基于深度学习的非稳态边界下渗流方程求解方法

IF 1.7 4区 工程技术 Q3 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS
Daolun Li, Luhang Shen, Wenshu Zha, Shuaijun Lv
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引用次数: 0

摘要

基于深度学习的偏微分方程求解方法已成为研究热点。该方法建立在将深度学习方法应用于偏微分方程的前期工作基础之上,避免了网格化和线性化的需要。然而,在不使用标记数据的情况下,基于深度学习的方法在有效求解复杂湍流系统方面面临困难。此外,还经常遇到收敛失败和解不稳定等问题。有鉴于此,本文提出了一种近似修正模型,用于求解具有非稳态边界的渗流方程。该模型由两个神经网络组成。第一个网络作为渐近块,根据解的渐近形式估计解的进展。第二个网络用于微调渐近块中发现的任何误差。非稳态边界问题的解决方案是通过叠加这些渐进块来实现的。在数值实验中,考虑了水库开采中的恒定流动情况和三级流动情况。结果表明,与数值解法相比,该方法非常有效。此外,误差分析表明,与其他基准方法相比,该方法具有更高的求解精度。
本文章由计算机程序翻译,如有差异,请以英文原文为准。

Deep learning-based method for solving seepage equation under unsteady boundary

Deep learning-based method for solving seepage equation under unsteady boundary

Deep learning-based methods for solving partial differential equations have become a research hotspot. The approach builds on the previous work of applying deep learning methods to partial differential equations, which avoid the need for meshing and linearization. However, deep learning-based methods face difficulties in effectively solving complex turbulent systems without using labeled data. Moreover, issues such as failure to converge and unstable solution are frequently encountered. In light of this objective, this paper presents an approximation-correction model designed for solving the seepage equation featuring unsteady boundaries. The model consists of two neural networks. The first network acts as an asymptotic block, estimating the progression of the solution based on its asymptotic form. The second network serves to fine-tune any errors identified in the asymptotic block. The solution to the unsteady boundary problem is achieved by superimposing these progressive blocks. In numerical experiments, both a constant flow scenario and a three-stage flow scenario in reservoir exploitation are considered. The obtained results show the method's effectiveness when compared to numerical solutions. Furthermore, the error analysis reveals that this method exhibits superior solution accuracy compared to other baseline methods.

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来源期刊
International Journal for Numerical Methods in Fluids
International Journal for Numerical Methods in Fluids 物理-计算机:跨学科应用
CiteScore
3.70
自引率
5.60%
发文量
111
审稿时长
8 months
期刊介绍: The International Journal for Numerical Methods in Fluids publishes refereed papers describing significant developments in computational methods that are applicable to scientific and engineering problems in fluid mechanics, fluid dynamics, micro and bio fluidics, and fluid-structure interaction. Numerical methods for solving ancillary equations, such as transport and advection and diffusion, are also relevant. The Editors encourage contributions in the areas of multi-physics, multi-disciplinary and multi-scale problems involving fluid subsystems, verification and validation, uncertainty quantification, and model reduction. Numerical examples that illustrate the described methods or their accuracy are in general expected. Discussions of papers already in print are also considered. However, papers dealing strictly with applications of existing methods or dealing with areas of research that are not deemed to be cutting edge by the Editors will not be considered for review. The journal publishes full-length papers, which should normally be less than 25 journal pages in length. Two-part papers are discouraged unless considered necessary by the Editors.
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