator-based framework for solving geometric PDEs. Once trained, our model can predict the solution of the same geometric PDE under arbitrary initial conditions (initial surfaces). To the best of our knowledge, this is the first attempt to solve geometric PDEs using the neural operator. Firstly, we employ a learned continuous Signed Distance Function (SDF) representation method (DeepSDF) to convert the initial mesh surface into an implicit level-set representation, thereby avoiding the difficulties associated with solving explicit geometric PDEs. Subsequently, by integrating the multi-scale module, we design a Multi-Scale Implicit U-Net enhanced Factorized Fourier Neural Operator (MS-IUFFNO) for solving implicit geometric PDEs. The innovative structure of the neural operator substantially improves the prediction accuracy and long-term stability for solving geometric PDEs with reduced computational complexity. In addition, we construct datasets to train neural operators to solve the mean curvature flow and Willmore flow, which are representative of geometric PDEs. Finally, a numerical benchmark is conducted to compare MS-IUFFNO to several classical neural operator models for solving the mean curvature flow and Willmore flow, where results show that our model exhibits superior performance in terms of prediction accuracy, extrapolation capability, and stability.
{"title":"MS-IUFFNO: Multi-scale implicit U-net enhanced factorized fourier neural operator for solving geometric PDEs","authors":"Shengjun Liu, Hanchao Liu, Ting Zhang, Xinru Liu","doi":"10.1016/j.cma.2025.117761","DOIUrl":"10.1016/j.cma.2025.117761","url":null,"abstract":"<div><div>Geometric partial differential equations (geometric PDEs) are defined on manifolds in Riemannian space, specifically tailored for modeling the temporal evolution of surfaces in natural sciences and engineering. For varying initial surfaces (initial conditions), traditional numerical methods require re-solving the equation even for the same geometric PDE, which significantly hinders the efficiency of simulations. The efficient predictive capabilities of neural networks (NNs) makes them a powerful tool for solving differential equations. The solution of geometric PDEs governs the continuous evolution of the surface over time, making it challenging for most NNs to handle solution prediction for geometric PDEs with varying initial surfaces. We propose a novel neural operator-based framework for solving geometric PDEs. Once trained, our model can predict the solution of the same geometric PDE under arbitrary initial conditions (initial surfaces). To the best of our knowledge, this is the first attempt to solve geometric PDEs using the neural operator. Firstly, we employ a learned continuous Signed Distance Function (SDF) representation method (DeepSDF) to convert the initial mesh surface into an implicit level-set representation, thereby avoiding the difficulties associated with solving explicit geometric PDEs. Subsequently, by integrating the multi-scale module, we design a Multi-Scale Implicit U-Net enhanced Factorized Fourier Neural Operator (MS-IUFFNO) for solving implicit geometric PDEs. The innovative structure of the neural operator substantially improves the prediction accuracy and long-term stability for solving geometric PDEs with reduced computational complexity. In addition, we construct datasets to train neural operators to solve the mean curvature flow and Willmore flow, which are representative of geometric PDEs. Finally, a numerical benchmark is conducted to compare MS-IUFFNO to several classical neural operator models for solving the mean curvature flow and Willmore flow, where results show that our model exhibits superior performance in terms of prediction accuracy, extrapolation capability, and stability.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"437 ","pages":"Article 117761"},"PeriodicalIF":6.9,"publicationDate":"2025-01-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143071660","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}
Pub Date : 2025-01-28DOI: 10.1016/j.cma.2025.117753
Xianghao Meng , James L. Beck , Yong Huang , Hui Li
In the last few decades, Markov chain Monte Carlo (MCMC) methods have been widely applied to Bayesian updating of structural dynamic models in the field of structural health monitoring. Recently, several MCMC algorithms have been developed that incorporate neural networks to enhance their performance for specific Bayesian model updating problems. However, a common challenge with these approaches lies in the fact that the embedded neural networks often necessitate retraining when faced with new tasks, a process that is time-consuming and significantly undermines the competitiveness of these methods. This paper introduces a newly developed adaptive meta-learning stochastic gradient Hamiltonian Monte Carlo (AM-SGHMC) algorithm. The idea behind AM-SGHMC is to optimize the sampling strategy by training adaptive neural networks, and due to the adaptive design of the network inputs and outputs, the trained sampler can be directly applied to various Bayesian updating problems of the same type of structure without further training, thereby achieving meta-learning. Additionally, practical issues for the feasibility of the AM-SGHMC algorithm for structural dynamic model updating are addressed, and two examples involving Bayesian updating of multi-story building models with different model fidelity are used to demonstrate the effectiveness and generalization ability of the proposed method.
{"title":"Adaptive meta-learning stochastic gradient Hamiltonian Monte Carlo simulation for Bayesian updating of structural dynamic models","authors":"Xianghao Meng , James L. Beck , Yong Huang , Hui Li","doi":"10.1016/j.cma.2025.117753","DOIUrl":"10.1016/j.cma.2025.117753","url":null,"abstract":"<div><div>In the last few decades, Markov chain Monte Carlo (MCMC) methods have been widely applied to Bayesian updating of structural dynamic models in the field of structural health monitoring. Recently, several MCMC algorithms have been developed that incorporate neural networks to enhance their performance for specific Bayesian model updating problems. However, a common challenge with these approaches lies in the fact that the embedded neural networks often necessitate retraining when faced with new tasks, a process that is time-consuming and significantly undermines the competitiveness of these methods. This paper introduces a newly developed adaptive meta-learning stochastic gradient Hamiltonian Monte Carlo (AM-SGHMC) algorithm. The idea behind AM-SGHMC is to optimize the sampling strategy by training adaptive neural networks, and due to the adaptive design of the network inputs and outputs, the trained sampler can be directly applied to various Bayesian updating problems of the same type of structure without further training, thereby achieving meta-learning. Additionally, practical issues for the feasibility of the AM-SGHMC algorithm for structural dynamic model updating are addressed, and two examples involving Bayesian updating of multi-story building models with different model fidelity are used to demonstrate the effectiveness and generalization ability of the proposed method.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"437 ","pages":"Article 117753"},"PeriodicalIF":6.9,"publicationDate":"2025-01-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143096635","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}
Pub Date : 2025-01-28DOI: 10.1016/j.cma.2025.117777
Han Dong , Hongjiang Wang , Jiahao Zhong , Chaohui Huang , Weizhe Wang , Yingzheng Liu
A reduced-order peridynamic (PD) model is developed to accelerate fracture simulations of composite materials. This reduced-order PD model is constructed based on a set of projection basis functions extracted from the flexibility matrix corresponding to the initial configuration, rather than from snapshots. Thus, this approach eliminates dependence on datasets with prior knowledge, resulting in superior generalization. During the calculation, the projection basis functions are adaptively updated with the damage evolution. Several two- and three-dimensional numerical examples involving the fracture of composites are investigated to validate the numerical accuracy and computational efficiency of the model. The proposed model accurately captures various fracture characteristics while significantly improving the computational efficiency. This work presents a feasible approach for accelerating fracture simulations, which is of great significance for shortening the design cycle of composite materials and enhancing the efficiency of failure analysis.
{"title":"A snapshot-free reduced-order peridynamic model for accelerating fracture analysis of composites","authors":"Han Dong , Hongjiang Wang , Jiahao Zhong , Chaohui Huang , Weizhe Wang , Yingzheng Liu","doi":"10.1016/j.cma.2025.117777","DOIUrl":"10.1016/j.cma.2025.117777","url":null,"abstract":"<div><div>A reduced-order peridynamic (PD) model is developed to accelerate fracture simulations of composite materials. This reduced-order PD model is constructed based on a set of projection basis functions extracted from the flexibility matrix corresponding to the initial configuration, rather than from snapshots. Thus, this approach eliminates dependence on datasets with prior knowledge, resulting in superior generalization. During the calculation, the projection basis functions are adaptively updated with the damage evolution. Several two- and three-dimensional numerical examples involving the fracture of composites are investigated to validate the numerical accuracy and computational efficiency of the model. The proposed model accurately captures various fracture characteristics while significantly improving the computational efficiency. This work presents a feasible approach for accelerating fracture simulations, which is of great significance for shortening the design cycle of composite materials and enhancing the efficiency of failure analysis.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"437 ","pages":"Article 117777"},"PeriodicalIF":6.9,"publicationDate":"2025-01-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143072093","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}
Pub Date : 2025-01-27DOI: 10.1016/j.cma.2025.117736
Riccardo Pellegrini , Zhaoyuan Wang , Frederick Stern , Matteo Diez
This paper introduces a nonlinear structural reduced order model (ROM) specifically developed for fluid–structure interaction (FSI) simulations involving high impact loads and large deflections, such as those arising in water slamming of flexible structures. The model is based on a nonlinear modal expansion trained offline using prestressed eigenfrequency analyses performed by nonlinear full-order computational structural dynamics based on finite elements. The training uses the eigenfrequencies as a function of the deflection and is non-intrusive, which means that the knowledge of the system’s full-order matrices is not required. Eigenfrequencies and deflections are evaluated under a prescribed set of static loads, which are derived from fully transient computational fluid dynamics (CFD) simulations. The resulting ROM is coupled with CFD using partitioned one- and two-way FSI schemes. Focusing on the impact of an elastic aluminum plate onto still water, the research investigates scenarios with varied horizontal and vertical velocities in three distinct experimental conditions, which cover moderate to strong hydroelastic interactions. Namely, the proposed nonlinear ROM and its linear counterpart are assessed against two FSI benchmark sets. The first set consists in comparing the ROM versus the full-order model (FOM) under prescribed external load, via one-way FSI coupling. The second set consists in comparing the ROM versus experimental data, via two-way tightly-coupled FSI. Comparisons of the nonlinear ROM versus the FOM under prescribed loads achieve an average error equal to 2.7%. Comparisons of the nonlinear ROM under two-way tightly-coupled FSI versus experiments show an average error equal to 4.5%. Comparisons of nonlinear versus linear ROM highlight the need for nonlinear models to accurately capture peak values and trends, especially in scenarios with large deflections.
{"title":"A non-intrusive nonlinear structural ROM for partitioned two-way fluid–structure interaction computations","authors":"Riccardo Pellegrini , Zhaoyuan Wang , Frederick Stern , Matteo Diez","doi":"10.1016/j.cma.2025.117736","DOIUrl":"10.1016/j.cma.2025.117736","url":null,"abstract":"<div><div>This paper introduces a nonlinear structural reduced order model (ROM) specifically developed for fluid–structure interaction (FSI) simulations involving high impact loads and large deflections, such as those arising in water slamming of flexible structures. The model is based on a nonlinear modal expansion trained offline using prestressed eigenfrequency analyses performed by nonlinear full-order computational structural dynamics based on finite elements. The training uses the eigenfrequencies as a function of the deflection and is non-intrusive, which means that the knowledge of the system’s full-order matrices is not required. Eigenfrequencies and deflections are evaluated under a prescribed set of static loads, which are derived from fully transient computational fluid dynamics (CFD) simulations. The resulting ROM is coupled with CFD using partitioned one- and two-way FSI schemes. Focusing on the impact of an elastic aluminum plate onto still water, the research investigates scenarios with varied horizontal and vertical velocities in three distinct experimental conditions, which cover moderate to strong hydroelastic interactions. Namely, the proposed nonlinear ROM and its linear counterpart are assessed against two FSI benchmark sets. The first set consists in comparing the ROM versus the full-order model (FOM) under prescribed external load, via one-way FSI coupling. The second set consists in comparing the ROM versus experimental data, via two-way tightly-coupled FSI. Comparisons of the nonlinear ROM versus the FOM under prescribed loads achieve an average error equal to 2.7%. Comparisons of the nonlinear ROM under two-way tightly-coupled FSI versus experiments show an average error equal to 4.5%. Comparisons of nonlinear versus linear ROM highlight the need for nonlinear models to accurately capture peak values and trends, especially in scenarios with large deflections.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"437 ","pages":"Article 117736"},"PeriodicalIF":6.9,"publicationDate":"2025-01-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143071664","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}
扫码关注我们
求助内容：
应助结果提醒方式：
京公网安备 11010802042870号