Application of Neural Networks to river hydraulics is fledgling, despite the field suffering from data scarcity, a challenge for machine learning techniques. Consequently, many purely data-driven Neural Networks proved to lack predictive capabilities. In this work, we propose to mitigate such problem by introducing physical information into the training phase. The idea is borrowed from Physics-Informed Neural Networks which have been recently proposed in other contexts. Physics-Informed Neural Networks embed physical information in the form of the residual of the Partial Differential Equations (PDEs) governing the phenomenon and, as such, are conceived as neural solvers, i.e. an alternative to traditional numerical solvers. Such approach is seldom suitable for environmental hydraulics, where epistemic uncertainties are large, and computing residuals of PDEs exhibits difficulties similar to those faced by classical numerical methods. Instead, we envisaged the employment of Neural Networks as neural operators, featuring physical constraints formulated without resorting to PDEs. The proposed novel methodology shares similarities with data augmentation and regularization. We show that incorporating such soft physical information can improve predictive capabilities.

翻译：神经网络在河流水力学中的应用尚处于起步阶段，尽管该领域面临数据稀缺这一机器学习技术的挑战。因此，许多纯数据驱动的神经网络被证明缺乏预测能力。本研究提出通过引入物理信息至训练阶段来缓解该问题。该思路借鉴了近期在其他领域提出的物理信息神经网络。物理信息神经网络以控制现象的偏微分方程残差形式嵌入物理信息，本质上被构想为神经求解器（即传统数值求解器的替代方案）。此类方法鲜少适用于环境水力学领域——该领域认知不确定性较大，且计算偏微分方程残差时会遭遇与传统数值方法类似的困难。作为替代方案，我们设想将神经网络作为神经算子使用，其物理约束无需借助偏微分方程即可构建。这一创新方法与数据增强及正则化技术存在相似性。研究表明，融入此类软物理信息可显著提升预测能力。