Reliable and Practical Inverse Modeling of Natural‐State Geothermal Systems Using Physics‐Informed Neural Networks: Three‐Dimensional Model Construction and Assimilation With Magnetotelluric Data

Abstract

Inverse modeling of geothermal systems is crucial for geothermal resource development and understanding of underground thermal structures; however, conventional modeling by calibrating numerical simulation has been known to have a high computational load and pitfalls to fall in local minima. Physics‐informed neural networks (PINNs) are an emerging method for inverse numerical modeling of partial differential equations using deep learning. Yet, in particular, 3D modeling in Earth science requires efficient training in physical laws and verification of effectiveness with limited data. This study examined the effectiveness of PINNs in the inverse modeling of natural‐state geothermal systems by predicting the 3D temperature, pressure, and permeability structure of the Kakkonda geothermal field in Japan based on synthetic well data. We introduced coefficient annealing into the loss function of the neural network to efficiently train the physical laws. Our results demonstrated that temperatures and pressures modeled by the PINN outperformed those by data‐driven machine learning in terms of prediction accuracy and physical interpretability with a limited amount of well data. The effects of setting boundary conditions and optimizers were also investigated to improve the method's applicability. We demonstrated the effectiveness of the transfer learning of pretrained networks in improving the permeability field's accuracy. This study further demonstrated that training the network by assimilating magnetotelluric data and well data improved the prediction accuracy of permeability and physical reliability.