Dual-Prior-Constrained Temporal Inversion and FNO Surrogate-Model-Driven Coordinated Optimization of Drilling Engineering Parameters

Real-time and accurate inversion of drilling-fluid hydraulic parameters while drilling, together with the coordinated optimization of drilling parameters, is critical for safe and efficient drilling in deep and complex formations. Conventional methods are limited by single-source observations, insufficient prior constraints, weak surrogate-model generalization, and isolated parameter optimization. To address these issues, this paper proposes a three-layer intelligent decision-making framework. The first layer is a dual-prior-constrained temporal inversion module that fuses a pre-drill mechanistic baseline prior with an offset-well statistical prior and estimates plastic viscosity, yield point, annular cuttings concentration, and equivalent eccentricity from standpipe-pressure and rotary-torque observations through a four-term loss function. The second layer is a Fourier neural operator (FNO) surrogate trained on data generated by an in-house two-phase hydraulics solver. All results reported here are obtained on such synthetic data: no field or laboratory measurements are used, and the offset-well statistical prior is prescribed—its mean from a regional depth trend and its covariance from an assumed inter-well variability—rather than fitted to measured offset-well logs. The third layer is a hydraulic–mechanical coupled multi-objective optimization framework that coordinates weight on bit, rotary speed, and flow rate using online Bayesian optimization and probabilistic safety constraints. Numerical experiments with 30 independent noise realizations show that the dual-prior constraints reduce the inversion root-mean-square error by up to 85% for the weakly identifiable parameters (cuttings concentration and equivalent eccentricity) and by 37% for plastic viscosity; that the FNO surrogate is about 240 times faster than the reference numerical simulation and attains a mean relative error of 0.31% for equivalent circulating density and 2.25% for annular pressure loss, about three times lower than the best baseline (a quadratic response surface, 0.95% and 7.16%), preserving that lead outside the training range, while remaining the only surrogate that can be evaluated on a different depth grid without retraining; and that three-parameter optimization improves the rate of penetration by 34.9%. At an equal total surrogate cost, the proposed online optimizer attains the highest mean gain of the methods compared (32.4% over 40 sliding windows, against 31.9% for an online NSGA-II with the same update frequency and 29.4% for a random-search control) while using 4.5 times fewer forward evaluations of the surrogate; the advantage over NSGA-II is small and not statistically resolved at this budget, whereas the advantage over random search is, and the proposed method also has the best worst-case window and the smallest window-to-window spread. The recommended operating points are re-verified with the reference forward solver. Imposing the two analytic closure relations of the forward model as soft physics residuals did not improve accuracy because the reference data satisfy them exactly and the constraint therefore carries no additional information. The framework provides an accurate, efficient, and robust solution for real-time intelligent drilling decision-making.