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.

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