Physics-Informed Neural Networks for Modeling Water Flows in a River Channel

The impacts incurred by floods regularly affect the planet's population, inflicting social and economic problems. Optimal control strategies based on reservoir management may aid in controlling floods and mitigating the resulting damage. To this end, an accurate dynamic representation of water systems is needed. In practice, flood control strategies rely on hydrological forecasting models obtained from conceptual or data-driven methods. Encouraged by recent works, this research proposes a novel surrogate model for water flow in a river channel based on physics-informed neural networks (PINNs). This approach achieved promising results regarding the assimilation of real-data measurements and the parameter identification of differential equations that govern the underlying dynamics. This article investigates PINN performance in a simulated environment built directly from a configuration of the Saint-Venant equations. The objective is to create a suitable model with high prediction accuracy and scientifically consistent behavior for use in real-time applications. The experiments revealed promising results for hydrological modeling and presented alternatives to solve the main challenges found in conventional methods while assisting in synthesizing real-world representations.

I. Introduction

The process of obtaining a mathematical model that describes the physical characteristics of a dynamic system can be considered as much science as art. Designers wish to unify the most suitable mathematical description while still representing reality with adequate precision. The term “most suitable” is relative; as a result, different models can describe the same dynamic. To sum up, the synthesis of models for dynamic systems is a nontrivial process [1].