Development of a Two-phase Physics-informed Machine Learning Model for Sequential Spatiotemporal Correction of Grid-based Flood Simulations

Accurate flood simulation is essential because climate change increases the risk of flash floods resulting from extreme rainfall. Traditional grid-based physical models exhibit spatiotemporal uncertainties due to parameter estimation difficulties and structural simplifications. This study developed a two-phase Physics-Informed Machine Learning (PIML) hybrid grid-based flood model by sequentially combining a physical model with machine learning to overcome these limitations. The methodology consisted of temporal (Phase 1) and spatial (Phase 2) corrections. In Phase 1, a PIML model, trained on flow observations (target) using discharges and lagged rainfall from a lumped model (inputs), estimated a temporal correction ratio to correct temporal errors. In Phase 2, a spatial machine learning (ML) model was trained on flood risk maps (target) using flood depth and topographical features (e.g., digital elevation model and slope data) of a distributed model as inputs. In the hybrid simulation, the temporal correction ratio (Phase 1) was applied to the grid cell flow of the distributed model. The resulting flood depth was then fed into the spatial ML model (Phase 2) to produce the final, sequentially corrected flood depth, thus reducing spatiotemporal uncertainty. When applied to the Gyeongan stream basin, Phase 1 significantly enhanced hydrograph accuracy compared with the physical model. The full hybrid model, including Phase 2, corrected the inundation estimation errors of the physical model in scenario analysis, improving spatial accuracy and aligning results with official frequency-based Flood Risk Maps. The proposed two-phase PIML integrates the interpretive strengths of physical models with the nonlinear pattern recognition of ML, thereby offering an alternative for enhancing the practical utility of grid-based flood simulations.