# Neural Multigrid Memory For Computational Fluid Dynamics

arXiv: https://arxiv.org/abs/2306.12545 · HTML: https://mlsanity.com/paper/2306.12545/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 12 of its 16 references that are in the map.
- First posted on arXiv 21 Jun 2023.

## Builds on (most cited first, 12 of 12)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [Fourier Neural Operator for Parametric Partial Differential Equations](https://mlsanity.com/paper/2010.08895/) (2020)
- [Convolutional LSTM Network: A Machine Learning Approach for Precipitation Nowcasting](https://mlsanity.com/paper/1506.04214/) (2015)
- [Scaling Vision Transformers](https://mlsanity.com/paper/2106.04560/) (2021)
- [PDEBENCH: An Extensive Benchmark for Scientific Machine Learning](https://mlsanity.com/paper/2210.07182/) (2022)
- [Towards Physics-informed Deep Learning for Turbulent Flow Prediction](https://mlsanity.com/paper/1911.08655/) (2019)
- [Deep Multi-View Spatial-Temporal Network for Taxi Demand Prediction](https://mlsanity.com/paper/1802.08714/) (2018)
- [Visual Dynamics: Probabilistic Future Frame Synthesis via Cross Convolutional Networks](https://mlsanity.com/paper/1607.02586/) (2016)
- [VPTR: Efficient Transformers for Video Prediction](https://mlsanity.com/paper/2203.15836/) (2022)
- [Multigrid Neural Memory](https://mlsanity.com/paper/1906.05948/) (2019)

## Built on by (most cited first, 1 of 1)

- [ConDiff: A Challenging Dataset for Neural Solvers of Partial Differential Equations](https://mlsanity.com/paper/2406.04709/) (2024)

## Abstract (arXiv)

Turbulent flow simulation plays a crucial role in various applications, including aircraft and ship design, industrial process optimization, and weather prediction. In this paper, we propose an advanced data-driven method for simulating turbulent flow, representing a significant improvement over existing approaches. Our methodology combines the strengths of Video Prediction Transformer (VPTR) (Ye & Bilodeau, 2022) and Multigrid Architecture (MgConv, MgResnet) (Ke et al., 2017). VPTR excels in capturing complex spatiotemporal dependencies and handling large input data, making it a promising choice for turbulent flow prediction. Meanwhile, Multigrid Architecture utilizes multiple grids with different resolutions to capture the multiscale nature of turbulent flows, resulting in more accurate and efficient simulations. Through our experiments, we demonstrate the effectiveness of our proposed approach, named MGxTransformer, in accurately predicting velocity, temperature, and turbulence intensity for incompressible turbulent flows across various geometries and flow conditions. Our results exhibit superior accuracy compared to other baselines, while maintaining computational efficiency. Our implementation in PyTorch is available publicly at https://github.com/Combi2k2/MG-Turbulent-Flow