A Computationally Efficient Stochastic Method for Quantifying the Effects of Multi‐Surrogate Model Uncertainty on Saltwater Remediation Optimization

Abstract Machine learning models are highly potential to substitute computationally intensive numerical simulation models in saltwater intrusion (SWI) remediation optimization. However, uncertainty inherent in machine learning models can propagate through predictions into optimization, resulting in inaccurate solutions. Unlike deterministic modeling that ignores uncertainty with fixed outputs, this study proposes a computationally efficient mixed integer multiobjective stochastic optimization (MIMOSO) method, which uniquely bridges the gap between Bayesian multi‐model uncertainty quantification and risk‐aware decision‐making. The method captures stochastic uncertainty propagation from model prediction to optimization by integrating with Bayesian model averaging (BMA). In contrast to traditional single‐surrogate approaches, the proposed method incorporates multiple machine learning approaches to alleviate computational burden. The framework enables to derive optimal but robust extraction‐injection strategies by considering various constraint‐violation levels. Two conflicting goals are addressed: minimizing total extraction‐injection and maximizing SWI remediation effect. Binary variables are introduced to control discrete operation states of the well system. The developed method is demonstrated in a “1,500‐foot” sand aquifer located in Baton Rouge, USA. Results exhibit that Pareto optimal remediation strategies are identified with associated SWI risk levels. MIMOSO advances the field by simultaneously resolving computational bottlenecks through machine learning surrogates and rigorously propagating multi‐source uncertainties via BMA. Compared to numerical simulation based optimization (≥2,000 hr), machine learning assisted model reduces computation time to 87 hr, achieving a 23‐fold efficiency improvement. Three metrics (hypervolume, spacing, and maximum spread) validate superior performance regarding both convergence and diversity. The methodology provides a promising way for risk‐aware real‐world aquifer remediation design.