# A Multi-Pass GAN for Fluid Flow Super-Resolution

arXiv: https://arxiv.org/abs/1906.01689 · HTML: https://mlsanity.com/paper/1906.01689/

## Key facts

- Cited by 14 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 4 Jun 2019.

## Built on by (most cited first, 14 of 14)

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- [Hyena Neural Operator for Partial Differential Equations](https://mlsanity.com/paper/2306.16524/) (2023)
- [Rotationally Equivariant Super-Resolution of Velocity Fields in Two-Dimensional Fluids Using Convolutional Neural Networks](https://mlsanity.com/paper/2202.11099/) (2022)
- [When do World Models Successfully Learn Dynamical Systems?](https://mlsanity.com/paper/2507.04898/) (2025)
- [Neural UpFlow: A Scene Flow Learning Approach to Increase the Apparent Resolution of Particle-Based Liquids](https://mlsanity.com/paper/2106.05143/) (2021)
- [Comparison of Generative Learning Methods for Turbulence Surrogates](https://mlsanity.com/paper/2411.16417/) (2024)
- [CoNOAir: A Neural Operator for Forecasting Carbon Monoxide Evolution in Cities](https://mlsanity.com/paper/2501.06007/) (2025)
- [Learning from Shader Program Traces](https://mlsanity.com/paper/2102.04533/) (2021)
- [Stacked Generative Machine Learning Models for Fast Approximations of Steady-State Navier-Stokes Equations](https://mlsanity.com/paper/2112.06419/) (2021)
- [Enhancing wind field resolution in complex terrain through a knowledge-driven machine learning approach](https://mlsanity.com/paper/2309.10172/) (2023)

## Abstract (arXiv)

We propose a novel method to up-sample volumetric functions with generative neural networks using several orthogonal passes. Our method decomposes generative problems on Cartesian field functions into multiple smaller sub-problems that can be learned more efficiently. Specifically, we utilize two separate generative adversarial networks: the first one up-scales slices which are parallel to the XY-plane, whereas the second one refines the whole volume along the Z-axis working on slices in the YZ-plane. In this way, we obtain full coverage for the 3D target function and can leverage spatio-temporal supervision with a set of discriminators. Additionally, we demonstrate that our method can be combined with curriculum learning and progressive growing approaches. We arrive at a first method that can up-sample volumes by a factor of eight along each dimension, i.e., increasing the number of degrees of freedom by 512. Large volumetric up-scaling factors such as this one have previously not been attainable as the required number of weights in the neural networks renders adversarial training runs prohibitively difficult. We demonstrate the generality of our trained networks with a series of comparisons to previous work, a variety of complex 3D results, and an analysis of the resulting performance.