How sparse and how noisy? Systematic benchmarking of inverse physics-informed neural networks for Manning friction estimation in shallow water equations

作者：Soheil Radfar · 发表于：The Physics of Fluids · 年份：2026 · DOI：10.1063/5.0349054 · 被引用次数：1 · 研究领域：Physics

Physics-informed neural networks (PINNs) offer a promising framework for inverse hydrodynamic modeling because they can combine sparse observations with governing physical constraints. However, their reliability for estimating hydraulic parameters under realistic data limitations remains insufficiently characterized. This study systematically benchmarks inverse PINN recovery of the Manning friction coefficient in the shallow water equations under controlled variations in observation sparsity, observation noise, and observed variable type. Two benchmark cases are considered: a one-dimensional MacDonald subcritical channel with an analytical steady reference solution and a two-dimensional sloped channel with a parabolic transverse bed generated using a balanced finite-volume solver. The Manning coefficient is treated as a trainable positive scalar and recovered jointly with the flow field using a two-phase optimization strategy that first fits the available observations and then incorporates the physics residual. Results show that the two-dimensional benchmark achieves stable friction recovery, with errors below 5% for as few as five observations of depth and velocity and noise levels up to 20% of the field standard deviation. Recovery remains stable up to 20% noise when 50 observations are used, and the residual error level coincides with the discretization error of the finite-volume reference solution itself, which bounds the accuracy attainable on that benchmark. In contrast...