# U-net architectures for fast prediction of incompressible laminar flows

arXiv: https://arxiv.org/abs/1910.13532 · HTML: https://mlsanity.com/paper/1910.13532/

## Key facts

- Cited by 17 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 25 Oct 2019.

## Built on by (most cited first, 17 of 17)

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- [Heat Conduction Plate Layout Optimization using Physics-driven Convolutional Neural Networks](https://mlsanity.com/paper/2201.10002/) (2022)
- [Identification of Physical Processes and Unknown Parameters of 3D Groundwater Contaminant Problems via Theory-guided U-net](https://mlsanity.com/paper/2205.00134/) (2022)
- [A Novel Deep Learning Approach for Emulating Computationally Expensive Postfire Debris Flows](https://mlsanity.com/paper/2504.07736/) (2025)
- [Physics-Informed Coarsening for Multigrid Graph Neural Surrogates](https://mlsanity.com/paper/2605.31013/) (2026)
- [CoFINN: Conservation Flux Informed Neural Networks for Physics Problems Governed by Conservation Laws](https://mlsanity.com/paper/2607.06587/) (2026)
- [ONE CYLinder: A Benchmark for Graph-Based Surrogate Modeling of Unsteady Bluff-Body Flows](https://mlsanity.com/paper/2609.08947/) (2026)

## Abstract (arXiv)

Machine learning is a popular tool that is being applied to many domains, from computer vision to natural language processing. It is not long ago that its use was extended to physics, but its capabilities remain to be accurately contoured. In this paper, we are interested in the prediction of 2D velocity and pressure fields around arbitrary shapes in laminar flows using supervised neural networks. To this end, a dataset composed of random shapes is built using Bezier curves, each shape being labeled with its pressure and velocity fields by solving Navier-Stokes equations using a CFD solver. Then, several U-net architectures are trained on the latter dataset, and their predictive efficiency is assessed on unseen shapes, using ad hoc error functions.