WellBench: An Open-Source Benchmark for Synthetic Well Log Generation

Pore pressure prediction is essential for safe well planning, yet machine learning models are limited by the scarcity of real well data. Synthetic data generation is a common approach, including interpolation methods, physics-informed generators, and data-driven models. To our knowledge, no prior work systematically compares these approaches under a matched hyperparameter-tuning budget using both distributional and downstream evaluation. We introduced WellBench, a multi-basin benchmark, and a Physics-Optimized Forward Model (POFM), a physics-based scientific simulator for synthetic well-log generation that integrates petrophysical relationships and is calibrated to real well-log distributions using Tree-structured Parzen Estimation (TPE). We compared POFM against a TPE-tuned CTGAN, SMOTE, and Smoothed Bootstrap across four regions. POFM achieved the highest Distance-to-Closest-Record (DCR), indicating the greatest separation from real training records, while the interpolation generators best reproduced the real marginals but yielded the lowest DCR. Across seven downstream models, only the interpolation generators achieved positive blind-well Train-Synthetic-Test-Real ($R^2$) (up to $\approx 0.98$), while CTGAN and POFM yielded negative $R^2$. Under a depth-held-out split, Train-Real-Test-Real (TRTR) failed at every real-data fraction, highlighting the challenge posed by limited real-data coverage. Yet TSTR with interpolation-based generators outperformed TRTR at every fraction. These results reveal a fundamental tradeoff between distributional fidelity and downstream utility. They also show that interpolation-based generators can outperform complex synthetic-data approaches when real data is scarce.