XI International Conference on Adaptive Modeling and Simulation最新文献_第6页

Adaptive mesh refinement procedures for the virtual element method 自适应网格细化程序的虚元法

XI International Conference on Adaptive Modeling and Simulation Pub Date : 1900-01-01 DOI: 10.23967/admos.2023.064

D. van Huyssteen, F. López-Rivarola, G. Etse, P. Steinmann

引用次数: 0

A Convergence Proof for Adaptive Parametric PDEs with Unbounded Coefficients 系数无界自适应参数偏微分方程的收敛性证明

XI International Conference on Adaptive Modeling and Simulation Pub Date : 1900-01-01 DOI: 10.23967/admos.2023.005

N. Farchmin, M. Eigel

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Error estimation for surrogate models with noisy small-sized training sets 带噪声小训练集的代理模型误差估计

XI International Conference on Adaptive Modeling and Simulation Pub Date : 1900-01-01 DOI: 10.23967/admos.2023.007

J. Wackers, Hayriye Pehlivan Solak, Riccardo, Pellegrini, A. Serani, M. Diez

{"title":"Error estimation for surrogate models with noisy small-sized training sets","authors":"J. Wackers, Hayriye Pehlivan Solak, Riccardo, Pellegrini, A. Serani, M. Diez","doi":"10.23967/admos.2023.007","DOIUrl":"https://doi.org/10.23967/admos.2023.007","url":null,"abstract":"Simulation-driven shape optimization often uses surrogate models, i.e. approximate models fitted through a dataset of simulation results for a limited number of designs. The shape optimization is then performed over this surrogate model. For efficiency, modern approaches often construct the datasets adaptively, adding simulation points one by one where they are most likely to discover the optimum design [3]. The uncertainty estimation of the surrogate model is essential to guide the choice of new sample points: underestimation of the uncertainty leads to sampling in suboptimal regions, missing the true optimum. Gaussian process regression naturally provides uncertainty estimations [4] and Stochastic Radial Basis Functions (SRBF) surrogate models estimate the uncertainty based on the spread of RBF fits with different kernels [5]. In the context of SRBF, this paper discusses two issues with uncertainty estimation. The first is that most existing techniques rely on knowledge about the global behaviour of the data, such as spatial correlations. However, the number of datapoints can be too small to reconstruct this global information from the data. We argue that in this situation, user-provided estimation of the function behaviour is a better choice (section 3). The second issue is that the dataset may contain noise, i.e. random errors without spatial correlation. Surrogate models can filter out this noise, but it introduces two separate uncertainties: the optimum amount of noise filtering is unknown, and for a small dataset (even with perfect noise filtering) the local mean of the data may not correspond to the true simulation response. In section 4 we introduce estimators for both uncertainties.","PeriodicalId":414984,"journal":{"name":"XI International Conference on Adaptive Modeling and Simulation","volume":"45 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125003734","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Dimensionality reduction and physics-based manifold learning for parametric models in biomechanics and tissue engineering 生物力学和组织工程中参数化模型的降维和基于物理的流形学习

XI International Conference on Adaptive Modeling and Simulation Pub Date : 1900-01-01 DOI: 10.23967/admos.2023.037

A. Muixí, A. Garcia-Gonzalez, S. Zlotnik, P. Díez

{"title":"Dimensionality reduction and physics-based manifold learning for parametric models in biomechanics and tissue engineering","authors":"A. Muixí, A. Garcia-Gonzalez, S. Zlotnik, P. Díez","doi":"10.23967/admos.2023.037","DOIUrl":"https://doi.org/10.23967/admos.2023.037","url":null,"abstract":"This work aims at describing dimensionality reduction methods, particularizing in Principal Component Analysis (PCA), the nonlinear version kernel Principal Component Analysis (kPCA) [1], and their potential application to data-assisted Credible models in biomechanics and tissue engineering. These methodologies are intended to discover the low dimensional manifold where an input physical data set lives. Reducing the dimensionality of a complex physical system is a potential tool towards real time Credible and accurate parametric models and patient-specific simulations. In this direction, the Proper Orthogonal Decomposition (POD) combines PCA with a reduced basis approach to reduce the number of degrees of freedom in parametric boundary value problems. Additionally, for systems whose solutions belong to nonlinear manifolds, kernel Proper Orthogonal Decomposition (kPOD) uses kPCA reduction to find a solution of the problem. The main features of kPOD are the use of local approximations, the possibility of enriching the reduced space with quadratic elements, the use of ad-hoc kernels that include previous knowledge of the input data, and the idea of using an iterative algorithm that explores the Voronoi diagram of the snapshots in the reduced space [2]. Besides, dimensionality reduction in combination with surrogate modelling aims at finding initial (and accurate) approximations of parametric systems without physics involved. All presented methodologies are shown to be strong tools in several fields. To show the potential of those techniques, here we present several examples of application in the biomechanical field, such as advection diffusion in scaffolds for tissue engineering, and vascular biomechanics","PeriodicalId":414984,"journal":{"name":"XI International Conference on Adaptive Modeling and Simulation","volume":"96 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114585913","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Adaptive Strategies for Frequency Domain MOR - A Comparative Framework 频率域MOR的自适应策略——一个比较框架

XI International Conference on Adaptive Modeling and Simulation Pub Date : 1900-01-01 DOI: 10.23967/admos.2023.002

Q. Aumann, S. Chellappa, A. Nayak

引用次数: 0

Assessment of tailings dams using Model Order Reduction 基于模型阶数约简的尾矿坝评价

XI International Conference on Adaptive Modeling and Simulation Pub Date : 1900-01-01 DOI: 10.23967/admos.2023.077

Sergio Zlotnik, C. Nasika, Pedro D´ıez, Pierre Gerard, Thierry Massart

{"title":"Assessment of tailings dams using Model Order Reduction","authors":"Sergio Zlotnik, C. Nasika, Pedro D´ıez, Pierre Gerard, Thierry Massart","doi":"10.23967/admos.2023.077","DOIUrl":"https://doi.org/10.23967/admos.2023.077","url":null,"abstract":"Tailing dams are structures built up during the mining process by compacting successive layers of earth. They contain the (usually toxic) left over after the process of separating the valuable fraction from the uneconomic fraction of an ore. This kind of dams exhibit a high rate of sudden and hazardous failures and, therefore, monitoring its state is a key process in the mining industry. The recent surge in the availability of sensors (e.g. Internet of Things) allows enhancing the data that can be gathered to monitor the mechanical and hydraulic state of the dams. Numerical models, on the other hand, can be used to enrich the local information collected by the sensors and provide a global view of the state of the dam. Although, for monitoring purposes, numerical models are only useful if they provide results fast enough to react to an unsafe state. In this presentation we describe the results presented in [1] and [2], where model order reduction techniques are applied in the context of data assimilation to learn about the state of tailing dams. A transient nonlinear hydro-mechanical model describing the groundwater ﬂow in unsaturated soil conditions is solved using Reduced Basis method [1]. Hyper-reduction techniques (DEIM, LDEM) are tested and show time gains up to 1 / 100 with respect to standard ﬁnite element methods [2].","PeriodicalId":414984,"journal":{"name":"XI International Conference on Adaptive Modeling and Simulation","volume":"147 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114893071","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

A modified Constitutive Relation Error (mCRE) framework to learn nonlinear constitutive models from strain measurements with thermodynamics-consistent Neural Networks 一种改进的本构关系误差框架，利用热力学一致神经网络从应变测量中学习非线性本构模型

XI International Conference on Adaptive Modeling and Simulation Pub Date : 1900-01-01 DOI: 10.23967/admos.2023.020

A. Benady, L. Chamoin, E. Baranger

引用次数: 1

Learning Viscoelastic Responses with a Thermodynamic Recurrent Neural Network with Maxwell Encoding 用Maxwell编码的热力学递归神经网络学习粘弹性响应

XI International Conference on Adaptive Modeling and Simulation Pub Date : 1900-01-01 DOI: 10.23967/admos.2023.022

Nicolas Pistenon, S. Cantournet, J. Bouvard, D. P. Muñoz, P. Kerfriden

{"title":"Learning Viscoelastic Responses with a Thermodynamic Recurrent Neural Network with Maxwell Encoding","authors":"Nicolas Pistenon, S. Cantournet, J. Bouvard, D. P. Muñoz, P. Kerfriden","doi":"10.23967/admos.2023.022","DOIUrl":"https://doi.org/10.23967/admos.2023.022","url":null,"abstract":"Neural network methods are increasingly used to build constitutive laws in computational mechanics [1]. Neural Networks may for instance be used a surrogates for micro-mechanical models, whereby evaluating the response of high-ﬁdelity numerical representative volume elements proves prohibitively expensive. Alternatively, Neural Networks may be used whenever traditional phenomenological approaches to constitutive modelling fails, i.e. whenever one fails to ﬁnd a functional form for the constitutive law that enables to represent the behaviour of the material faithfully over the entirety of possible loading scenarios. One example is the viscoelastic behaviour of polymers, which remains diﬃcult to describe accurately. The state of the art on these machine learning methods for the prediction of behavioural laws with a dependence on loading history do not show models with both a strong interpolatory, extrapolatory capacity and with a number of data consistent with today’s experimental capabilities [2]. To enforce a better bias, one used mechanical knowledge by introducing some mechanical regularisation terms [3], [4] or to considered structural approaches [5]. In this work, we describe a novel Neural Network strategy that combines a Maxwell model, which is extensively used as to describe linear viscoelastic responses, and a Thermodynamic Recurrent Neural Network. The coupling between the phenomenological and data-driven blocks of our model is done in two ways. Firstly, the Neural Network, and more precisely LSTM cells, corrects the response provided by the Maxwell model, which closely resembles the residual connections","PeriodicalId":414984,"journal":{"name":"XI International Conference on Adaptive Modeling and Simulation","volume":"42 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127340869","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

A posteriori error estimates for the Crank-Nicolson method: application to parabolic partial differential equations with small random input data Crank-Nicolson方法的后检误差估计:应用于小随机输入数据的抛物型偏微分方程

XI International Conference on Adaptive Modeling and Simulation Pub Date : 1900-01-01 DOI: 10.23967/admos.2023.029

N. Shravani, Gujji Murali, †. MohanReddy, §. MichaelVynnycky

{"title":"A posteriori error estimates for the Crank-Nicolson method: application to parabolic partial differential equations with small random input data","authors":"N. Shravani, Gujji Murali, †. MohanReddy, §. MichaelVynnycky","doi":"10.23967/admos.2023.029","DOIUrl":"https://doi.org/10.23967/admos.2023.029","url":null,"abstract":"In this article, we present residual-based a posteriori error estimates for the parabolic partial differential equation (PDE) with small random input data in the L 2 P (Ω; L 2 (0 , T ; H 1 ( D )))-norm, where (Ω , F , P ) is a complete probability space, D is the physical domain, T > 0 is the ﬁnal time. Such a class of PDEs arises due to a lack of complete understanding of the physical model. To this end, the perturbation technique [2019, Arch. Comput. Methods Eng., 26, pp. 1313-1377] is exploited to express the exact random solution in terms of the power series with respect to the uncertainty parameter, whence we obtain decoupled deterministic problems. Each problem is then discretized in space by the ﬁnite element method and advanced in time by the Crank-Nicolson scheme. Quadratic reconstructions are introduced to obtain optimal bounds in the temporal direction. The work generalizes the isotropic results obtained in [2009, SIAM J. Sci. Comput., 31, pp. 2757-2783] for the deterministic parabolic PDEs to the parabolic PDE with small random input data. Numerical results demonstrate the eﬀectiveness of the bounds.","PeriodicalId":414984,"journal":{"name":"XI International Conference on Adaptive Modeling and Simulation","volume":"41 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125831001","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

High Continuity Basis’s Impact on Continuous Global L2 (CGL2) Recovery 高连续性基础对连续全局L2 (CGL2)恢复的影响

XI International Conference on Adaptive Modeling and Simulation Pub Date : 1900-01-01 DOI: 10.23967/admos.2023.044

T. Kvamsdal, A. Abdulhaque, M. Kumar, K. Johannessen, A. Kvarving, K. Okstad

{"title":"High Continuity Basis’s Impact on Continuous Global L2 (CGL2) Recovery","authors":"T. Kvamsdal, A. Abdulhaque, M. Kumar, K. Johannessen, A. Kvarving, K. Okstad","doi":"10.23967/admos.2023.044","DOIUrl":"https://doi.org/10.23967/admos.2023.044","url":null,"abstract":"In the recovery-based estimates method, we employ a projection technique to recover a post-processed quantity (usually the stresses or the gradient computed from the FE-approximation). The error is estimated by taking the difference between the recovered quantity and the FE-solution. An easy procedure to implement is the continuous global L2 (CGL2) recovery initially used for a posteriori error estimation by Zienkiewicz and Zhu [1]. Kumar, Kvamsdal and Johannessen [2] developed CGL2 and Superconvergent Patch Recovery (SPR) error estimation methods applicable for adaptive refinement using LR B-splines [3] and observed very good results for both the CGL2 and the SPR recovery technique. However, Cai and Zhang reported in [4] a case of malfunction for the CGL2-recovery applied to second order triangular and tetrahedral Lagrange finite element. Here we will start out by presenting a motivational example that illustrates the benefits of using high regularity splines in the CGL2 based gradient recovery procedure compared to using the classical Lagrange FEM basis functions. We will then show the performance on some benchmark problems comparing the use of splines","PeriodicalId":414984,"journal":{"name":"XI International Conference on Adaptive Modeling and Simulation","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127746321","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0