基于PINNs的高度非线性Richards入渗模型研究

中国民航大学学报 ›› 2023, Vol. 41 ›› Issue (5): 6-12.

基于PINNs的高度非线性Richards入渗模型研究

霍海峰，黄昊宇，李其昂，胡彪，张兆文

（中国民航大学交通科学与工程学院，天津300300）

收稿日期:2022-11-30 修回日期:2023-05-10 出版日期:2023-11-16 发布日期:2023-11-16
作者简介:霍海峰（1983—），男，河北石家庄人，副教授，博士，研究方向为岩土工程及路基路面工程.
基金资助:
天津市交通运输委员会科技发展项目计划（2019-18）

Research on highly nonlinear Richards infiltration model based on PINNs

HUO Haifeng, HUANG Haoyu, LI Qiang, HU Biao, ZHANG Zhaowen

(College of Transportation Science and Engineering, CAUC, Tianjin 300300, China)

Received:2022-11-30 Revised:2023-05-10 Online:2023-11-16 Published:2023-11-16

摘要/Abstract

摘要： 针对具有高度非线性系数的非饱和土Richards入渗模型，利用物理信息神经网络（PINNs，physics-informedneuralnetworks）进行求解，并通过有限差分方法对网络预测结果进行验证，发现PINNs预测结果与有限差分预测结果基本吻合；再研究超参数对PINNs误差的影响，确定训练集大小、网络层数等因素对PINNs训练集及测试集误差的影响，在合理的超参数调整下，PINNs预测模型在高度非线性入渗模型中表现出良好的训练效果。该计算方法可广泛应用于热传导、水汽迁移及应力平衡等机场工程问题求解。

关键词: 高度非线性系数, 入渗模型, 物理信息神经网络, 有限差分方法, 超参数调整

Abstract: For the Richards infiltration model of unsaturated soil with highly nonlinear coefficients, the physics-informed neural networks(PINNs) is applied to solve it and the network prediction results are verified by the finite difference method. It is found that the prediction results of PINNs are basically consistent with the prediction results of finite difference method. The influence of hyperparameter on the error of PINNs is further investigated to determine the impact of factors such as training set size and number of network layers on PINNs training set and test set errors. With reasonable hyperparameter adjustment, the PINNs prediction model exhibits good training performance in the highly nonlinear infiltration model. This computational method can be widely applied to solve airport engineering problems such as heat conduction, water vapor migration and stress balance.

Key words: highly nonlinear coefficient, infiltration model, physics -informed neural networks (PINNs), finite differ鄄 ence method, hyperparameter adjustment

中图分类号:

霍海峰, 黄昊宇, 李其昂, 胡彪, 张兆文. 基于PINNs的高度非线性Richards入渗模型研究[J]. 中国民航大学学报, 2023, 41(5): 6-12.

HUO Haifeng, HUANG Haoyu, LI Qiang, HU Biao, ZHANG Zhaowen. Research on highly nonlinear Richards infiltration model based on PINNs[J]. Journal of Civil Aviation University of China, 2023, 41(5): 6-12.

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