# Predictive Limitations of Physics-Informed Neural Networks in Vortex Shedding

arXiv: https://arxiv.org/abs/2306.00230 · HTML: https://mlsanity.com/paper/2306.00230/

## Key facts

- Cited by 12 papers in the map (data through 14 Oct 2026).
- Builds on 5 of its 26 references that are in the map.
- First posted on arXiv 31 May 2023.

## Builds on (most cited first, 5 of 5)

- [On the Spectral Bias of Neural Networks](https://mlsanity.com/paper/1806.08734/) (2018)
- [Characterizing possible failure modes in physics-informed neural networks](https://mlsanity.com/paper/2109.01050/) (2021)
- [On the Role of Fixed Points of Dynamical Systems in Training Physics-Informed Neural Networks](https://mlsanity.com/paper/2203.13648/) (2022)
- [Experience report of physics-informed neural networks in fluid simulations: pitfalls and frustration](https://mlsanity.com/paper/2205.14249/) (2022)
- [Emerging trends in machine learning for computational fluid dynamics](https://mlsanity.com/paper/2211.15145/) (2022)

## Built on by (most cited first, 12 of 12)

- [Weak baselines and reporting biases lead to overoptimism in machine learning for fluid-related partial differential equations](https://mlsanity.com/paper/2407.07218/) (2024)
- [Stacked networks improve physics-informed training: applications to neural networks and deep operator networks](https://mlsanity.com/paper/2311.06483/) (2023)
- [Data-Driven Physics-Informed Neural Networks: A Digital Twin Perspective](https://mlsanity.com/paper/2401.08667/) (2024)
- [Deep Learning of the Evolution Operator Enables Forecasting of Out-of-Training Dynamics in Chaotic Systems](https://mlsanity.com/paper/2502.20603/) (2025)
- [Integration Matters for Learning PDEs with Backward SDEs](https://mlsanity.com/paper/2505.01078/) (2025)
- [FlamePINN-1D: Physics-informed neural networks to solve forward and inverse problems of 1D laminar flames](https://mlsanity.com/paper/2406.09071/) (2024)
- [Practical Aspects on Solving Differential Equations Using Deep Learning: A Primer](https://mlsanity.com/paper/2408.11266/) (2024)
- [Automatic Differentiation for Inverse Problems with Applications in Quantum Transport](https://mlsanity.com/paper/2307.09311/) (2023)
- [A neural operator for predicting vibration frequency response curves from limited data](https://mlsanity.com/paper/2603.10149/) (2026)
- [General Explicit Network (GEN): A novel deep learning architecture for solving partial differential equations](https://mlsanity.com/paper/2604.03321/) (2026)
- [Forward Trajectory Steering for Hamilton-Jacobi Reachability Analysis](https://mlsanity.com/paper/2608.11480/) (2026)
- [Complementary, Not Cumulative: Interaction Effects in Physics-Informed Neural Networks for Navier-Stokes Vortex Shedding](https://mlsanity.com/paper/2608.19632/) (2026)

## Abstract (arXiv)

The recent surge of interest in physics-informed neural network (PINN) methods has led to a wave of studies that attest to their potential for solving partial differential equations (PDEs) and predicting the dynamics of physical systems. However, the predictive limitations of PINNs have not been thoroughly investigated. We look at the flow around a 2D cylinder and find that data-free PINNs are unable to predict vortex shedding. Data-driven PINN exhibits vortex shedding only while the training data (from a traditional CFD solver) is available, but reverts to the steady state solution when the data flow stops. We conducted dynamic mode decomposition and analyze the Koopman modes in the solutions obtained with PINNs versus a traditional fluid solver (PetIBM). The distribution of the Koopman eigenvalues on the complex plane suggests that PINN is numerically dispersive and diffusive. The PINN method reverts to the steady solution possibly as a consequence of spectral bias. This case study reaises concerns about the ability of PINNs to predict flows with instabilities, specifically vortex shedding. Our computational study supports the need for more theoretical work to analyze the numerical properties of PINN methods. The results in this paper are transparent and reproducible, with all data and code available in public repositories and persistent archives; links are provided in the paper repository at urlhttps://github.com/barbagroup/jcspaperpinn, and a Reproducibility Statement within the paper.