# PMRT: A Training Recipe for Fast, 3D High-Resolution Aerodynamic Prediction

arXiv: https://arxiv.org/abs/2509.17182 · HTML: https://mlsanity.com/paper/2509.17182/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 33 of its 52 references that are in the map.
- First posted on arXiv 21 Sep 2025.

## Builds on (most cited first, 30 of 33)

- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [Squeeze-and-Excitation Networks](https://mlsanity.com/paper/1709.01507/) (2017)
- [Delving Deep into Rectifiers: Surpassing Human-Level Performance on ImageNet Classification](https://mlsanity.com/paper/1502.01852/) (2015)
- [Progressive Growing of GANs for Improved Quality, Stability, and Variation](https://mlsanity.com/paper/1710.10196/) (2017)
- [Group Normalization](https://mlsanity.com/paper/1803.08494/) (2018)
- [Deep High-Resolution Representation Learning for Visual Recognition](https://mlsanity.com/paper/1908.07919/) (2019)
- [Swin Transformer V2: Scaling Up Capacity and Resolution](https://mlsanity.com/paper/2111.09883/) (2021)
- [EfficientNetV2: Smaller Models and Faster Training](https://mlsanity.com/paper/2104.00298/) (2021)
- [Deep Networks with Stochastic Depth](https://mlsanity.com/paper/1603.09382/) (2016)
- [Learning to Simulate Complex Physics with Graph Networks](https://mlsanity.com/paper/2002.09405/) (2020)
- [Learning Mesh-Based Simulation with Graph Networks](https://mlsanity.com/paper/2010.03409/) (2020)
- [Cyclical Learning Rates for Training Neural Networks](https://mlsanity.com/paper/1506.01186/) (2015)
- [VATT: Transformers for Multimodal Self-Supervised Learning from Raw Video, Audio and Text](https://mlsanity.com/paper/2104.11178/) (2021)
- [Machine Learning for Fluid Mechanics](https://mlsanity.com/paper/1905.11075/) (2019)
- [AdaViT: Adaptive Tokens for Efficient Vision Transformer](https://mlsanity.com/paper/2112.07658/) (2021)
- [Geometry-Informed Neural Operator for Large-Scale 3D PDEs](https://mlsanity.com/paper/2309.00583/) (2023)
- [Kornia: an Open Source Differentiable Computer Vision Library for PyTorch](https://mlsanity.com/paper/1910.02190/) (2019)
- [Patch n' Pack: NaViT, a Vision Transformer for any Aspect Ratio and Resolution](https://mlsanity.com/paper/2307.06304/) (2023)
- [Fixing the train-test resolution discrepancy](https://mlsanity.com/paper/1906.06423/) (2019)
- [FlexiViT: One Model for All Patch Sizes](https://mlsanity.com/paper/2212.08013/) (2022)
- [Deep Learning Methods for Reynolds-Averaged Navier-Stokes Simulations of Airfoil Flows](https://mlsanity.com/paper/1810.08217/) (2018)
- [Prediction of Aerodynamic Flow Fields Using Convolutional Neural Networks](https://mlsanity.com/paper/1905.13166/) (2019)
- [Concurrent Spatial and Channel Squeeze & Excitation in Fully Convolutional Networks](https://mlsanity.com/paper/1803.02579/) (2018)
- [SNIPER: Efficient Multi-Scale Training](https://mlsanity.com/paper/1805.09300/) (2018)
- [DrivAerNet++: A Large-Scale Multimodal Car Dataset with Computational Fluid Dynamics Simulations and Deep Learning Benchmarks](https://mlsanity.com/paper/2406.09624/) (2024)
- [AB-UPT: Scaling Neural CFD Surrogates for High-Fidelity Automotive Aerodynamics Simulations via Anchored-Branched Universal Physics Transformers](https://mlsanity.com/paper/2502.09692/) (2025)
- [ResFormer: Scaling ViTs with Multi-Resolution Training](https://mlsanity.com/paper/2212.00776/) (2022)
- [fVDB: A Deep-Learning Framework for Sparse, Large-Scale, and High-Performance Spatial Intelligence](https://mlsanity.com/paper/2407.01781/) (2024)
- [X-MeshGraphNet: Scalable Multi-Scale Graph Neural Networks for Physics Simulation](https://mlsanity.com/paper/2411.17164/) (2024)
- [Factorized Implicit Global Convolution for Automotive Computational Fluid Dynamics Prediction](https://mlsanity.com/paper/2502.04317/) (2025)

## Abstract (arXiv)

The aerodynamic optimization of cars requires close collaboration between aerodynamicists and stylists, while slow, expensive simulations remain a bottleneck. Surrogate models have been shown to accurately predict aerodynamics within the design space for which they were trained. However, many of these models struggle to scale to higher resolutions because of the 3D nature of the problem and data scarcity. We propose Progressive Multi-Resolution Training (PMRT), a probabilistic multi-resolution training schedule that enables training a U-Net to predict the drag coefficient (cd) and high-resolution velocity fields (512 x 128 x 128) in 24 hours on a single NVIDIA H100 GPU, 7x cheaper than the high-resolution-only baseline, with similar accuracy. PMRT samples batches from three resolutions based on probabilities that change during training, starting with an emphasis on lower resolutions and gradually shifting toward higher resolutions. Since this is a training methodology, it can be adapted to other high-resolution-focused backbones. We also show that a single model can be trained across five datasets from different solvers, including a real-world dataset, by conditioning on the simulation parameters. In the DrivAerML dataset, our models achieve a cd R2 of 0.975, matching literature baselines at a fraction of the training cost.