# FR3D: Three-dimensional Flow Reconstruction and Force Estimation for Unsteady Flows Around Extruded Bluff Bodies via Conformal Mapping Aided Convolutional Autoencoders

arXiv: https://arxiv.org/abs/2302.01802 · HTML: https://mlsanity.com/paper/2302.01802/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 11 of its 46 references that are in the map.
- First posted on arXiv 3 Feb 2023.

## Builds on (most cited first, 11 of 11)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [High-Resolution Image Synthesis with Latent Diffusion Models](https://mlsanity.com/paper/2112.10752/) (2021)
- [Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift](https://mlsanity.com/paper/1502.03167/) (2015)
- [Generative Adversarial Networks](https://mlsanity.com/paper/2203.00667/) (2022)
- [Efficient collective swimming by harnessing vortices through deep reinforcement learning](https://mlsanity.com/paper/1802.02674/) (2018)
- [Global field reconstruction from sparse sensors with Voronoi tessellation-assisted deep learning](https://mlsanity.com/paper/2101.00554/) (2021)
- [Convolutional-network models to predict wall-bounded turbulence from wall quantities](https://mlsanity.com/paper/2006.12483/) (2020)
- [Flow Completion Network: Inferring the Fluid Dynamics from Incomplete Flow Information using Graph Neural Networks](https://mlsanity.com/paper/2205.04739/) (2022)
- [State estimation with limited sensors -- A deep learning based approach](https://mlsanity.com/paper/2101.11513/) (2021)
- [Graph Neural Networks for Aerodynamic Flow Reconstruction from Sparse Sensing](https://mlsanity.com/paper/2301.03228/) (2023)
- [Deep learning fluid flow reconstruction around arbitrary two-dimensional objects from sparse sensors using conformal mappings](https://mlsanity.com/paper/2202.03798/) (2022)

## Abstract (arXiv)

In many practical fluid dynamics experiments, measuring variables such as velocity and pressure is possible only at a limited number of sensor locations, textcolorblackfor a few two-dimensional planes, or for a small 3D domain in the flow. However, knowledge of the full fields is necessary to understand the dynamics of many flows. Deep learning reconstruction of full flow fields from sparse measurements has recently garnered significant research interest, as a way of overcoming this limitation. This task is referred to as the flow reconstruction (FR) task. In the present study, we propose a convolutional autoencoder based neural network model, dubbed FR3D, which enables FR to be carried out for three-dimensional flows around extruded 3D objects with different cross-sections. An innovative mapping approach, whereby multiple fluid domains are mapped to an annulus, enables FR3D to generalize its performance to objects not encountered during training. We conclusively demonstrate this generalization capability using a dataset composed of 80 training and 20 testing geometries, all randomly generated. We show that the FR3D model reconstructs pressure and velocity components with a few percentage points of error. Additionally, using these predictions, we accurately estimate the Q-criterion fields as well lift and drag forces on the geometries.