Operator Inference for Physical and Generalized Surrogate Groundwater Modeling

Abstract Groundwater flow and solute transport models, governed by partial differential equations (PDEs), are computationally intensive, particularly in large‐scale. Traditional numerical models are prohibitively expensive, and existing surrogate models often fail under out‐of‐distribution (OOD) conditions, such as unseen initial conditions, boundary configurations or altered source terms. To address these challenges, we propose a novel framework based on Operator Inference (OpInf), a physics‐informed surrogate modeling approach. OpInf preserves the structure of governing equations, ensuring physical consistency and interpretability, while significantly improving computational efficiency and generalization capabilities. By leveraging Proper Orthogonal Decomposition (POD) for dimensionality reduction and inferring reduced operators directly from simulation data, OpInf enables robust prediction of system behavior. We evaluate the proposed method through two case studies: the two‐dimensional and three‐dimensional solute transport problem under different point‐source concentration fluctuation release conditions with heterogeneous hydraulic conductivity. The inversion framework is further appraised by integrating OpInf with Wasserstein Generative Adversarial Networks with Gradient Penalty (WGAN‐GP) parameterization methods and the Ensemble Smoother (ES) data assimilation. Results demonstrate that OpInf relatively outperforms other surrogate models, particularly under OOD conditions and the inversion efficiency can be increased by over 99%. We establish OpInf as a transformative tool for dynamic surrogate groundwater modeling, offering robust generalization, reduced computational costs, and strong potential for real‐world applications.