Three-dimensional in-situ stress inversion from hydraulic fracturing measurements: A physically constrained Bayesian optimization approach with SH-azimuth consistency

Conventional in-situ stress inversion based mainly on stress-magnitude fitting may yield non-unique solutions with similar magnitude residuals but inconsistent principal stress orientations. Moreover, traditional data-driven methods usually require large training datasets, limiting their applicability when high-fidelity forward simulations are expensive. To address these limitations, this study proposes a physically constrained Bayesian optimization framework, termed SOC-BO, for sample-efficient and geomechanically consistent in-situ stress inversion from hydraulic fracturing (HF) measurements. The inversion is formulated as a constrained optimization problem in which a measurement-point-normalized objective function is constructed to reduce the scale-dominance effect caused by large spatial variations in stress magnitude, while the measured maximum horizontal principal stress ( S H ) azimuths are introduced as explicit physical constraints. Through the probability of feasibility, the sequential procedure allocates high-fidelity simulations to candidates having both low normalized component misfit and acceptable S H -azimuth consistency. The method was validated using HF measurements from an ultra-long, deeply buried tunnel on the eastern margin of the Qinghai–Tibet Plateau. SOC-BO identified the best feasible solution within 67 forward simulations. Compared with unconstrained Bayesian optimization under the same initial design, SOC-BO reduced the forward-simulation budget by 28.7% and the optimal objective value by 12.5%. Compared with a genetic-algorithm-optimized backpropagation neural network under the same forward-simulation budget, the stress-magnitude and S H -azimuth RMSEs were reduced by 34% and 36%, respectively. These results indicate that SOC-BO provides a physically constrained and sample-efficient approach to improve parameter identifiability and suppress S H -azimuth inconsistent non-unique solutions in HF-based inversion when the regional stress direction is sufficiently coherent and local directional uncertainty can be quantified.