Dimensionally Consistent Formation Pressure Prediction from Borehole Sensing Data Using Pressure Ratio Symbolic...

Formation pressure labels are often stored as equivalent mud weight (EMW), whereas engineering analysis requires true pressure and validation strategies that account for the strong depth dependence of borehole data. This study develops a dimensionally consistent pressure ratio symbolic regression framework in which vertical overburden stress provides the pressure scale and a compact dimensionless correction is learned from reference-scaled borehole variables. After converting EMW-based labels to MPa and applying transparent quality control criteria, 1877 of 2025 depth-indexed records were retained. Redundant and deterministically derived variables were identified through correlation analysis, variance inflation factors, principal component analysis, and deterministic relation checks and were excluded from the compact symbolic search. Five contiguous depth blocks with a 20 m purge zone were used for leakage-resistant validation, with symbolic-structure selection repeated within each outer training fold. The selected four-coefficient expression, comprising an intercept and three predictor-dependent terms, retained only depth and acoustic slowness. Fixed-structure depth-block validation yielded a coefficient of determination (R²) of 0.3008, a root mean square error (RMSE) of 3.5439 MPa, a mean absolute error (MAE) of 2.6964 MPa, and a mean absolute relative error (MARE) of 10.02%, while the conservative nested symbolic pipeline yielded MARE = 11.60%. External zero-shot evaluation on 974 samples from an external well, 98.36% of which were outside the calibration depth range, yielded R² = 0.0265, RMSE = 7.0024 MPa, MAE = 5.5723 MPa, and MARE = 11.51% against an independent D-exponent-based engineering pressure reference (PP_DX). Sparse local recalibration using 10 depth-spaced PP_DX engineering reference points, with ±20 m neighborhoods excluded from evaluation, improved performance to R² = 0.8684, RMSE = 2.8431 MPa, MAE = 2.1108 MPa, and MARE = 4.39% on the remaining 564 samples. These results indicate that the proposed framework provides an explicit and independently auditable pressure equation that preserves the overall pressure scale under substantial depth domain shift and can be efficiently recalibrated using sparse local pressure information. Site-specific calibration remains necessary for accurate reproduction of local pressure variations.