On the Application of Physics-Informed Neural Networks in the Modeling of Roll Waves

Roll wave instability in free-surface flows is a long-studied phenomenon in fluid mechanics. Existing methods to predict roll wave properties are time-consuming, expensive, or inaccurate, prompting further exploration by the scientific community. In this regard, the present study evaluates the performance of Physics-Informed Neural Networks (PINNs) in modeling roll waves for laminar flows of Newtonian fluids. The objective was to determine if PINNs can successfully model roll wave behavior using a limited dataset and a set of governing differential equations from the literature. Seven different configurations for PINNs were defined, especially for oscillatory phenomena. PINNs were trained using a subset of numerical results from 2D transient flow simulations, together with a Saint-Venant-like set of equations, which can be used to obtain marginal curves of stability and further solutions for 1D roll wave instabilities. PINNs were used to predict wave interface heights and average streamwise velocities, which were compared to reference numerical data to assess accuracy. Results showed that PINNs accurately predicted roll wave properties such as frequency and wavelength. Wave heights and average velocities were also predicted with satisfactory accuracy, though the performance was poorer at wave peaks. Overall, PINNs exhibited better performance in predicting flow height than velocity. Additionally, PINN performance decreased with higher Froude numbers, which can be attributed to the underlying mathematical assumptions of the mathematical model. This study demonstrates the potential of PINNs as mathematical tools for studying roll wave behavior and other oscillatory flows, providing valuable insights and highlighting challenges in their application.