Accurate flood forecasting is essential for mitigating disaster risks and protecting communities. However, purely data-driven machine learning models often struggle in data-scarce environments and may violate fundamental hydrological principles. Standard Long Short-Term Memory (LSTM) networks can generate physically inconsistent predictions, particularly when extrapolating to extreme weather conditions. To address these limitations, we propose a Physics-Informed Machine Learning (PIML) framework that incorporates hydrological knowledge directly into the loss function of an LSTM model. Specifically, a Trend Alignment constraint penalizes directional inconsistencies between precipitation and discharge trends, improving model robustness without requiring complex hydrodynamic equations. This regularization encourages the model to learn physically plausible hydrograph behavior, even with limited training data, while enhancing reliability during peak flood events. Experimental results show that the proposed physics-informed model outperforms a standard LSTM baseline in data-scarce settings, increasing the Nash-Sutcliffe Efficiency (NSE) from 0.20 to 0.23 when trained on only 5% of the available data. Additional stress tests under simulated extreme climate scenarios demonstrate that the baseline model exhibits unstable behavior, whereas the physics-informed model maintains directional consistency and physical plausibility. Although accurately predicting extreme peak magnitudes remains challenging with limited data, the proposed approach substantially reduces unphysical fluctuations common in purely data-driven models. These findings demonstrate that simple physical constraints can significantly improve the reliability of deep learning models for real-time flood forecasting, offering a practical solution for ungauged basins and evolving climate conditions.
Landslide susceptibility prediction is critical for geohazard risk assessment and mitigation. Conventional data-driven paradigm achieves high predictive accuracy but require sufficient conditioning factors and large-scale landslide inventories. However, in practical engineering applications across mountainous and plateau regions, data-scarce conditions are commonly observed, where such data requirements are rarely satisfied, rendering conventional data-driven paradigm inapplicable. To address this issue, we propose a knowledge-data dually driven paradigm for accurate landslide susceptibility prediction under data-scarce conditions. The essential idea behind the proposed novel paradigm is the integration of the geomorphic prior knowledge with scarce landslide data. To validate the proposed paradigm, we first applied it to a data-rich region in central Italy, where a conventional data-driven paradigm trained on the full dataset served as the baseline. By utilizing only 30% of the available landslide data, the proposed paradigm achieved comparable predictive accuracy to the baseline, demonstrating its effectiveness under data-scarce conditions. The paradigm was further evaluated in a genuinely data-scarce environment for application, the Qilian Permafrost Region of the Tibetan Plateau, where it also yielded reliable susceptibility predictions, confirming its applicability under data-scarce conditions.