Deep convolutional architectures for extrapolative forecasts in time-dependent flow problems.

IF 2 Q3 MECHANICS Advanced Modeling and Simulation in Engineering Sciences Pub Date : 2023-01-01 Epub Date: 2023-11-30 DOI:10.1186/s40323-023-00254-y
Pratyush Bhatt, Yash Kumar, Azzeddine Soulaïmani
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引用次数: 1

Abstract

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.

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时变流问题中外推预测的深度卷积架构。
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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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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