Enterprise AI Analysis
A Loss-Function Enhancement Method for Multi-Station River Water Level Forecasting under Extreme Sample Sparsity
In multi-station daily river water level forecasting, extreme high-water events are rare but critical for flood control and operational decision-making. However, due to sparse sampling, single-variable inputs, and the extremely low proportion of extreme samples, deep time-series models trained with mean squared error (MSE) tend to overfit normal conditions and exhibit noticeable underestimation during flood peaks.
Executive Impact: Enhancing Flood Forecasting Reliability
Deep time-series models trained with Mean Squared Error (MSE) often overfit normal conditions and underestimate flood peaks due to sparse sampling and the rarity of extreme events in multi-station daily river water level forecasting. This leads to amplified errors and delayed peak responses, hindering effective flood control and operational decision-making.
This study proposes an architecture-independent loss enhancement framework, termed Extreme-Aware Loss (EAL). EAL consists of a Single-threshold Extreme-aware MSE (SEAM), which increases the optimization contribution of extreme samples, and an underestimation penalty module (UE), which suppresses systematic underestimation of extreme water levels. The method can be seamlessly integrated into LSTM, GRU, TCN, and other networks without altering model structures.
Experiments on nine representative hydrological stations demonstrate that EAL significantly improves extreme-related metrics while maintaining overall accuracy, enhancing peak identification and temporal characterization. These results indicate that EAL provides effective support for flood warning and hydrological risk management.
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Extreme-RMSE Reduction
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Hit Rate Increase
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Peak Magnitude Error Reduction
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EAL
Enhances Extreme Event Forecasting
The Extreme-Aware Loss (EAL) framework addresses data sparsity and extreme event imbalance by combining a Single-threshold Extreme-aware MSE (SEAM) and an Underestimation Penalty (UE). This model-agnostic approach improves sensitivity to rare flood peaks without altering core network architectures.
Enterprise Process Flow
Historial multi-station water levels
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Data Preprocessing
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Backbone Sequence Model (LSTM/GRU/TCN)
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Extreme-Aware Loss (EAL) (SEAM + UE)
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Gradient Update
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Predicted Water Level
| Metric | Baseline Performance (GRU) | EAL Performance (GRU+EAL) |
|---|---|---|
| Extreme-RMSE | 0.441 |
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| HitRate | 0.918 |
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| PeakMagMAE | 0.112 |
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| Overall Accuracy (RMSE) | 0.287 |
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Ablation Study: Complementary Roles of SEAM and UE
The ablation study confirms the distinct and complementary contributions of EAL's components. Underestimation Penalty (UE) primarily reduces peak-magnitude and flow-volume underestimation, leading to the largest improvement in PeakMagMAE. Meanwhile, Single-threshold Extreme-aware MSE (SEAM) is most effective in enhancing extreme-event recall and reducing peak-timing error. Their combination achieves the best overall performance, validating the synergistic robustness of EAL in capturing flood peaks.
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