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

arXiv: https://arxiv.org/abs/2205.14249 · HTML: https://mlsanity.com/paper/2205.14249/

## Key facts

- Cited by 21 papers in the map (data through 14 Oct 2026).
- Builds on 8 of its 32 references that are in the map.
- First posted on arXiv 27 May 2022.

## Builds on (most cited first, 8 of 8)

- [Gaussian Error Linear Units (GELUs)](https://mlsanity.com/paper/1606.08415/) (2016)
- [DGM: A deep learning algorithm for solving partial differential equations](https://mlsanity.com/paper/1708.07469/) (2017)
- [When and why PINNs fail to train: A neural tangent kernel perspective](https://mlsanity.com/paper/2007.14527/) (2020)
- [DeepXDE: A deep learning library for solving differential equations](https://mlsanity.com/paper/1907.04502/) (2019)
- [Physics-informed neural networks (PINNs) for fluid mechanics: A review](https://mlsanity.com/paper/2105.09506/) (2021)
- [MeshfreeFlowNet: A Physics-Constrained Deep Continuous Space-Time Super-Resolution Framework](https://mlsanity.com/paper/2005.01463/) (2020)
- [Physics-based Deep Learning](https://mlsanity.com/paper/2109.05237/) (2021)
- [Evolutional Deep Neural Network](https://mlsanity.com/paper/2103.09959/) (2021)

## Built on by (most cited first, 21 of 21)

- [An Expert's Guide to Training Physics-informed Neural Networks](https://mlsanity.com/paper/2308.08468/) (2023)
- [Weak baselines and reporting biases lead to overoptimism in machine learning for fluid-related partial differential equations](https://mlsanity.com/paper/2407.07218/) (2024)
- [Can Physics-Informed Neural Networks beat the Finite Element Method?](https://mlsanity.com/paper/2302.04107/) (2023)
- [CROM: Continuous Reduced-Order Modeling of PDEs Using Implicit Neural Representations](https://mlsanity.com/paper/2206.02607/) (2022)
- [Implicit Neural Spatial Representations for Time-dependent PDEs](https://mlsanity.com/paper/2210.00124/) (2022)
- [Stacked networks improve physics-informed training: applications to neural networks and deep operator networks](https://mlsanity.com/paper/2311.06483/) (2023)
- [Predictive Limitations of Physics-Informed Neural Networks in Vortex Shedding](https://mlsanity.com/paper/2306.00230/) (2023)
- [On the Generalization of PINNs outside the training domain and the Hyperparameters influencing it](https://mlsanity.com/paper/2302.07557/) (2023)
- [Diff-SPORT: Diffusion-based Sensor Placement Optimization and Reconstruction of Turbulent flows in urban environments](https://mlsanity.com/paper/2506.00214/) (2025)
- [Understanding the Difficulty of Solving Cauchy Problems with PINNs](https://mlsanity.com/paper/2405.02561/) (2024)
- [Examining the robustness of Physics-Informed Neural Networks to noise for Inverse Problems](https://mlsanity.com/paper/2509.20191/) (2025)
- [Implicit Neural Representation For Accurate CFD Flow Field Prediction](https://mlsanity.com/paper/2408.06486/) (2024)
- [Practical Aspects on Solving Differential Equations Using Deep Learning: A Primer](https://mlsanity.com/paper/2408.11266/) (2024)
- [Softly Constrained Denoisers for Diffusion Models Applied to Partial Differential Equations](https://mlsanity.com/paper/2512.14980/) (2025)
- [Sampling from Boltzmann densities with physics informed low-rank formats](https://mlsanity.com/paper/2412.07637/) (2024)
- [Reliable and efficient inverse analysis using physics-informed neural networks with normalized distance functions and adaptive weight tuning](https://mlsanity.com/paper/2504.18091/) (2025)
- [THINNs: Thermodynamically Informed Neural Networks](https://mlsanity.com/paper/2509.19467/) (2025)
- [PINN Balls: Scaling Second-Order Methods for PINNs with Domain Decomposition and Adaptive Sampling](https://mlsanity.com/paper/2510.21262/) (2025)
- [Leveraging Differentiable PDE Solvers for Semi-Neural Spatial Reconstruction From Sparse Measurements](https://mlsanity.com/paper/2601.20496/) (2026)
- [General Explicit Network (GEN): A novel deep learning architecture for solving partial differential equations](https://mlsanity.com/paper/2604.03321/) (2026)
- [Physics Informed Neural Network model for the dynamical study of Abdominal Aortic Aneurysm](https://mlsanity.com/paper/2609.15104/) (2026)

## Abstract (arXiv)

Though PINNs (physics-informed neural networks) are now deemed as a complement to traditional CFD (computational fluid dynamics) solvers rather than a replacement, their ability to solve the Navier-Stokes equations without given data is still of great interest. This report presents our not-so-successful experiments of solving the Navier-Stokes equations with PINN as a replacement for traditional solvers. We aim to, with our experiments, prepare readers for the challenges they may face if they are interested in data-free PINN. In this work, we used two standard 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 16x16 finite-difference simulation, which took less than 20 seconds. The 2D cylinder flow, on the other hand, did not produce 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, especially in terms of solving flow problems without any given data. More work is needed to make PINN feasible for real-world problems in such applications.