PINN-Curvas-Sinteticas: Innovative Application of Physics-Informed Neural Networks in Logging Curve Prediction

This project applies Physics-Informed Neural Networks (PINN) to predict density curves from regular logging data, addressing missing or damaged wellbore data issues. By integrating physical constraints into the neural network's loss function, it enhances generalization ability and provides reliable alternatives for density curve prediction in oil and gas exploration. The open-source project is maintained by OilCoder on GitHub.

In oil and gas exploration, density curves (RHOB/DEN) are critical for porosity calculation, lithology identification, and reservoir quality evaluation. However, they often go missing or get damaged (e.g., wellbore collapse). Traditional solutions like re-logging are costly/time-consuming, while pure data-driven ML models lack generalization on new wells. PINN offers a solution by embedding physical laws into models.

1. Physical Relationship: DEN_expected = A·NPHI + D·(NPHI×GR) (A=-0.556, D=0.086, R²=0.338) to capture shale content.
2. Loss Function: L_total = L_data (MSE) + λ·L_physical (deviation from physical expectation).
3. Intelligent Weight: Zero λ in washout areas to ignore unreliable constraints.

• Input: 5 curves (GR, RT/RILD, RILM, NPHI/CNLS, SP).
• Model: MLP (5→64→64→32→1) with Adam optimizer (lr=1e-3) and fixed seed=42.
• Preprocessing: Washout detection, outlier handling (5-detector consensus), log transformation for resistivity, Yeo-Johnson/Z-score normalization, DEN constrained to [1.5,3.1] g/cc.

• LOWO: Leave-One-Well-Out to avoid data leakage (simulates new well prediction).
• Two-Level Protocol: 1. LOWO on 27 wells to select optimal λ; 2. Blind test on 3 independent wells (ensemble/single model).

• LOWO: PINN (λ=0.5) improves MAE by 3.6% (0.140→0.135) and R² by18.5% (0.276→0.327) (22/27 wells better).
• Blind Wells: PINN improves all 3 wells (ensemble: MAE↓0.004, R²↑0.038; single model: MAE↓0.007, R²↑0.086).
• Insight: Physical constraints enhance generalization on unseen wells.

• Industry: Data completion for missing curves, cost reduction, better reservoir decision support.
• Research: Domain knowledge fusion, LOWO as spatiotemporal evaluation reference, physical constraints boost robustness.
• Scalability: Extendable to other logging tasks (sonic time difference, resistivity reconstruction).
• Outlook: Balances data/knowledge-driven approaches for scientific ML reliability.