论文标题

一种深度学习方法,用于使用物理知识的神经网络(PINN)预测二维土壤巩固

A Deep Learning Approach for Predicting Two-dimensional Soil Consolidation Using Physics-Informed Neural Networks (PINN)

论文作者

Lu, Yue, Mei, Gang, Piccialli, Francesco

论文摘要

土壤整合与岩土建筑物和基础的渗漏,稳定性和沉降密切相关,并直接影响上层建筑的使用和安全性。如今,土壤的单向巩固理论在某些条件和近似计算中被广泛使用。土壤巩固的多方向理论比实际应用中的单向理论更合理,但是在索引确定和解决方案方面,它要复杂得多。为了解决上述问题,在本文中,我们提出了一种使用物理知识的神经网络(PINN)预测二维土壤巩固的孔隙水压的深度学习方法。在提出的方法中,(1)构建了完全连接的神经网络,(2)计算结构域,部分微分方程(PDE)和约束定义以生成模型训练的数据,以及(3)二维土壤巩固和神经网络的模型的PDE与模型的损失相关联。通过与PDE的数值解决方案进行二维整合,可以验证所提出方法的有效性。使用这种方法,可以简单有效地预测过量的孔隙水压。此外,在中国天津港的一个真实情况下,该方法用于预测基础的土壤过多的孔隙水压。提出的深度学习方法可用于研究大型且复杂的多向土壤巩固。

Soil consolidation is closely related to seepage, stability, and settlement of geotechnical buildings and foundations, and directly affects the use and safety of superstructures. Nowadays, the unidirectional consolidation theory of soils is widely used in certain conditions and approximate calculations. The multi-directional theory of soil consolidation is more reasonable than the unidirectional theory in practical applications, but it is much more complicated in terms of index determination and solution. To address the above problem, in this paper, we propose a deep learning method using physics-informed neural networks (PINN) to predict the excess pore water pressure of two-dimensional soil consolidation. In the proposed method, (1) a fully connected neural network is constructed, (2) the computational domain, partial differential equation (PDE), and constraints are defined to generate data for model training, and (3) the PDE of two-dimensional soil consolidation and the model of the neural network is connected to reduce the loss of the model. The effectiveness of the proposed method is verified by comparison with the numerical solution of PDE for two-dimensional consolidation. Using this method, the excess pore water pressure could be predicted simply and efficiently. In addition, the method was applied to predict the soil excess pore water pressure in the foundation in a real case at Tianjin port, China. The proposed deep learning approach can be used to investigate the large and complex multi-directional soil consolidation.

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