ILMWR V4: A Physics-Constrained Spatial–Temporal Graph Digital Twin for Real-Time 2D Flood Forecasting

Real-time flood forecasting requires a balance between the physical consistency of hydrodynamic models and the computational efficiency of data-driven surrogates. We present ILMWR V4, a physics-constrained spatial–temporal framework that couples a two-dimensional HLLC shallow-water solver with a hierarchical graph-based surrogate for rapid flood-field prediction. The framework contains two complementary tiers. Tier A provides station-level early warning through a hybrid rainfall–runoff formulation, inverse Manning stage recovery, and a physics-guided multi-task recurrent model with temporal attention. Tier B constructs physics-generated flood trajectories from a two-dimensional HLLC solver and learns their spatio-temporal evolution using Phys-STMGN, which combines a causal dilated Temporal Convolutional Network with hierarchical FPS–Voronoi graph processing and geometry-aware coarse-to-fine interpolation. The spatial surrogate predicts the temporal evolution of the conservative hydraulic state U = [h, hu, hv] rather than directly reconstructing flood depth, and is trained using HLLC trajectory matching, mass-balance regularization, wet/dry consistency, and multi-step autoregressive rollout losses. Environmental forcing from ERA5, including rainfall, soil-water variables, and temperature, is incorporated as explicit temporal information, while known future rainfall can be provided to the spatial predictor during forecasting. The hierarchical graph processor is adopted from recent mesh-based multiscale graph simulation and specialized here for flood hydraulics rather than presented as a new graph-coarsening operator. An event-level validation protocol is used to reduce temporal leakage and assess event-to-event generalization. The resulting framework provides a reproducible bridge between physics-based flood simulation and fast spatial forecasting, with the HLLC solver retained as a numerical teacher, physics validator, and fallback mechanism.