# Three-dimensional Deep Shape Optimization with a Limited Dataset

arXiv: https://arxiv.org/abs/2506.12326 · HTML: https://mlsanity.com/paper/2506.12326/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 25 of its 75 references that are in the map.
- First posted on arXiv 14 Jun 2025.

## Builds on (most cited first, 25 of 25)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [PointNet: Deep Learning on Point Sets for 3D Classification and Segmentation](https://mlsanity.com/paper/1612.00593/) (2016)
- [ShapeNet: An Information-Rich 3D Model Repository](https://mlsanity.com/paper/1512.03012/) (2015)
- [DeepSDF: Learning Continuous Signed Distance Functions for Shape Representation](https://mlsanity.com/paper/1901.05103/) (2019)
- [Implicit Neural Representations with Periodic Activation Functions](https://mlsanity.com/paper/2006.09661/) (2020)
- [Convolutional Occupancy Networks](https://mlsanity.com/paper/2003.04618/) (2020)
- [PointFlow: 3D Point Cloud Generation with Continuous Normalizing Flows](https://mlsanity.com/paper/1906.12320/) (2019)
- [A-SDF: Learning Disentangled Signed Distance Functions for Articulated Shape Representation](https://mlsanity.com/paper/2104.07645/) (2021)
- [MeshSDF: Differentiable Iso-Surface Extraction](https://mlsanity.com/paper/2006.03997/) (2020)
- [Deep Generative Models in Engineering Design: A Review](https://mlsanity.com/paper/2110.10863/) (2021)
- [Learning Smooth Neural Functions via Lipschitz Regularization](https://mlsanity.com/paper/2202.08345/) (2022)
- [DualSDF: Semantic Shape Manipulation using a Two-Level Representation](https://mlsanity.com/paper/2004.02869/) (2020)
- [Robust Watertight Manifold Surface Generation Method for ShapeNet Models](https://mlsanity.com/paper/1802.01698/) (2018)
- [Machine Learning in Aerodynamic Shape Optimization](https://mlsanity.com/paper/2202.07141/) (2022)
- [Geodesic Convolutional Shape Optimization](https://mlsanity.com/paper/1802.04016/) (2018)
- [Airfoil Design Parameterization and Optimization using B'ezier Generative Adversarial Networks](https://mlsanity.com/paper/2006.12496/) (2020)
- [Integrating Deep Learning into CAD/CAE System: Generative Design and Evaluation of 3D Conceptual Wheel](https://mlsanity.com/paper/2006.02138/) (2020)
- [Topology Optimization via Machine Learning and Deep Learning: A Review](https://mlsanity.com/paper/2210.10782/) (2022)
- [Generative Design by Reinforcement Learning: Enhancing the Diversity of Topology Optimization Designs](https://mlsanity.com/paper/2008.07119/) (2020)
- [DeepJEB: 3D Deep Learning-based Synthetic Jet Engine Bracket Dataset](https://mlsanity.com/paper/2406.09047/) (2024)
- [Ship-D: Ship Hull Dataset for Design Optimization using Machine Learning](https://mlsanity.com/paper/2305.08279/) (2023)
- [t-METASET: Tailoring Property Bias of Large-Scale Metamaterial Datasets through Active Learning](https://mlsanity.com/paper/2202.10565/) (2022)
- [Deep Learning-Based Inverse Design for Engineering Systems: Multidisciplinary Design Optimization of Automotive Brakes](https://mlsanity.com/paper/2202.13309/) (2022)
- [An efficient 146-line 3D sensitivity analysis code of stress-based topology optimization written in MATLAB](https://mlsanity.com/paper/2104.01210/) (2021)
- [Towards Goal, Feasibility, and Diversity-Oriented Deep Generative Models in Design](https://mlsanity.com/paper/2206.07170/) (2022)

## Built on by (most cited first, 2 of 2)

- [Zero-shot rib design: merging training-free generative prior with topology optimization](https://mlsanity.com/paper/2609.10643/) (2026)
- [PhysicsBench: A Unified Leaderboard for Generative and Predictive Models in Engineering Design and Simulation](https://mlsanity.com/paper/2608.24056/) (2026)

## Abstract (arXiv)

Generative models have attracted considerable attention for their ability to produce novel shapes. However, their application in mechanical design remains constrained due to the limited size and variability of available datasets. This study proposes a deep learning-based optimization framework specifically tailored for shape optimization with limited datasets, leveraging positional encoding and a Lipschitz regularization term to robustly learn geometric characteristics and maintain a meaningful latent space. Through extensive experiments, the proposed approach demonstrates robustness, generalizability and effectiveness in addressing typical limitations of conventional optimization frameworks. The validity of the methodology is confirmed through multi-objective shape optimization experiments conducted on diverse three-dimensional datasets, including wheels and cars, highlighting the model's versatility in producing practical and high-quality design outcomes even under data-constrained conditions.