Simulation and parameter identification of groundwater flow model basedon PINNs algorithms

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.