Calibration of Manning's roughness coefficients for shallow-water flows on complex bathymetries using optimization algorithms and surrogate neural network models

This paper presents an effective methodology for the automatic calibration of Manning's roughness coefficients, which are crucial parameters for modeling shallow free-surface flows. Traditionally determined through empirical methods, these coefficients are subject to significant variability, making their determination challenging, especially in flow areas with complex bathymetry. The conventional trial-and-error approach, widely used to select these coefficients, is often tedious and time-consuming, particularly in applications constrained by time and data availability. The proposed methodology aims to determine the optimal values of Manning's coefficients distributed over the flow domain while minimizing global discrepancies between simulations and field measurements. The calibration approach is formulated as an inverse optimization problem and addressed using metaheuristic optimization algorithms such as the Genetic Algorithm or Particle Swarm Optimization, combined with an ensemble model of deep neural networks. The database for training the neural networks is obtained using a newly developed finite volume-based shallow-water equations solver, parallelized on multiple GPUs, to generate large datasets of solutions for machine learning purposes. The performance of this approach is evaluated through various flow scenarios. Compared to conventional techniques, this methodology stands out for its simplicity, computational efficiency, and robustness. Additionally, Hybrid Particle Swarm Optimization (HPSO) proves to be particularly effective, notably for its speed. The developed codes are available at: https://github.com/ETS-GRANIT/CuteFlow.