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.

神经网络在河流水力学中的应用尚不成熟，尽管该领域存在数据稀缺等机器学习技术挑战。因此，本研究旨在通过在训练阶段引入物理信息来缓解这一问题，并展示了这种方法可以提高预测能力。