We describe a Physics-Informed Neural Network (PINN) that simulates the flow
induced by the astronomical tide in a synthetic port channel, with dimensions
based on the Santos - S\~ao Vicente - Bertioga Estuarine System. PINN models
aim to combine the knowledge of physical systems and data-driven machine
learning models. This is done by training a neural network to minimize the
residuals of the governing equations in sample points. In this work, our flow
is governed by the Navier-Stokes equations with some approximations. There are
two main novelties in this paper. First, we design our model to assume that the
flow is periodic in time, which is not feasible in conventional simulation
methods. Second, we evaluate the benefit of resampling the function evaluation
points during training, which has a near zero computational cost and has been
verified to improve the final model, especially for small batch sizes. Finally,
we discuss some limitations of the approximations used in the Navier-Stokes
equations regarding the modeling of turbulence and how it interacts with PINNs.

本文提出了一种基于 PINN 的物理模拟神经网络，用于模拟合成港口通道中由天文潮汐引起的流动，该模型的两个创新点是将流动设置为周期性的，并在训练期间重新采样函数评估点以提高模型精度，并讨论了使用 NS 方程模拟湍流模型的局限性及其与 PINN 的交互作用。