The complex structure of bituminous mixtures ranging from nanoscale binder components to macroscale pavement performance requires a comprehensive approach to material characterization and performance prediction. This paper provides a critical analysis of advanced techniques in paving materials modeling. It focuses on four main approaches: finite element method (FEM), discrete element method (DEM), phase field method (PFM), and artificial neural networks (ANNs). The review highlights how these computational methods enable more accurate predictions of material behavior, from asphalt binder rheology to mixture performance, while reducing reliance on extensive empirical testing. Key advances, such as the smooth integration of information across multiple scales and the emergence of physics-informed neural networks (PINNs), are discussed as promising avenues for enhancing model accuracy and computational efficiency. This review not only provides a comprehensive overview of current methodologies but also outlines future research directions aimed at developing more sustainable, cost-effective, and durable paving solutions through advanced multiscale modeling techniques.
{"title":"Exploring the roles of numerical simulations and machine learning in multiscale paving materials analysis: Applications, challenges, best practices","authors":"Mahmoud Khadijeh, Cor Kasbergen, Sandra Erkens, Aikaterini Varveri","doi":"10.1016/j.cma.2024.117462","DOIUrl":"10.1016/j.cma.2024.117462","url":null,"abstract":"<div><div>The complex structure of bituminous mixtures ranging from nanoscale binder components to macroscale pavement performance requires a comprehensive approach to material characterization and performance prediction. This paper provides a critical analysis of advanced techniques in paving materials modeling. It focuses on four main approaches: finite element method (FEM), discrete element method (DEM), phase field method (PFM), and artificial neural networks (ANNs). The review highlights how these computational methods enable more accurate predictions of material behavior, from asphalt binder rheology to mixture performance, while reducing reliance on extensive empirical testing. Key advances, such as the smooth integration of information across multiple scales and the emergence of physics-informed neural networks (PINNs), are discussed as promising avenues for enhancing model accuracy and computational efficiency. This review not only provides a comprehensive overview of current methodologies but also outlines future research directions aimed at developing more sustainable, cost-effective, and durable paving solutions through advanced multiscale modeling techniques.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"433 ","pages":"Article 117462"},"PeriodicalIF":6.9,"publicationDate":"2024-10-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142529319","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 : 2024-10-28DOI: 10.1016/j.cma.2024.117471
Tianyi Hu, Hector Gomez
Partial differential equations whose solution is dominated by a combination of hyperbolic and dispersive waves are common in multiphase flows. We show that for these problems, the application of classical stabilized finite elements based on Streamline-Upwind/Petrov–Galerkin (SUPG) without accounting for the dispersive features of the solution leads to a downwind discretization and an unstable numerical solution. To address this challenge, we propose the Dispersive-SUPG (D-SUPG) formulation. We apply the Dispersive-SUPG formulation to the Korteweg–de Vries equation and Direct van der Waals Simulations. Numerical results show that Dispersive-SUPG is a high-order accurate and efficient stabilized method, capable of producing stable results when the solution is dominated by either hyperbolic or dispersive waves. We finally applied the proposed algorithm to study cavitating flow over a 2D wedge and a 3D hemisphere and obtained good agreement with theory and experiments.
{"title":"Quo vadis, wave? Dispersive-SUPG for direct van der Waals simulation (DVS)","authors":"Tianyi Hu, Hector Gomez","doi":"10.1016/j.cma.2024.117471","DOIUrl":"10.1016/j.cma.2024.117471","url":null,"abstract":"<div><div>Partial differential equations whose solution is dominated by a combination of hyperbolic and dispersive waves are common in multiphase flows. We show that for these problems, the application of classical stabilized finite elements based on Streamline-Upwind/Petrov–Galerkin (SUPG) without accounting for the dispersive features of the solution leads to a <em>downwind</em> discretization and an unstable numerical solution. To address this challenge, we propose the Dispersive-SUPG (D-SUPG) formulation. We apply the Dispersive-SUPG formulation to the Korteweg–de Vries equation and Direct van der Waals Simulations. Numerical results show that Dispersive-SUPG is a high-order accurate and efficient stabilized method, capable of producing stable results when the solution is dominated by either hyperbolic or dispersive waves. We finally applied the proposed algorithm to study cavitating flow over a 2D wedge and a 3D hemisphere and obtained good agreement with theory and experiments.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"433 ","pages":"Article 117471"},"PeriodicalIF":6.9,"publicationDate":"2024-10-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142529235","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 : 2024-10-25DOI: 10.1016/j.cma.2024.117467
Jingwen Song , Zhanhua Liang , Pengfei Wei , Michael Beer
Bayesian (probabilistic) model updating is a fundamental concept in computational science, allowing for the incorporation of prior beliefs with observed data to reduce prediction uncertainty of a computer simulator. However, the efficient evaluation of posterior probability density functions (PDFs) of model parameters poses challenges, particularly for computationally expansive simulators. This work presents a sampling-based adaptive Bayesian quadrature method to fill this gap. The method is based on approximating the simulator under investigation with a Gaussian process (GP) model, and then a conditional sampling procedure is introduced for generating sample paths, this way to infer a probability distribution for the evidence term. This inferred probability distribution indeed measures the prediction uncertainty of the evidence term, and thus based on which, an acquisition function is proposed to identify the site at which the prediction uncertainty of the GP model contributes the most to that of the evidence term. All the above ingredients finally form an adaptive algorithm for updating the posterior PDFs of model parameters with pre-specified accuracy tolerance. Case studies across numerical examples and engineering applications validate the ability of the proposed method to deal with multi-modal problems, and demonstrate its superiority in terms of computational efficiency and precision for estimating model evidence and posterior PDFs.
贝叶斯（概率）模型更新是计算科学中的一个基本概念，它允许将先验信念与观测数据相结合，以减少计算机模拟器预测的不确定性。然而，对模型参数的后验概率密度函数（PDF）进行有效评估是一项挑战，尤其是对计算量巨大的模拟器而言。本研究提出了一种基于采样的自适应贝叶斯正交方法来填补这一空白。该方法基于用高斯过程（GP）模型逼近所研究的模拟器，然后引入条件采样程序生成样本路径，从而推断出证据项的概率分布。这种推断出的概率分布确实衡量了证据项的预测不确定性，因此在此基础上提出了一种获取函数，以确定 GP 模型的预测不确定性对证据项的预测不确定性影响最大的位置。所有上述要素最终形成了一种自适应算法，用于更新模型参数的后验 PDF，并预先指定精度容限。通过对数值实例和工程应用的案例研究，验证了所提方法处理多模式问题的能力，并证明了其在估计模型证据和后验 PDF 的计算效率和精度方面的优越性。
{"title":"Sampling-based adaptive Bayesian quadrature for probabilistic model updating","authors":"Jingwen Song , Zhanhua Liang , Pengfei Wei , Michael Beer","doi":"10.1016/j.cma.2024.117467","DOIUrl":"10.1016/j.cma.2024.117467","url":null,"abstract":"<div><div>Bayesian (probabilistic) model updating is a fundamental concept in computational science, allowing for the incorporation of prior beliefs with observed data to reduce prediction uncertainty of a computer simulator. However, the efficient evaluation of posterior probability density functions (PDFs) of model parameters poses challenges, particularly for computationally expansive simulators. This work presents a sampling-based adaptive Bayesian quadrature method to fill this gap. The method is based on approximating the simulator under investigation with a Gaussian process (GP) model, and then a conditional sampling procedure is introduced for generating sample paths, this way to infer a probability distribution for the evidence term. This inferred probability distribution indeed measures the prediction uncertainty of the evidence term, and thus based on which, an acquisition function is proposed to identify the site at which the prediction uncertainty of the GP model contributes the most to that of the evidence term. All the above ingredients finally form an adaptive algorithm for updating the posterior PDFs of model parameters with pre-specified accuracy tolerance. Case studies across numerical examples and engineering applications validate the ability of the proposed method to deal with multi-modal problems, and demonstrate its superiority in terms of computational efficiency and precision for estimating model evidence and posterior PDFs.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"433 ","pages":"Article 117467"},"PeriodicalIF":6.9,"publicationDate":"2024-10-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142529233","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 : 2024-10-25DOI: 10.1016/j.cma.2024.117478
Xiantao Fan , Deepak Akhare , Jian-Xun Wang
Simulating spatiotemporal turbulence with high fidelity remains a cornerstone challenge in computational fluid dynamics (CFD) due to its intricate multiscale nature and prohibitive computational demands. Traditional approaches typically employ closure models, which attempt to represent small-scale features in an unresolved manner. However, these methods often sacrifice accuracy and lose high-frequency/wavenumber information, especially in scenarios involving complex flow physics. In this paper, we introduce an innovative neural differentiable modeling framework designed to enhance the predictability and efficiency of spatiotemporal turbulence simulations. Our approach features differentiable hybrid modeling techniques that seamlessly integrate deep neural networks with numerical PDE solvers within a differentiable programming framework, synergizing deep learning with physics-based CFD modeling. Specifically, a hybrid differentiable neural solver is constructed on a coarser grid to capture large-scale turbulent phenomena, followed by the application of a Bayesian conditional diffusion model that generates small-scale turbulence conditioned on large-scale flow predictions. Two innovative hybrid architecture designs are studied, and their performance is evaluated through comparative analysis against conventional large eddy simulation techniques with physics-based subgrid-scale closures and purely data-driven neural solvers. The findings underscore the potential of the neural differentiable modeling framework to significantly enhance the accuracy and computational efficiency of turbulence simulations. This study not only demonstrates the efficacy of merging deep learning with physics-based numerical solvers but also sets a new precedent for advanced CFD modeling techniques, highlighting the transformative impact of differentiable programming in scientific computing.
{"title":"Neural differentiable modeling with diffusion-based super-resolution for two-dimensional spatiotemporal turbulence","authors":"Xiantao Fan , Deepak Akhare , Jian-Xun Wang","doi":"10.1016/j.cma.2024.117478","DOIUrl":"10.1016/j.cma.2024.117478","url":null,"abstract":"<div><div>Simulating spatiotemporal turbulence with high fidelity remains a cornerstone challenge in computational fluid dynamics (CFD) due to its intricate multiscale nature and prohibitive computational demands. Traditional approaches typically employ closure models, which attempt to represent small-scale features in an unresolved manner. However, these methods often sacrifice accuracy and lose high-frequency/wavenumber information, especially in scenarios involving complex flow physics. In this paper, we introduce an innovative neural differentiable modeling framework designed to enhance the predictability and efficiency of spatiotemporal turbulence simulations. Our approach features differentiable hybrid modeling techniques that seamlessly integrate deep neural networks with numerical PDE solvers within a differentiable programming framework, synergizing deep learning with physics-based CFD modeling. Specifically, a hybrid differentiable neural solver is constructed on a coarser grid to capture large-scale turbulent phenomena, followed by the application of a Bayesian conditional diffusion model that generates small-scale turbulence conditioned on large-scale flow predictions. Two innovative hybrid architecture designs are studied, and their performance is evaluated through comparative analysis against conventional large eddy simulation techniques with physics-based subgrid-scale closures and purely data-driven neural solvers. The findings underscore the potential of the neural differentiable modeling framework to significantly enhance the accuracy and computational efficiency of turbulence simulations. This study not only demonstrates the efficacy of merging deep learning with physics-based numerical solvers but also sets a new precedent for advanced CFD modeling techniques, highlighting the transformative impact of differentiable programming in scientific computing.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"433 ","pages":"Article 117478"},"PeriodicalIF":6.9,"publicationDate":"2024-10-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142529318","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 : 2024-10-24DOI: 10.1016/j.cma.2024.117455
Francisco S. Vieira, Aurélio L. Araújo
In this work we propose a novel peridynamic topology optimization formulation to improve fracture resistance. The main strength of peridynamics is based on the straightforwardness in which crack propagation can be predicted, as a natural part of a peridynamic numerical simulation. This property can be leveraged in a topology optimization framework, in order to obtain fracture resistance designs. Hence, we formulate a meshfree density-based nonlocal topology optimization framework using a bond-based peridynamic formulation. As it is demonstrated in this paper, the classical compliance based solutions are far from optimal in terms of fracture resistance and the designs obtained with the proposed formulation can provide fracture resistant solutions while only reducing slightly the structural stiffness. The proposed formulation is presented along with all the details of the sensitivity analysis and additional numerical aspects of the implementation. Moreover, the peridynamic material model used is presented along with its numerical implementation. Numerical examples demonstrate the accuracy of the computed sensitivities and illustrate the impact and effectiveness of the presented formulation. A thorough study of the optimization parameters is presented and various optimization convergence studies are taken in order to obtain a stable optimization process. All the results are compared to classical compliance minimization designs to illustrate the advantages and capabilities of the proposed framework.
{"title":"Peridynamic topology optimization to improve fracture resistance of structures","authors":"Francisco S. Vieira, Aurélio L. Araújo","doi":"10.1016/j.cma.2024.117455","DOIUrl":"10.1016/j.cma.2024.117455","url":null,"abstract":"<div><div>In this work we propose a novel peridynamic topology optimization formulation to improve fracture resistance. The main strength of peridynamics is based on the straightforwardness in which crack propagation can be predicted, as a natural part of a peridynamic numerical simulation. This property can be leveraged in a topology optimization framework, in order to obtain fracture resistance designs. Hence, we formulate a meshfree density-based nonlocal topology optimization framework using a bond-based peridynamic formulation. As it is demonstrated in this paper, the classical compliance based solutions are far from optimal in terms of fracture resistance and the designs obtained with the proposed formulation can provide fracture resistant solutions while only reducing slightly the structural stiffness. The proposed formulation is presented along with all the details of the sensitivity analysis and additional numerical aspects of the implementation. Moreover, the peridynamic material model used is presented along with its numerical implementation. Numerical examples demonstrate the accuracy of the computed sensitivities and illustrate the impact and effectiveness of the presented formulation. A thorough study of the optimization parameters is presented and various optimization convergence studies are taken in order to obtain a stable optimization process. All the results are compared to classical compliance minimization designs to illustrate the advantages and capabilities of the proposed framework.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"433 ","pages":"Article 117455"},"PeriodicalIF":6.9,"publicationDate":"2024-10-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142529321","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}
Snow exhibits unique mechanical behaviour due to its evolving properties influenced by temperature, stress conditions, and viscous effects. This paper introduces a nonlinear constitutive model for snow, featuring new formulations for the yield function and strain rate potential, and incorporating viscosity, sintering, and degradation effects. The model is numerically integrated into the Abaqus/Standard FEM software using a fully implicit backward Euler method for time integration and Powell’s hybrid method for linearizing the nonlinear system of equations. The robustness and stability of the numerical scheme ensure accurate simulation of snow behaviour under various loading conditions. The model is finally validated against experimental data available in the literature, demonstrating its effectiveness and reliability in capturing the complex mechanical response of snow.
雪因其受温度、应力条件和粘性效应影响而不断变化的特性，表现出独特的力学行为。本文介绍了雪的非线性结构模型，包括屈服函数和应变率势的新公式，并纳入了粘度、烧结和降解效应。该模型采用全隐式后向欧拉法进行时间积分，并采用鲍威尔混合法对非线性方程组进行线性化，从而在 Abaqus/Standard FEM 软件中实现了数值积分。数值方案的鲁棒性和稳定性确保了在各种加载条件下对雪地行为的精确模拟。该模型最后根据文献中的实验数据进行了验证，证明了其在捕捉雪的复杂机械响应方面的有效性和可靠性。
{"title":"An elasto-visco-plastic constitutive model for snow: Theory and finite element implementation","authors":"Gianmarco Vallero, Monica Barbero, Fabrizio Barpi, Mauro Borri-Brunetto, Valerio De Biagi","doi":"10.1016/j.cma.2024.117465","DOIUrl":"10.1016/j.cma.2024.117465","url":null,"abstract":"<div><div>Snow exhibits unique mechanical behaviour due to its evolving properties influenced by temperature, stress conditions, and viscous effects. This paper introduces a nonlinear constitutive model for snow, featuring new formulations for the yield function and strain rate potential, and incorporating viscosity, sintering, and degradation effects. The model is numerically integrated into the Abaqus/Standard FEM software using a fully implicit backward Euler method for time integration and Powell’s hybrid method for linearizing the nonlinear system of equations. The robustness and stability of the numerical scheme ensure accurate simulation of snow behaviour under various loading conditions. The model is finally validated against experimental data available in the literature, demonstrating its effectiveness and reliability in capturing the complex mechanical response of snow.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"433 ","pages":"Article 117465"},"PeriodicalIF":6.9,"publicationDate":"2024-10-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142529270","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 : 2024-10-24DOI: 10.1016/j.cma.2024.117425
Agnimitra Dasgupta , Harisankar Ramaswamy , Javier Murgoitio-Esandi , Ken Y. Foo , Runze Li , Qifa Zhou , Brendan F. Kennedy , Assad A. Oberai
We propose a framework to perform Bayesian inference using conditional score-based diffusion models to solve a class of inverse problems in mechanics involving the inference of a specimen’s spatially varying material properties from noisy measurements of its mechanical response to loading. Conditional score-based diffusion models are generative models that learn to approximate the score function of a conditional distribution using samples from the joint distribution. More specifically, the score functions corresponding to multiple realizations of the measurement are approximated using a single neural network, the so-called score network, which is subsequently used to sample the posterior distribution using an appropriate Markov chain Monte Carlo scheme based on Langevin dynamics. Training the score network only requires simulating the forward model. Hence, the proposed approach can accommodate black-box forward models and complex measurement noise. Moreover, once the score network has been trained, it can be re-used to solve the inverse problem for different realizations of the measurements. We demonstrate the efficacy of the proposed approach on a suite of high-dimensional inverse problems in mechanics that involve inferring heterogeneous material properties from noisy measurements. Some examples we consider involve synthetic data, while others include data collected from actual elastography experiments. Further, our applications demonstrate that the proposed approach can handle different measurement modalities, complex patterns in the inferred quantities, non-Gaussian and non-additive noise models, and nonlinear black-box forward models. The results show that the proposed framework can solve large-scale physics-based inverse problems efficiently.
{"title":"Conditional score-based diffusion models for solving inverse elasticity problems","authors":"Agnimitra Dasgupta , Harisankar Ramaswamy , Javier Murgoitio-Esandi , Ken Y. Foo , Runze Li , Qifa Zhou , Brendan F. Kennedy , Assad A. Oberai","doi":"10.1016/j.cma.2024.117425","DOIUrl":"10.1016/j.cma.2024.117425","url":null,"abstract":"<div><div>We propose a framework to perform Bayesian inference using conditional score-based diffusion models to solve a class of inverse problems in mechanics involving the inference of a specimen’s spatially varying material properties from noisy measurements of its mechanical response to loading. Conditional score-based diffusion models are generative models that learn to approximate the score function of a conditional distribution using samples from the joint distribution. More specifically, the score functions corresponding to multiple realizations of the measurement are approximated using a single neural network, the so-called score network, which is subsequently used to sample the posterior distribution using an appropriate Markov chain Monte Carlo scheme based on Langevin dynamics. Training the score network only requires simulating the forward model. Hence, the proposed approach can accommodate black-box forward models and complex measurement noise. Moreover, once the score network has been trained, it can be re-used to solve the inverse problem for different realizations of the measurements. We demonstrate the efficacy of the proposed approach on a suite of high-dimensional inverse problems in mechanics that involve inferring heterogeneous material properties from noisy measurements. Some examples we consider involve synthetic data, while others include data collected from actual elastography experiments. Further, our applications demonstrate that the proposed approach can handle different measurement modalities, complex patterns in the inferred quantities, non-Gaussian and non-additive noise models, and nonlinear black-box forward models. The results show that the proposed framework can solve large-scale physics-based inverse problems efficiently.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"433 ","pages":"Article 117425"},"PeriodicalIF":6.9,"publicationDate":"2024-10-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142529271","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 : 2024-10-24DOI: 10.1016/j.cma.2024.117457
Jiayuan Dong , Christian Jacobsen , Mehdi Khalloufi , Maryam Akram , Wanjiao Liu , Karthik Duraisamy , Xun Huan
Bayesian optimal experimental design (OED) seeks experiments that maximize the expected information gain (EIG) in model parameters. Directly estimating the EIG using nested Monte Carlo is computationally expensive and requires an explicit likelihood. Variational OED (vOED), in contrast, estimates a lower bound of the EIG without likelihood evaluations by approximating the posterior distributions with variational forms, and then tightens the bound by optimizing its variational parameters. We introduce the use of normalizing flows (NFs) for representing variational distributions in vOED; we call this approach vOED-NFs. Specifically, we adopt NFs with a conditional invertible neural network architecture built from compositions of coupling layers, and enhanced with a summary network for data dimension reduction. We present Monte Carlo estimators to the lower bound along with gradient expressions to enable a gradient-based simultaneous optimization of the variational parameters and the design variables. The vOED-NFs algorithm is then validated in two benchmark problems, and demonstrated on a partial differential equation-governed application of cathodic electrophoretic deposition and an implicit likelihood case with stochastic modeling of aphid population. The findings suggest that a composition of 4–5 coupling layers is able to achieve lower EIG estimation bias, under a fixed budget of forward model runs, compared to previous approaches. The resulting NFs produce approximate posteriors that agree well with the true posteriors, able to capture non-Gaussian and multi-modal features effectively.
{"title":"Variational Bayesian optimal experimental design with normalizing flows","authors":"Jiayuan Dong , Christian Jacobsen , Mehdi Khalloufi , Maryam Akram , Wanjiao Liu , Karthik Duraisamy , Xun Huan","doi":"10.1016/j.cma.2024.117457","DOIUrl":"10.1016/j.cma.2024.117457","url":null,"abstract":"<div><div>Bayesian optimal experimental design (OED) seeks experiments that maximize the expected information gain (EIG) in model parameters. Directly estimating the EIG using nested Monte Carlo is computationally expensive and requires an explicit likelihood. Variational OED (vOED), in contrast, estimates a lower bound of the EIG without likelihood evaluations by approximating the posterior distributions with variational forms, and then tightens the bound by optimizing its variational parameters. We introduce the use of normalizing flows (NFs) for representing variational distributions in vOED; we call this approach vOED-NFs. Specifically, we adopt NFs with a conditional invertible neural network architecture built from compositions of coupling layers, and enhanced with a summary network for data dimension reduction. We present Monte Carlo estimators to the lower bound along with gradient expressions to enable a gradient-based simultaneous optimization of the variational parameters and the design variables. The vOED-NFs algorithm is then validated in two benchmark problems, and demonstrated on a partial differential equation-governed application of cathodic electrophoretic deposition and an implicit likelihood case with stochastic modeling of aphid population. The findings suggest that a composition of 4–5 coupling layers is able to achieve lower EIG estimation bias, under a fixed budget of forward model runs, compared to previous approaches. The resulting NFs produce approximate posteriors that agree well with the true posteriors, able to capture non-Gaussian and multi-modal features effectively.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"433 ","pages":"Article 117457"},"PeriodicalIF":6.9,"publicationDate":"2024-10-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142529269","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 : 2024-10-24DOI: 10.1016/j.cma.2024.117461
Cheng Fu , Massimiliano Cremonesi , Umberto Perego , Blaž Hudobivnik , Peter Wriggers
Explicit solvers are commonly used for simulating fast dynamic and highly nonlinear engineering problems. However, these solvers are only conditionally stable, requiring very small time-step increments determined by the characteristic length of the smallest, and often most distorted, element in the mesh. In the Lagrangian description of fluid motion, the computational mesh quickly deteriorates. To circumvent this problem, the Particle Finite Element Method (PFEM) creates a new mesh (e.g., through a Delaunay tessellation, based on node positions) when the current one becomes overly distorted. A fast and efficient remeshing technique is therefore of pivotal importance for an effective PFEM implementation in explicit dynamics. Unfortunately, the 3D Delaunay tessellation does not guarantee well-shaped elements, often generating zero- or near-zero-volume elements (slivers), which drastically reduce the stable time-step size. Available mesh optimization techniques have limited applicability due to their high computational cost when runtime remeshing is required. An innovative possibility to overcome this problem is the use of the Virtual Element Method (VEM), a variant of the finite element method that can make use of polyhedral elements of arbitrary shapes and number of nodes. This paper presents the formulation of a 3D first-order Particle Virtual Element Method (PVEM) for weakly compressible flows. Starting from a tetrahedral mesh, poorly shaped elements, such as slivers, are agglomerated to form polyhedral Virtual Elements (VEs) with a controlled characteristic length. This approach ensures full control over the minimum time-step size in explicit dynamics simulations, maintaining stability throughout the entire analysis.
{"title":"Particle Virtual Element Method (PVEM): an agglomeration technique for mesh optimization in explicit Lagrangian free-surface fluid modelling","authors":"Cheng Fu , Massimiliano Cremonesi , Umberto Perego , Blaž Hudobivnik , Peter Wriggers","doi":"10.1016/j.cma.2024.117461","DOIUrl":"10.1016/j.cma.2024.117461","url":null,"abstract":"<div><div>Explicit solvers are commonly used for simulating fast dynamic and highly nonlinear engineering problems. However, these solvers are only conditionally stable, requiring very small time-step increments determined by the characteristic length of the smallest, and often most distorted, element in the mesh. In the Lagrangian description of fluid motion, the computational mesh quickly deteriorates. To circumvent this problem, the Particle Finite Element Method (PFEM) creates a new mesh (e.g., through a Delaunay tessellation, based on node positions) when the current one becomes overly distorted. A fast and efficient remeshing technique is therefore of pivotal importance for an effective PFEM implementation in explicit dynamics. Unfortunately, the 3D Delaunay tessellation does not guarantee well-shaped elements, often generating zero- or near-zero-volume elements (slivers), which drastically reduce the stable time-step size. Available mesh optimization techniques have limited applicability due to their high computational cost when runtime remeshing is required. An innovative possibility to overcome this problem is the use of the Virtual Element Method (VEM), a variant of the finite element method that can make use of polyhedral elements of arbitrary shapes and number of nodes. This paper presents the formulation of a 3D first-order Particle Virtual Element Method (PVEM) for weakly compressible flows. Starting from a tetrahedral mesh, poorly shaped elements, such as slivers, are agglomerated to form polyhedral Virtual Elements (VEs) with a controlled characteristic length. This approach ensures full control over the minimum time-step size in explicit dynamics simulations, maintaining stability throughout the entire analysis.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"433 ","pages":"Article 117461"},"PeriodicalIF":6.9,"publicationDate":"2024-10-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142529268","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 : 2024-10-24DOI: 10.1016/j.cma.2024.117464
Leilei Chen , Ruijin Huo , Haojie Lian , Bo Yu , Mengxi Zhang , Sundararajan Natarajan , Stéphane P.A. Bordas
This paper presents a novel perburbation-based method for uncertainty quantification of acoustic fields and their shape sensitivities. In this work, the frequencies of impinging acoustic waves are regarded as random variables. Taylor’s series expansions of acoustic boundary integral equations are derived to obtain th-order derivatives of acoustic state functions with respect to frequencies. Acoustic shape sensitivity is obtained by directly differentiating acoustic boundary integral equation with respect to shape design variables, and then the th-order derivatives of shape sensitivity with respect to random frequencies are formulated with Taylor’s series expansions. Based on the th-order perturbation theory, the statistical characteristics of acoustic state functions and their shape sensitivities can be evaluated. Numerical examples are presented to demonstrate the validity and effectiveness of the proposed algorithm.
本文提出了一种基于扰动的新方法，用于声场及其形状敏感性的不确定性量化。在这项工作中，冲击声波的频率被视为随机变量。通过对声学边界积分方程进行泰勒级数展开，得到声学状态函数相对于频率的 n 次导数。通过直接微分声学边界积分方程中的形状设计变量来获得声学形状灵敏度，然后利用泰勒级数展开求得形状灵敏度相对于随机频率的 n 次导数。基于 nth 阶扰动理论，可以评估声学状态函数的统计特性及其形状敏感性。通过数值示例证明了所提算法的有效性和有效性。
{"title":"Uncertainty quantification of 3D acoustic shape sensitivities with generalized nth-order perturbation boundary element methods","authors":"Leilei Chen , Ruijin Huo , Haojie Lian , Bo Yu , Mengxi Zhang , Sundararajan Natarajan , Stéphane P.A. Bordas","doi":"10.1016/j.cma.2024.117464","DOIUrl":"10.1016/j.cma.2024.117464","url":null,"abstract":"<div><div>This paper presents a novel perburbation-based method for uncertainty quantification of acoustic fields and their shape sensitivities. In this work, the frequencies of impinging acoustic waves are regarded as random variables. Taylor’s series expansions of acoustic boundary integral equations are derived to obtain <span><math><mi>n</mi></math></span>th-order derivatives of acoustic state functions with respect to frequencies. Acoustic shape sensitivity is obtained by directly differentiating acoustic boundary integral equation with respect to shape design variables, and then the <span><math><mi>n</mi></math></span>th-order derivatives of shape sensitivity with respect to random frequencies are formulated with Taylor’s series expansions. Based on the <span><math><mi>n</mi></math></span>th-order perturbation theory, the statistical characteristics of acoustic state functions and their shape sensitivities can be evaluated. Numerical examples are presented to demonstrate the validity and effectiveness of the proposed algorithm.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"433 ","pages":"Article 117464"},"PeriodicalIF":6.9,"publicationDate":"2024-10-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142529272","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}
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