In real-world fluid dynamics, turbulence is prevalent, from swirling coffee in a cup to galaxy formation. Physics-informed neural networks (PINNs) are pivotal in scientific machine learning and have been applied to engineering turbulence problems; however, they encounter challenges due to the chaotic and computationally intense nature of turbulence simulations. We introduce a PINN model for simulating turbulent wakes in multi-turbine configurations using a hybrid physics-data training strategy. Our method integrates data losses with boundary and partial differential equation losses, as formulated by the 2-equation k−ε turbulence model. Using sparse data for a single flow variable restricted to a plane, the model simulated flow variables in the three-dimensional domain, showing excellent agreement with the reference (shear stress transport k–ω numerical solver) in various scenarios. Training data are viewed as simulated observational data on a coarse grid, 50× coarser than what the numerical solver requires. A transfer learning strategy is implemented to accelerate training in new cases, achieving 7.5× faster speed with only one-fourth of the data compared to training from scratch. Our results indicate that the hybrid training method for PINNs can be successfully applied in practical scenarios with limited sensory data to create neural surrogates for multi-turbine wind farms.
Gafoor et al. (Fri,) studied this question.