利用深度空间和时间卷积自动编码器为随机大规模和时间依赖性流动问题进行降阶建模。

IF 2 Q3 MECHANICS Advanced Modeling and Simulation in Engineering Sciences Pub Date : 2023-01-01 Epub Date: 2023-05-19 DOI:10.1186/s40323-023-00244-0
Azzedine Abdedou, Azzeddine Soulaimani
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引用次数: 0

摘要

本文提出了一种基于卷积自动编码器的非侵入式降阶模型,作为一种数据驱动工具,为随机时空大尺度流动问题建立高效的非线性降阶模型。其目的是对输入参数被视为不确定的相关流量输出进行准确、快速的不确定性分析。数据由一组高保真快照构成,这些快照是使用内部高保真流动求解器收集的,与不确定输入参数的样本相对应。该方法使用一维卷积自动编码器来减少流动求解器使用的非结构网格的空间维度。另一个卷积自编码器用于时间压缩。然后,使用基于回归的多层感知器将两个压缩级生成的编码潜向量映射到输入参数。所提出的模型可以快速预测未见的参数值,从而高效计算输出统计矩。通过两个基准测试(一维伯格斯和斯托克解法)和一个假定的大坝断流问题(非结构化网格和复杂水深河流),比较了所提方法与基于人工神经网络的线性降阶技术的准确性。数值结果表明,所提出的方法具有很强的预测能力,能够准确地近似输出的统计矩。特别是,与传统的正交分解法不同,预测的统计矩是无振荡的。所提出的还原框架易于实现,可应用于偏微分方程控制的其他参数和时间相关问题,这些问题在许多工程和科学问题中都经常遇到。
本文章由计算机程序翻译,如有差异,请以英文原文为准。

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Reduced-order modeling for stochastic large-scale and time-dependent flow problems using deep spatial and temporal convolutional autoencoders.

A non-intrusive reduced-order model based on convolutional autoencoders is proposed as a data-driven tool to build an efficient nonlinear reduced-order model for stochastic spatiotemporal large-scale flow problems. The objective is to perform accurate and rapid uncertainty analyses of the flow outputs of interest for which the input parameters are deemed uncertain. The data are constituted from a set of high-fidelity snapshots, collected using an inhouse high-fidelity flow solver, which correspond to a sample of the uncertain input parameters. The method uses a 1D-convolutional autoencoder to reduce the spatial dimension of the unstructured meshes used by the flow solver. Another convolutional autoencoder is used for the time compression. The encoded latent vectors, generated from the two compression levels, are then mapped to the input parameters using a regression-based multilayer perceptron. The proposed model allows for rapid predictions for unseen parameter values, allowing the output statistical moments to be computed efficiently. The accuracy of the proposed approach is compared to that of the linear reduced-order technique based on an artificial neural network through two benchmark tests (the one-dimensional Burgers and Stoker's solutions) and a hypothetical dam break flow problem, with an unstructured mesh and over a complex bathymetry river. The numerical results show that the proposed methods present strong predictive capabilities to accurately approximate the statistical moments of the outputs. In particular, the predicted statistical moments are oscillations-free, unlike those obtained with the traditional proper orthogonal decomposition method. The proposed reduction framework is simple to implement and can be applied to other parametric and time-dependent problems governed by partial differential equations, which are commonly encountered in many engineering and science problems.

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来源期刊
Advanced Modeling and Simulation in Engineering Sciences
Advanced Modeling and Simulation in Engineering Sciences Engineering-Engineering (miscellaneous)
CiteScore
6.80
自引率
0.00%
发文量
22
审稿时长
30 weeks
期刊介绍: The research topics addressed by Advanced Modeling and Simulation in Engineering Sciences (AMSES) cover the vast domain of the advanced modeling and simulation of materials, processes and structures governed by the laws of mechanics. The emphasis is on advanced and innovative modeling approaches and numerical strategies. The main objective is to describe the actual physics of large mechanical systems with complicated geometries as accurately as possible using complex, highly nonlinear and coupled multiphysics and multiscale models, and then to carry out simulations with these complex models as rapidly as possible. In other words, this research revolves around efficient numerical modeling along with model verification and validation. Therefore, the corresponding papers deal with advanced modeling and simulation, efficient optimization, inverse analysis, data-driven computation and simulation-based control. These challenging issues require multidisciplinary efforts – particularly in modeling, numerical analysis and computer science – which are treated in this journal.
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