基于PINNs算法的地下水渗流模型求解及参数反演

Simulation and parameter identification of groundwater flow model based on PINNs algorithms

地下水渗流模型的渗流流速计算(正向求解)和渗流参数反演(反向求解)工程意义重要,但目前能同时解决两类问题的算法较少。针对该问题,引入了物理信息神经网络(PINNs)算法,并加入硬约束进行改进,在正向求解方面,分别建立了渗流方程与达西定律耦合的水头、流速同时求解方法(PINNs-H-I),以及先计算水头再通过自动微分求解流速的计算方法(PINNs-H-II)。对于反向求解,分别采用单(多)物理场神经网络模型的PINNs算法反演均质(非均质)渗流参数。通过算例分析表明,相比软约束PINNs算法,通过施加硬约束可同时改善正向求解和反向求解的性能,另外在正向渗流速度计算中PINNs-H-II方法具有更高的计算精度,同时单(多)物理场神经网络模型PINNs算法反演的均质(非均质)渗流参数与实际值符合较好。

The simulation of the Darcy velocity(forward problem)and the identification of seepage parameters(backward problem)in the groundwater flow model are of significance to practical projects,while at present,few algorithms can be used to simultaneously tackle these two problems.The physics-informed neural networks(PINNs)algorithms with the hard constraints are introduced for investigating these two problems at the same time.For the forward problem,two methods are established for deriving the Darcy velocity.One is to address the groundwater head and Darcy velocity concurrently by coupling the seepage flow equation with the Darcy’s law(PINNs-H-I),and the other is to calculate the groundwater head first and then solve the Darcy velocity by automatic differentiation(PINNs-H-II).For the backward problem,the PINNs algorithms for the single and multi-physical field neural network models are used to identify the seepage parameters of homogeneous and non-homogeneous seepages,respectively.Furthermore,several examples are presented,and the results show that the hard-constraint PINNs algorithms exhibit better performances for the forward and backward problems compared with the soft-constraint ones.In addition,it is noted that PINNs-H-II possesses higher calculation accuracy,and both the PINNs algorithms for the single and multi-physical field neural network models can accurately identify the seepage parameters in the homogeneous and non-homogeneous seepage.