A modular coupled physics-informed neural network framework for urban flood prediction

Urban pluvial flooding driven by localized extreme rainfall increasingly exceeds the capacity of metropolitan drainage systems. Manhole surcharge overflow interacting with surface runoff produces complex inundation dynamics that are difficult to capture in real time. High-fidelity 1D–2D coupled numerical models are too computationally expensive for operational deployment, whereas purely data-driven deep-learning surrogates, although fast, do not enforce conservation laws or provide physically interpretable behaviour. We propose a modular coupled physics-informed neural network (MC-PINN) that bridges this gap. MC-PINN consists of a 1D PINN for sewer network flow governed by the Saint-Venant equations and a 2D PINN for surface flow governed by shallow-water equations, coupled through manhole overflow acting as a boundary condition. Mass continuity is enforced at the interface and momentum is strongly constrained via physics-based residual losses, enabling a hybrid surrogate with near real-time inference potential. To demonstrate feasibility, we present a manufactured-solution proof-of-concept in which a 1D advection PINN and a 2D diffusion PINN are coupled via a shared interface signal. The example shows that MC-PINN can jointly approximate both PDE fields and a consistent interface, supporting the mathematical viability of the modular coupling.