[Paper Review] Experience Report of Physics-Informed Neural Networks in Fluid Simulations: Pitfalls and Frustration

Pi-Yueh Chuang, Lorena A. Barba|arXiv (Cornell University)|Jan 1, 2022

Model Reduction and Neural Networks4 citations

TL;DR

This paper reports on the challenges and failures of using physics-informed neural networks (PINNs) to solve the Navier-Stokes equations without any data, focusing on two benchmark fluid flow problems: the 2D Taylor-Green vortex at Re=100 and the 2D cylinder flow at Re=200. Despite achieving acceptable results for the Taylor-Green case after 32 hours of training, PINN failed to capture vortex shedding in the cylinder flow, instead converging to a steady-state solution, highlighting significant limitations in solving complex, unsteady flows without data or perturbations.

ABSTRACT

<strong>Poster presented at the SciPy Conference, Austin, TX, July 2022</strong> Proceedings: https://conference.scipy.org/proceedings/scipy2022/PiYueh_Chuang.html Preprint on arXiv: https://arxiv.org/abs/2205.14249

Motivation & Objective

• To evaluate the feasibility of using physics-informed neural networks (PINNs) as a replacement for traditional computational fluid dynamics (CFD) solvers in data-free settings.
• To identify and document the key challenges, computational costs, and convergence issues encountered when applying PINNs to real-world fluid dynamics problems.
• To provide a candid experience report on PINN's limitations, especially in capturing unsteady, chaotic flow phenomena like vortex shedding.
• To guide future researchers by sharing practical pitfalls and frustrations to avoid misaligned expectations in data-free PINN applications.

Proposed method

• The study implements a PINN framework using fully-connected neural networks to solve the 2D incompressible Navier-Stokes equations with no external data.
• The loss function combines residuals from the Navier-Stokes equations, continuity equation, and boundary/initial conditions, all computed via automatic differentiation.
• For the Taylor-Green vortex, training was conducted with a 16×16 finite-difference simulation as a benchmark for accuracy and convergence.
• For the cylinder flow, the PINN was trained with the same architecture and loss formulation, but with a different geometry and boundary conditions.
• Hyperparameter tuning was attempted, including network depth, width, and activation functions, though computational cost limited systematic exploration.
• The authors explored introducing perturbations to initial conditions to encourage unsteady solutions, inspired by known numerical instabilities in PDE solvers.

Experimental results

Research questions

• RQ1 Can PINNs successfully simulate unsteady, chaotic fluid flows such as vortex shedding behind a cylinder without any training data?
• RQ2 How does the training time and computational cost of PINNs compare to traditional finite-difference CFD solvers for comparable accuracy?
• RQ3 Why does PINN fail to capture time-dependent instabilities in the cylinder flow, even when the network architecture is increased in complexity?
• RQ4 To what extent do hyperparameter choices and network design affect the convergence and physical plausibility of PINN solutions?
• RQ5 Can introducing artificial perturbations or multiple initial conditions improve the ability of PINNs to capture unsteady flow dynamics?

Key findings

• The PINN solver achieved acceptable accuracy for the 2D Taylor-Green vortex at Re=100, matching a 16×16 finite-difference simulation, but required approximately 32 hours of training—significantly longer than the less than 20 seconds needed by the traditional solver.
• For the 2D cylinder flow at Re=200, the PINN failed to capture vortex shedding and instead converged to a steady-state solution, despite extensive hyperparameter tuning and increased network complexity.
• The failure was not due to insufficient model capacity, as increasing network depth and width did not restore unsteady behavior, suggesting deeper issues in optimization or loss landscape.
• The PINN solver exhibited a strong tendency to converge to steady-state solutions, even when the underlying PDEs support unsteady dynamics, indicating a fundamental challenge in training PINNs for such problems.
• Introducing perturbations to initial conditions or using multiple time snapshots as constraints may be necessary to break the symmetry and encourage unsteady solutions, though this was not sufficient in the current setup.
• The study concludes that data-free PINNs are not yet reliable for real-world fluid dynamics problems requiring accurate simulation of unsteady, chaotic flows.