The Hi-Fi Yellow River paradigm: From static models to AI-driven scenarios [version 1]

In 2000, the concept of the “Three Yellow River Initiative” (Prototype, Model, Digital) established a comprehensive framework for Yellow River study and management. After two decades, the limitations of these isolated modelling approaches have become increasingly apparent, particularly the insurmountable scaling challenges of physical models and the inherent simplification gaps of digital simulations that cannot capture the nonlinear, multi-scale water-sediment dynamics of the river. This paper introduces the Hi-Fi (High-Fidelity) Yellow River paradigm, an intelligent, closed-loop governance system that leverages artificial intelligence to enable instantaneous scenario manifold switching for water management based on real-time observations from the Prototype Yellow River. We formalize this paradigm using contact geometry: the state space of river dynamics forms a contact manifold $(\mathcal{E},\mathrm{\Theta })$, where the transition from model prediction to observed reality manifests as a transversal transition between scenario manifolds along $\mathrm{k}\mathrm{e}\mathrm{r}(\mathrm{d}\mathrm{\Theta })$. This mathematical framework rigorously captures the core of high-fidelity research—grounding governance decisions in real-world scenarios rather than simplified representations—while providing kinematic constraints for adaptive water-sediment regulation strategies. The framework unifies the “Three Yellow River Initiative” into a single reality-responsive intelligent system, transforming static prediction-based governance into dynamic, scenario-driven decision-making for the Yellow River basin.