Integration of PINN with Conventional Well Logging for Few-Shot TOC Prediction in Ultradeep Source Rocks

Accurate prediction of total organic carbon (TOC) content in ultradeep source rocks exceeding 8,000 m burial depth represents a critical challenge in petroleum geoscience, where traditional methods demonstrate severe limitations due to extreme data scarcity and complex nonlinear relationships between logging responses and organic matter distribution. This study introduces a physics-informed neural network (PINN) framework that enables robust TOC prediction from minimal calibration data by integrating fundamental petrophysical constraints directly into the neural network optimization process. The proposed PINN architecture incorporates three critical petrophysical constraints as explicit loss terms: the inverse relationship between formation density and organic content, reflecting kerogen's distinctive low-density properties; the positive correlation between gamma ray response and TOC due to uranium enrichment in organic-rich intervals; and empirical consistency validation through modified rock physics relationships calibrated for ultradeep conditions. This physics-informed approach ensures predictions honor fundamental geological principles while learning from sparse data, effectively bridging the gap between data-driven flexibility and physics-based reliability. Application to the Lower Cambrian Yuertus Formation in the Tarim Basin's L3 well validates the framework's effectiveness under extreme conditions. With limited core-calibrated TOC measurements from depths exceeding 8,500 m, the PINN model integrates multiple wireline logs including natural gamma ray, deep resistivity, bulk density, and acoustic transit time to generate continuous high-resolution TOC profiles. Quantitative evaluation demonstrates that PINN achieves R ² of 0.9451 and an RMSE of 0.8571, representing R ² improvements of 282%, 18%, 14%, 13%, and 11% compared to the ΔlogR method, multiple regression analysis (MRA), multilayer perceptron (MLP), random forest (RF), and support vector machine (SVM) models, respectively. Critically, the PINN model achieves both RMSE and MAE values below unity, ensuring geological consistency across depth intervals where purely data-driven models produce unstable predictions. Qualitatively, the PINN predictions remain geologically consistent across all depth intervals, avoiding the instabilities observed in purely data-driven models and reliably capturing the nonlinear relationships between petrophysical logs and TOC content. This breakthrough establishes physics-informed learning as an effective paradigm for petrophysical characterization in data-scarce ultradeep environments, directly addressing the petroleum industry's critical need for reliable formation evaluation where conventional approaches fail.