用物理约束神经网络替代水文模型，实现快速精准的河流水位预测。
Physics-Informed Neural Network Surrogate Models for River Stage Prediction
- 将圣维南方程融入神经网络训练，保证物理一致性。
- 在单条河段上逼近HEC-RAS数值解，相对误差普遍较低。
- 计算效率远超传统模型，支持实时推理，适合工程应用。
本文研究了将物理信息神经网络（PINNs）作为河流水位预测的代理模型的可行性，旨在降低计算成本的同时保持预测精度。主要贡献表明，在单一河流数据上训练的PINN能够成功逼近HEC-RAS数值解，预测精度高，相对误差普遍较低，尽管部分河段存在较高偏差。通过在学习过程中嵌入控制圣维南方程，所提出的基于PINN的代理模型强化了物理一致性，并显著提升了计算效率，相比HEC-RAS有明显优势。我们从准确性和计算速度两方面评估模型性能，结果表明其能紧密逼近HEC-RAS预测结果，同时支持实时推断。这些结果凸显了PINN在单河段水动力模拟中作为高效代理模型的潜力，为计算高效的河流水位预报提供了新路径。未来工作将探索提升PINN在更通用多河流场景下的训练稳定性和鲁棒性。
原文摘要 · Abstract (English)
This work investigates the feasibility of using Physics-Informed Neural Networks (PINNs) as surrogate models for river stage prediction, aiming to reduce computational cost while maintaining predictive accuracy. Our primary contribution demonstrates that PINNs can successfully approximate HEC-RAS numerical solutions when trained on a single river, achieving strong predictive accuracy with generally low relative errors, though some river segments exhibit higher deviations. By integrating the governing Saint-Venant equations into the learning process, the proposed PINN-based surrogate model enforces physical consistency and significantly improves computational efficiency compared to HEC-RAS. We evaluate the model's performance in terms of accuracy and computational speed, demonstrating that it closely approximates HEC-RAS predictions while enabling real-time inference. These results highlight the potential of PINNs as effective surrogate models for single-river hydrodynamics, offering a promising alternative for computationally efficient river stage forecasting. Future work will explore techniques to enhance PINN training stability and robustness across a more generalized multi-river model.
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