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在时间依赖的流量问题中,用于推断预测的深度卷积架构

Pratyush Bhatt¹, Yash Kumar¹, Azzeddine Soulaïmani²

¹Department of Mechanical Engineering, Delhi Technological University, P4X9+Q8X, Bawana Rd, Shahbad Daulatpur Village, Rohini, New Delhi, 110042 Delhi India.

Advanced modeling and simulation in engineering sciences

|December 4, 2023

概括

深度学习模型,包括卷积自编码器 (CAE) 和卷积神经网络 (CNN),有效预测部分微分方程 (PDEs) 的解决方案. 在时间空间问题上,CNN的未来步骤预测器表现出比LSTM和TCN更高的准确性.

科学领域:

计算流体动力学计算流体动力学
科学机器学习科学机器学习
数字分析数字分析

背景情况:

部分微分方程 (PDEs) 支配着许多物理系统,但通过计算来解决它们可能是资源密集的.
现有的深度学习模型,如LSTM,TCN和CNN,适用于时间序列预测和空间特征提取.
减少顺序建模 (ROM) 技术对于大规模和参数化问题的高效计算至关重要.

研究的目的:

开发和评估深度学习模型,以计算高效地预测偏向主导部分微分方程 (PDEs) 的解决方案.
调查卷积自编码器 (CAE) 在数据压缩和CNN在非侵入性ROM框架中的时间步骤预测的有效性.
评估拟议模型的长期预测准确性和推断能力,以基准问题和现实场景为准.

主要方法:

采用深度学习技术,特别是用于压缩的卷积自动编码器 (CAE) 和用于未来步骤预测的CNN.
通过压缩高准确度PDE解决方案 (快照) 在将其输入预测模型之前,利用非侵入性减少顺序建模.
测试了1D汉堡方程和斯托克破问题上的模型,以获得准确性和推断,并将最佳模型应用于2D河破场景.

主要成果:

卷积神经网络 (CNN) 未来步骤预测器在测试时空问题的预测准确性方面显著超过了长期短期记忆 (LSTM) 和时间卷积网络 (TCN).
提出的模型成功地减少了获得高保真解决方案的计算时间和功率要求.
这些模型表现出有效的长期预测准确性,包括在训练领域之外的表现 (外推).

结论:

与基于CAE的压缩集成的CNN未来步骤预测器,为科学和工程应用中解决PDE提供了高度准确和高效的方法.
基于深度学习的非侵入性减少顺序建模为传统计算成本高昂的方法提供了可行的替代方案.
提出的方法对复杂的现实世界模拟具有前景,例如预测复杂的河流几何结构中的水断层.

关键词:

在美国,CNN是CNN.深度的自动编码器这是LSTM的LSTM.非侵入性的减少顺序建模.TCN TCN 是一个数字.时间依赖的流量问题

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