Experience report of physics-informed neural networks in fluid simulations: pitfalls and frustration

The deep learning boom motivates researchers and practitioners of computational fluid dynamics eager to integrate the two areas.The PINN (physics-informed neural network) method is one such attempt. While most reports in the literature show positive outcomes of applying the PINN method, our experiments with it stifled such optimism. This work presents our not-so-successful story of using PINN to solve two fundamental flow problems: 2D Taylor-Green vortex at $Re = 100$ and 2D cylinder flow at $Re = 200$. The PINN method solved the 2D Taylor-Green vortex problem with acceptable results, and we used this flow as an accuracy and performance benchmark. About 32 hours of training were required for the PINN method's accuracy to match the accuracy of a $16 \times 16$ finite-difference simulation, which took less than 20 seconds. The 2D cylinder flow, on the other hand, did not even result in a physical solution. The PINN method behaved like a steady-flow solver and did not capture the vortex shedding phenomenon. By sharing our experience, we would like to emphasize that the PINN method is still a work-in-progress. More work is needed to make PINN feasible for real-world problems.