A Physics-Informed Neural Network to Model Port Channels

TL;DR

This paper presents a physics-informed neural network model for simulating tidal flows in port channels, incorporating periodic flow assumptions and resampling techniques to enhance accuracy, with discussions on turbulence modeling limitations.

Contribution

The paper introduces a novel PINN architecture that assumes periodic flow and evaluates resampling strategies, improving flow simulation accuracy in complex port channels.

Findings

Resampling during training improves model accuracy.

Assuming periodic flow enables efficient simulation of tidal dynamics.

Discusses limitations of Navier-Stokes approximations for turbulence.

Abstract

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.