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

• Published in: Journal of geophysical research. Machine learning and computation Vol. 2; no. 3
• Main Authors: Ishitsuka, K., Ishizu, K., Watanabe, N., Yamaya, Y., Suzuki, A., Bandai, T., Ohta, Y., Mogi, T., Asanuma, H., Kajiwara, T., Sugimoto, T.
• Format: Journal Article
• Language: English
• Published: 01.09.2025
• ISSN: 2993-5210; 2993-5210
• DOI: 10.1029/2025JH000683

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. Constructing subsurface numerical models for geothermal systems is a fundamental step for site characterization, resource potential assessment, and sustainable use of geothermal resources. This study developed a machine learning approach called physics‐informed neural networks for modeling natural‐state geothermal systems. This machine learning approach increases reliability and interpretability by training the well measurements and the physical laws of geothermal systems. The developed approach was examined by applying it to a 3D numerical model of the Kakkonda geothermal field, Japan, and the results showed superior prediction accuracy and physical reliability than those of purely data‐driven methods. This study also highlighted the importance of training strategies of physics‐informed neural networks to accelerate the training of physical laws. The effectiveness of assimilating electromagnetic observations on the ground surface in the developed approach was further demonstrated in terms of refining the permeable reservoir zone and improving the physical validity of the model. These results showed that the machine learning approach is promising for creating subsurface models for geothermal systems. A physics‐informed neural network (PINN) demonstrated its effectiveness for 3D inverse modeling of natural‐state geothermal systems The PINN prediction was improved by balancing loss components and outperformed data‐driven approaches in accuracy and interpretability Assimilation with magnetotelluric data improved accuracy and physical validity, showing the effectiveness of data integration with the PINN