# Geodesic Convolutional Shape Optimization

arXiv: https://arxiv.org/abs/1802.04016 · HTML: https://mlsanity.com/paper/1802.04016/

## Key facts

- Cited by 37 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 12 Feb 2018.

## Built on by (most cited first, 30 of 37)

- [MeshUDF: Fast and Differentiable Meshing of Unsigned Distance Field Networks](https://mlsanity.com/paper/2111.14549/) (2021)
- [DrivAerNet++: A Large-Scale Multimodal Car Dataset with Computational Fluid Dynamics Simulations and Deep Learning Benchmarks](https://mlsanity.com/paper/2406.09624/) (2024)
- [Deep Learning on Implicit Neural Representations of Shapes](https://mlsanity.com/paper/2302.05438/) (2023)
- [DrivAerNet: A Parametric Car Dataset for Data-Driven Aerodynamic Design and Prediction](https://mlsanity.com/paper/2403.08055/) (2024)
- [Aero-Nef: Neural Fields for Rapid Aircraft Aerodynamics Simulations](https://mlsanity.com/paper/2407.19916/) (2024)
- [Swarm Reinforcement Learning For Adaptive Mesh Refinement](https://mlsanity.com/paper/2304.00818/) (2023)
- [Grounding Graph Network Simulators using Physical Sensor Observations](https://mlsanity.com/paper/2302.11864/) (2023)
- [MMGP: a Mesh Morphing Gaussian Process-based machine learning method for regression of physical problems under non-parameterized geometrical variability](https://mlsanity.com/paper/2305.12871/) (2023)
- [Surrogate Modeling of Car Drag Coefficient with Depth and Normal Renderings](https://mlsanity.com/paper/2306.06110/) (2023)
- [AhmedML: High-Fidelity Computational Fluid Dynamics Dataset for Incompressible, Low-Speed Bluff Body Aerodynamics](https://mlsanity.com/paper/2407.20801/) (2024)
- [SimJEB: Simulated Jet Engine Bracket Dataset](https://mlsanity.com/paper/2105.03534/) (2021)
- [DeepMesh: Differentiable Iso-Surface Extraction](https://mlsanity.com/paper/2106.11795/) (2021)
- [DEBOSH: Deep Bayesian Shape Optimization](https://mlsanity.com/paper/2109.13337/) (2021)
- [WindsorML: High-Fidelity Computational Fluid Dynamics Dataset For Automotive Aerodynamics](https://mlsanity.com/paper/2407.19320/) (2024)
- [Drag-guided diffusion models for vehicle image generation](https://mlsanity.com/paper/2306.09935/) (2023)
- [Enabling Uncertainty Estimation in Iterative Neural Networks](https://mlsanity.com/paper/2403.16732/) (2024)
- [PartSDF: Part-Based Implicit Neural Representation for Composite 3D Shape Parametrization and Optimization](https://mlsanity.com/paper/2502.12985/) (2025)
- [Performance and accuracy assessments of an incompressible fluid solver coupled with a deep Convolutional Neural Network](https://mlsanity.com/paper/2109.09363/) (2021)
- [Mesh Convolutional Autoencoder for Semi-Regular Meshes of Different Sizes](https://mlsanity.com/paper/2110.09401/) (2021)
- [LatentHuman: Shape-and-Pose Disentangled Latent Representation for Human Bodies](https://mlsanity.com/paper/2111.15113/) (2021)
- [HybridSDF: Combining Deep Implicit Shapes and Geometric Primitives for 3D Shape Representation and Manipulation](https://mlsanity.com/paper/2109.10767/) (2021)
- [Benchmarking Convolutional Neural Network and Graph Neural Network based Surrogate Models on a Real-World Car External Aerodynamics Dataset](https://mlsanity.com/paper/2504.06699/) (2025)
- [3DID: Direct 3D Inverse Design for Aerodynamics with Physics-Aware Optimization](https://mlsanity.com/paper/2512.08987/) (2025)
- [Learning Relaxation for Multigrid](https://mlsanity.com/paper/2207.11255/) (2022)
- [Generative Thermal Design Through Boundary Representation and Multi-Agent Cooperative Environment](https://mlsanity.com/paper/2208.07952/) (2022)
- [Three-dimensional Deep Shape Optimization with a Limited Dataset](https://mlsanity.com/paper/2506.12326/) (2025)
- [A Reward-Directed Diffusion Framework for Generative Design Optimization](https://mlsanity.com/paper/2508.01509/) (2025)
- [Image-based Artificial Intelligence empowered surrogate model and shape morpher for real-time blank shape optimisation in the hot stamping process](https://mlsanity.com/paper/2212.05885/) (2022)
- [Implicit Neural Representation For Accurate CFD Flow Field Prediction](https://mlsanity.com/paper/2408.06486/) (2024)
- [DrivAer Transformer: A high-precision and fast prediction method for vehicle aerodynamic drag coefficient based on the DrivAerNet++ dataset](https://mlsanity.com/paper/2504.08217/) (2025)

## Abstract (arXiv)

Aerodynamic shape optimization has many industrial applications. Existing methods, however, are so computationally demanding that typical engineering practices are to either simply try a limited number of hand-designed shapes or restrict oneself to shapes that can be parameterized using only few degrees of freedom. In this work, we introduce a new way to optimize complex shapes fast and accurately. To this end, we train Geodesic Convolutional Neural Networks to emulate a fluidynamics simulator. The key to making this approach practical is remeshing the original shape using a polycube map, which makes it possible to perform the computations on GPUs instead of CPUs. The neural net is then used to formulate an objective function that is differentiable with respect to the shape parameters, which can then be optimized using a gradient-based technique. This outperforms state- of-the-art methods by 5 to 20% for standard problems and, even more importantly, our approach applies to cases that previous methods cannot handle.