A review of machine learning hydrological models integrating physical mechanisms

With advancements in information technology and physical modelling, physics-informed machine learning methods are emerging as a research focus in hydrology due to their superior accuracy, physical consistency, and ability to effectively handle uncertainties and nonlinear characteristics. In this paper, we systematically review the latest applications and developments of physics-informed machine learning in hydrological modelling over the past decade. We categorize the integration approaches into six distinct types: mismatch correction, parameter optimization, data augmentation, physical constraints, structural embedding, and formula integration. Special emphasis is placed on analyzing the progress and limitations of dual-driven models that synergize data and physical principles. Future directions are proposed to advance hydrological modelling through physics-machine learning integration, including model parameter optimization, interpretability enhancement, small-sample scenario adaptations, and improved mid-to-long-term scale simulations. The development of novel hybrid approaches combining physics and artificial intelligence is envisioned to drive transformative progress in hydrological model development.