| 摘要: |
| 流域水文模型参数对水文模拟预报的精度具有重要影响。在水文模型的数学表达由差分形式向微分形式发展的背景下，如何利用微分形式水文模型过程连续、时间尺度灵活的特点，进行模型参数优化是值得研究的问题。提出一种基于神经常微分方程（Neural Ordinary Differential Equations，NODE）的水文模型参数优化方法，将神经网络嵌入水文模型的微分动力系统，使用常微分方程数值求解器正向模拟连续水文过程，计算损失函数并反向传播梯度信息以更新神经网络参数，从而实现水文模型参数优化。以新安江模型为例，设计了理想数值实验和典型流域应用两种验证方案，并与SCE-UA优化方法进行了对比。结果显示，基于NODE优化方法确定的新安江模型参数，与理想参数“真值”的误差平均不超过9.8%；相较于SCE-UA方法，NODE得到的优化参数对流量过程具有更高的模拟精度。研究表明，基于NODE的参数优化方法通过微分方程正向求解和梯度信息反向传播，可有效搜索参数空间，适用于微分形式水文模型的参数优化问题。 |
| 关键词: 神经常微分方程 参数优化 水文模型 深度学习 新安江模型 |
| DOI： |
| 分类号: |
| 基金项目:国家自然科学基金项目（52379007），水利部重大科技项目（SKR-2022032） |
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| Study on Parameter Optimization Method of Hydrological Model Based on Neural Ordinary Differential Equations |
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Qin Xiangzhao1, Liang Zhongmin1, Zhao Jianfei1, Li Binquan1, Duan Yanan2, Hu Yiming1, Wang Jun1
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1.College of Hydrology and Water Resources, Hohai University;2.Jiangsu Province Water Conservancy Engineering Sci-tech Consulting Co., Ltd.
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| Abstract: |
| The accuracy of hydrological simulation and forecast is significantly influenced by the parameters of watershed hydrological models. In the context of hydrological model expressions evolving from discrete to differential forms, it is worth investigating how to utilize the continuous process and flexible time scales of differential hydrological models for parameter optimization. A hydrological model parameter optimization method based on Neural Ordinary Differential Equations (NODE) is proposed, in which the neural network is embedded into the differential dynamical system of the hydrological model, and the continuous hydrological process is simulated forward using an ODE numerical solver. The loss function is calculated and the gradient information is propagated backward to update the neural network parameters, thereby optimizing the hydrological model parameters. Taking parameter optimization of Xinanjiang model as an example, ideal numerical experiment and typical watershed application are conducted for validation, and compared with the SCE-UA optimization method. The results show that the average error between the Xinanjiang model parameters determined by the NODE optimization method and the ideal parameter "true value" is not more than 9.8%. Compared with the SCE-UA method, the optimized parameters obtained by NODE have higher simulation accuracy for the discharge process. The research shows that the parameter optimization method based on NODE can effectively search the parameter space through the forward solution of differential equation and the back propagation of gradient information, which is suitable for the parameter optimization problem of differential form hydrological model. |
| Key words: neural ordinary differential equations parameter optimization hydrological model deep learning Xinanjiang model |
