基于PINNs算法的一维潜水流方程的渗流参数反演
Inversion of seepage parameters for one-dimensional unconfined aquifer flow equations based on PINNs algorithm
舒伟 1孟胤全 1邓芳 1蒋建国 1吴吉春1
作者信息
- 1. 南京大学地球科学与工程学院,南京,210023
- 折叠
摘要
在地下水领域中,渗流参数反演有助于了解地下水流动的性质,帮助确定地下水资源的分布、移动和质量,这对于地下水资源管理、水文模型开发和地下水补给的可持续性非常重要.近年来,神经网络方法快速发展,然而其针对潜水流渗流参数反演的研究较少.基于此,首次将物理信息神经网络(Physics-Informed Neural Networks,PINNs)方法结合软硬约束设置来解决潜水含水层渗透系数反演问题,以一维稳态非均质潜水流以及非稳态均质潜水流(含溶质运移)的渗透系数反演为例,对比了不同问题中PINNs软约束方法(PINNs-S)和硬约束方法(PINNs-H)反演渗透系数的表现.PINNs算例结果表明,PINNs算法反演渗透系数具有较高的计算精度.此外,PINNs硬约束算法和软约束算法各有优劣,在实际应用中应根据具体问题和实验效果来合理选择.
Abstract
In the field of groundwater,the inversion of seepage parameters contributes to understanding the nature of groundwater flow,which is essential for determining the distribution,movement,and quality of groundwater resources.This plays a significant role in groundwater resource management,hydrological model development,and the sustainability of groundwater recharge.Despite the rapid development of neural network methods in recent years,there is limited research focused on the inversion of seepage parameters for unconfined flow.Addressing this,the present study pioneers the application of Physics-Informed Neural Networks(PINNs)combined with both soft and hard constraints to solve the problem of permeability coefficient inversion in unconfined aquifers.Taking the permeability coefficient inversion in one-dimensional steady-state heterogeneous unconfined flow as well as unsteady-state homogeneous unconfined flow(including solute transport)as examples,this paper compares the performance of the PINNs soft constraint method(PINNs-S)and hard constraint method(PINNs-H)in inverting permeability coefficients.The PINNs case studies indicate that the PINNs algorithm inverts permeability coefficients with high computational accuracy.Furthermore,the PINNs hard constraint and soft constraint methods have their advantages and disadvantages,and the appropriate approach should be selected based on the specific problem and experimental results in practical applications.
关键词
物理信息神经网络/潜水/硬约束/软约束/渗流参数反演Key words
Physics-Informed Neural Networks/unconfined flow/hard constraints/soft constraints/inversion of seepage parameters引用本文复制引用
基金项目
国家重点研发计划(2021YFA0715900)
出版年
2024
国家科技期刊平台
NSTL
万方数据