A Stochastic Dynamical Framework for Digital Twin Models of Coastal Systems
Résumé
We develop a stochastic dynamical framework for modelling digital twin systems in coastal environments subject to uncertainty, partial observations, and control. The true coastal state is modelled as a diffusion process governed by stochastic differential equations, capturing the evolution of sediment transport, erosion, and hydrodynamic interactions. The digital twin is defined as a coupled estimator process informed by noisy observations and data assimilation updates. We analyze the joint process comprising the true state and the digital twin, establishing conditions under which the coupled system admits a unique invariant measure and is ergodic. Furthermore, we study rare transitions between environmental regimes using large deviation theory, providing asymptotic estimates for the probabilities of extreme coastal events. With its mathematical foundation, this framework offers a promising avenue for constructing and controlling predictive, adaptive, and resilient digital twins for coastal protection applications.
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