Self-potential forward modeling method based on physics-informed neural networks

Self-potential method is a common method of environmental geophysical exploration. Researchers often use finite element method (FEM) to carry out forward modeling. Forward modeling is an important part of research, but the FEM has some problems, such as large amount of calculation, long time and so on. In this regard, we propose a method based on physics-informed neural networks (PINNs) for forward modeling of a kind of self-potential called streaming potential. The particularity of streaming potential is that its formation involves both flow field and electric field. In order to verify the feasibility of the PINNs method, we set up a two-dimensional (2D) scene and the corresponding boundary conditions, and tried to calculate the hydraulic head distribution and the corresponding self-potential distribution in the saturated and unsaturated flow region under stable conditions by using neural network. We have adopted two different network structure designs. One is to use the same neural network to calculate the hydraulic head distribution and electrical potential distribution in the region at the same time. The other is to use two different neural networks to calculate the hydraulic head and electrical potential respectively. In both methods, we have added the corresponding partial differential equation (PDE) to constrain the network training process. Then, we compare their results with the traditional FEM. We find that such a neural network with physical constraints can effectively obtain the spatial distribution of the unknown quantity we need. Compared with the FEM, PINNs method can be used in the case of incomplete boundary conditions. In addition, compared with other deep learning (DL) methods, the results of PINNs method are more interpretable.