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Reduced-order modeling for stochastic large-scale and time-dependent flow problems using deep spatial and temporal convolutional autoencoders. 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 Pub Date : 2023-01-01 Epub Date: 2023-05-19 DOI: 10.1186/s40323-023-00244-0
Azzedine Abdedou, Azzeddine Soulaimani

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.

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。
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引用次数: 0
A "data-driven uncertainty" computational method to model and predict instabilities of a frictional system. 一种“数据驱动的不确定性”计算方法来模拟和预测摩擦系统的不稳定性。
Q1 Mathematics Pub Date : 2023-01-01 DOI: 10.1186/s40323-023-00241-3
Farouk Maaboudallah, Noureddine Atalla

Most of the recently developed methods for predicting instabilities of frictional systems couple stochastic algorithms with the finite element method (FEM). They use random variables to model the uncertainty of input parameters through standard probability laws. Regardless of the fact that advanced numerical schemes are available nowadays, a systematic and accurate method to describe finely the uncertainties upstream the model, and thus predict its response is still missing. In this contribution, we present a data-driven stochastic finite element scheme to predict the dynamic behavior of a rubbing system. The proposed framework relies on data-driven approach and uses four steps. In the first, the measured data are integrated directly, for the uncertainty quantification, by means of the random balance design (RBD). In the second step, the generated stochastic data are evaluated in an iterative way to solve friction-induced vibration problem. In the third step, the resulted data are reordered in such a way that the corresponding values of each measured input parameters are ranked in ascending order. Finally, the Fourier spectrum is introduced on the reordered results to compute the sensitivity indices. Thus, instead of Monte Carlo-based formalism or Fourier Amplitude Sensitivity Test (FAST), the computational cost of the proposed method is kept down to O ( N ) with N the number of samples. We investigate the efficiency of the suggested solver on a reduced brake system. Altogether, the suggested procedure achieves excellent accuracy at a much reduced computational time compared to the methods available in the literature.

近年来发展起来的预测摩擦系统不稳定性的方法大多是将随机算法与有限元方法相结合。他们使用随机变量通过标准概率定律来模拟输入参数的不确定性。尽管目前已有先进的数值格式,但仍缺乏一种系统准确的方法来精细描述模型上游的不确定性,从而预测其响应。在这篇贡献中,我们提出了一个数据驱动的随机有限元方案来预测摩擦系统的动态行为。提出的框架依赖于数据驱动的方法,并使用四个步骤。首先,采用随机平衡设计(RBD)对测量数据进行直接积分,进行不确定度的量化。第二步,对生成的随机数据进行迭代求值,求解摩擦激振问题。在第三步中,以这样一种方式对结果数据进行重新排序,即每个测量输入参数的对应值按升序排列。最后,在重排序结果上引入傅里叶谱来计算灵敏度指标。因此,代替基于蒙特卡罗的形式主义或傅立叶振幅灵敏度测试(FAST),该方法的计算成本在样本数量为N的情况下保持在O (N)。我们研究了所建议的求解器在减速制动系统上的效率。总的来说,与文献中可用的方法相比,建议的程序在大大减少的计算时间内实现了出色的准确性。
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引用次数: 0
Deep convolutional architectures for extrapolative forecasts in time-dependent flow problems. 时变流问题中外推预测的深度卷积架构。
Q1 Mathematics Pub Date : 2023-01-01 Epub Date: 2023-11-30 DOI: 10.1186/s40323-023-00254-y
Pratyush Bhatt, Yash Kumar, Azzeddine Soulaïmani

Physical systems whose dynamics are governed by partial differential equations (PDEs) find numerous applications in science and engineering. The process of obtaining the solution from such PDEs may be computationally expensive for large-scale and parameterized problems. In this work, deep learning techniques developed especially for time-series forecasts, such as LSTM and TCN, or for spatial-feature extraction such as CNN, are employed to model the system dynamics for advection-dominated problems. This paper proposes a Convolutional Autoencoder(CAE) model for compression and a CNN future-step predictor for forecasting. These models take as input a sequence of high-fidelity vector solutions for consecutive time steps obtained from the PDEs and forecast the solutions for the subsequent time steps using auto-regression; thereby reducing the computation time and power needed to obtain such high-fidelity solutions. Non-intrusive reduced-order modeling techniques such as deep auto-encoder networks are utilized to compress the high-fidelity snapshots before feeding them as input to the forecasting models in order to reduce the complexity and the required computations in the online and offline stages. The models are tested on numerical benchmarks (1D Burgers' equation and Stoker's dam-break problem) to assess the long-term prediction accuracy, even outside the training domain (i.e. extrapolation). The most accurate model is then used to model a hypothetical dam break in a river with complex 2D bathymetry. The proposed CNN future-step predictor revealed much more accurate forecasting than LSTM and TCN in the considered spatiotemporal problems.

动力学由偏微分方程(PDEs)控制的物理系统在科学和工程中有许多应用。对于大规模和参数化的问题,从这种偏微分方程中获得解的过程可能在计算上很昂贵。在这项工作中,专门为时间序列预测(如LSTM和TCN)或空间特征提取(如CNN)开发的深度学习技术被用于模拟平流主导问题的系统动力学。本文提出了卷积自编码器(CAE)模型用于压缩,CNN未来步预测器用于预测。这些模型以从偏微分方程中获得的连续时间步长的高保真向量解序列作为输入,并使用自回归预测后续时间步长的解;从而减少了获得这种高保真度解决方案所需的计算时间和功率。利用深度自编码器网络等非侵入式降阶建模技术对高保真度快照进行压缩,然后将其作为预测模型的输入,以降低在线和离线阶段的复杂性和所需的计算量。这些模型在数值基准(1D Burgers’方程和Stoker’s dam-break问题)上进行了测试,以评估长期预测的准确性,甚至在训练领域之外(即外推)。然后用最精确的模型用复杂的二维测深法来模拟河流中假设的溃坝。在考虑的时空问题上,CNN未来步预测器的预测精度明显高于LSTM和TCN。
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引用次数: 1
The Pseudo-Direct Numerical Simulation Method considered as a Reduced Order Model 作为降阶模型的伪直接数值模拟方法
Q1 Mathematics Pub Date : 2022-10-28 DOI: 10.1186/s40323-022-00235-7
S. Idelsohn, J. M. Giménez, N. Nigro
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引用次数: 1
Empowering engineering with data, machine learning and artificial intelligence: a short introductive review 用数据、机器学习和人工智能赋能工程:一篇简短的介绍性综述
Q1 Mathematics Pub Date : 2022-10-27 DOI: 10.1186/s40323-022-00234-8
F. Chinesta, E. Cueto
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引用次数: 8
A deformation-dependent coupled Lagrangian/semi-Lagrangian meshfree hydromechanical formulation for landslide modeling 滑坡模型的变形相关耦合拉格朗日/半拉格朗日无网格流体力学公式
Q1 Mathematics Pub Date : 2022-09-30 DOI: 10.1186/s40323-022-00233-9
Jonghyuk Baek, Ryan T. Schlinkman, Frank N. Beckwith, Jiun-Shyan Chen
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引用次数: 3
A multi-point constraint unfitted finite element method 多点约束非拟合有限元法
Q1 Mathematics Pub Date : 2022-09-21 DOI: 10.1186/s40323-022-00232-w
B. Freeman
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引用次数: 2
Thermo-mechanical simulations of powder bed fusion processes: accuracy and efficiency 粉末床熔化过程的热机械模拟:准确性和效率
Q1 Mathematics Pub Date : 2022-09-12 DOI: 10.1186/s40323-022-00230-y
C. Burkhardt, P. Steinmann, J. Mergheim
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引用次数: 8
A partitioned material point method and discrete element method coupling scheme 提出了分块质点法与离散元法的耦合方案
Q1 Mathematics Pub Date : 2022-08-16 DOI: 10.1186/s40323-022-00229-5
Singer, Veronika, Sautter, Klaus B., Larese, Antonia, Wüchner, Roland, Bletzinger, Kai-Uwe
Mass-movement hazards involving fast and large soil deformation often include huge rocks or other significant obstacles increasing tremendously the risks for humans and infrastructures. Therefore, numerical investigations of such disasters are in high economic demand for prediction as well as for the design of countermeasures. Unfortunately, classical numerical approaches are not suitable for such challenging multiphysics problems. For this reason, in this work we explore the combination of the Material Point Method, able to simulate elasto-plastic continuum materials and the Discrete Element Method to accurately calculate the contact forces, in a coupled formulation. We propose a partitioned MPM-DEM coupling scheme, thus the solvers involved are treated as black-box solvers, whereas the communication of the involved sub-systems is shifted to the shared interface. This approach allows to freely choose the best suited solver for each model and to combine the advantages of both physics in a generalized manner. The examples validate the novel coupling scheme and show its applicability for the simulation of large strain flow events interacting with obstacles.
土体快速大变形的体块运动危害通常包括巨大的岩石或其他重大障碍物,极大地增加了人类和基础设施的风险。因此,这类灾害的数值研究对预测和对策设计都有很高的经济要求。不幸的是,经典的数值方法不适合这种具有挑战性的多物理场问题。因此,在这项工作中,我们探索了能够模拟弹塑性连续体材料的材料点法和精确计算接触力的离散元法的结合,在一个耦合公式中。我们提出了一种分区的MPM-DEM耦合方案,将所涉及的求解器视为黑盒求解器,而将所涉及的子系统的通信转移到共享接口。这种方法允许为每个模型自由选择最适合的求解器,并以一种广义的方式结合两种物理的优点。算例验证了该耦合方案的可行性,并表明该方案适用于大应变流与障碍物相互作用的模拟。
{"title":"A partitioned material point method and discrete element method coupling scheme","authors":"Singer, Veronika, Sautter, Klaus B., Larese, Antonia, Wüchner, Roland, Bletzinger, Kai-Uwe","doi":"10.1186/s40323-022-00229-5","DOIUrl":"https://doi.org/10.1186/s40323-022-00229-5","url":null,"abstract":"Mass-movement hazards involving fast and large soil deformation often include huge rocks or other significant obstacles increasing tremendously the risks for humans and infrastructures. Therefore, numerical investigations of such disasters are in high economic demand for prediction as well as for the design of countermeasures. Unfortunately, classical numerical approaches are not suitable for such challenging multiphysics problems. For this reason, in this work we explore the combination of the Material Point Method, able to simulate elasto-plastic continuum materials and the Discrete Element Method to accurately calculate the contact forces, in a coupled formulation. We propose a partitioned MPM-DEM coupling scheme, thus the solvers involved are treated as black-box solvers, whereas the communication of the involved sub-systems is shifted to the shared interface. This approach allows to freely choose the best suited solver for each model and to combine the advantages of both physics in a generalized manner. The examples validate the novel coupling scheme and show its applicability for the simulation of large strain flow events interacting with obstacles.","PeriodicalId":37424,"journal":{"name":"Advanced Modeling and Simulation in Engineering Sciences","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2022-08-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138510042","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: 4
A Lagrangian–Eulerian procedure for the coupled solution of the Navier–Stokes and shallow water equations for landslide-generated waves 滑坡产生波的Navier-Stokes方程和浅水方程耦合解的拉格朗日-欧拉过程
Q1 Mathematics Pub Date : 2022-07-30 DOI: 10.1186/s40323-022-00225-9
Masó, Miguel, Franci, Alessandro, de-Pouplana, Ignasi, Cornejo, Alejandro, Oñate, Eugenio
This work presents a partitioned method for landslide-generated wave events. The proposed strategy combines a Lagrangian Navier Stokes multi-fluid solver with an Eulerian method based on the Boussinesq shallow water equations. The Lagrangian solver uses the Particle Finite Element Method to model the landslide runout, its impact against the water body and the consequent wave generation. The results of this fully-resolved analysis are stored at selected interfaces and then used as input for the shallow water solver to model the far-field wave propagation. This one-way coupling scheme reduces drastically the computational cost of the analyses while maintaining high accuracy in reproducing the key phenomena of the cascading natural hazard. Several numerical examples are presented to show the accuracy and robustness of the proposed coupling strategy and its applicability to large-scale landslide-generated wave events. The validation of the partitioned method is performed versus available results of other numerical methods, analytical solutions and experimental measures.
本文提出了滑坡波事件的分区方法。该策略将拉格朗日Navier - Stokes多流体求解器与基于Boussinesq浅水方程的欧拉方法相结合。拉格朗日解算器采用粒子有限元法模拟滑坡跳动、对水体的冲击以及随之产生的波浪。这种完全解析的分析结果存储在选定的界面上,然后用作浅水求解器的输入,以模拟远场波的传播。这种单向耦合方案大大降低了分析的计算成本,同时保持了重现级联自然灾害关键现象的高精度。数值算例表明了所提出的耦合策略的准确性和鲁棒性,以及该策略对大规模滑坡波事件的适用性。对比其他数值方法、解析解和实验测量的结果,对划分方法进行了验证。
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引用次数: 2
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Advanced Modeling and Simulation in Engineering Sciences
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