Simulation-based Inverse Mapping Framework for Runoff Prediction

While accurate parameter estimation in physically-based hydrological models is critical, applying supervised learning for this purpose presents inherent limitations. This is because supervised learning requires parameter ground truth as labels, yet obtaining spatially complete observations of these physical parameters in real-world basins is practically impossible. To address this challenge, this study proposes a "simulation-based inverse mapping framework" capable of reconstructing the spatial distribution of physical parameters solely from flow data, without relying on observed parameter ground truth. This approach utilizes a physically-based hydrological model as a data generator. The training dataset is constructed by filtering Sobol-sequence-generated parameter candidates; only realistic combinations that satisfy physical constraints—specifically the Budyko water balance and the negative correlation between NDVI and Curve Number (CN)—are selected. Furthermore, the Cross-Entropy Method (CEM) was employed to refine the training data, optimizing for both hydrological plausibility and predictive accuracy. The developed deep learning model is trained to take observed flow time series as input and inversely predict the basin's physical parameter fields (e.g., CN, hydraulic conductivity). When applied to the test period, the model demonstrated high flow reproduction performance with a satisfactory Nash–Sutcliffe Efficiency (NSE). In conclusion, this study demonstrates that by integrating physical modeling processes with the computational power of deep learning, it is possible to effectively estimate hydrological parameters and achieve reliable runoff analysis, even in the absence of parameter ground truth.