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Abstract Applications of process‐based models (PBM) for predictions are confounded by multiple uncertainties and computational burdens, resulting in appreciable errors. A novel modeling framework combining a high‐fidelity PBM with surrogate and machine learning (ML) models is developed to tackle these challenges and applied for streamflow prediction. A surrogate model permits high computational efficiency of a PBM solution at a minimum loss of its accuracy. A novel probabilistic ML model partitions the PBM‐surrogate prediction errors into reducible and irreducible types, quantifying their distributions that arise due to both explicitly perceived uncertainties (such as parametric) or those that are entirely hidden to the modeler (not included or unexpected). Using this approach, we demonstrate a substantial improvement of streamflow predictive accuracy for a case study urbanized watershed. Such a framework provides an efficient solution combining the strengths of high‐fidelity and physics‐agnostic models for a wide range of prediction problems in geosciences.