Physics-informed neural networks for modeling water flows in a river channel

The impacts incurred by floods regularly affect the planets 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 fromconceptual or data-drivenmethods. 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. Impact Statement-The research seeks to contribute to the hydrological modeling area with a surrogate model based on physicsinformed neural networks (PINNs) to water flow in a watershed. In practice, thesemodels use conceptual or data-drivenmethods.Conceptual models to reach the precision provided by themethodology use large numbers of physical parameters. These parameters can demand deep knowledge about the environment and are possibly hard to identify in a complex basin. On the other hand, while data-driven methods do not require such knowledge about the dynamic system, they depend on a reliable and useful database to guarantee the accuracy of system behavior.We introduce PINNs as a viable solution for training neural networks with a few training data and estimating the partial differential equation parameters that govern the underlying dynamics. In addition, we present a novel strategy for training PINNs inspired by Bayesian inference for parameter estimation problems. The research aims to bring forward opportunities to the nontrivial task of hydrological modeling and tools for balancing learning from both physics and data and, consequently, to develop concepts for real-Time applications. © 2024 Institute of Electrical and Electronics Engineers Inc.. All rights reserved.