Three-dimensional Deep Shape Optimization with a Limited Dataset

2025-06-14

AI Summary

In mechanical design, 3D shape optimization is severely constrained by scarce and low-diversity training data. Method: This paper proposes an end-to-end deep generative optimization framework for multi-objective shape design of complex geometries (e.g., wheel hubs and automotive components). It innovatively integrates positional encoding to enhance geometric representation, employs Lipschitz regularization to ensure latent-space interpretability and gradient-based optimization stability, and establishes a differentiable implicit-space parameterization coupled with multi-objective co-optimization. Results: Experiments demonstrate that the framework generates high-fidelity, manufacturable 3D shapes under extremely limited data, simultaneously satisfying structural performance and geometric plausibility. It significantly outperforms conventional parametric and GAN-based approaches in generalization capability, effectively decoupling the longstanding bottleneck between generative modeling and differentiable optimization in small-data regimes.

Technology Category

• Machine Learning: Deep Generative Models & Autoencoders
• Search and Optimization: Sampling/Simulation-based Search
• Computer Vision: Learning & Optimization for CV

Application Category

• Economics, Online Markets and Human Computation: Uses of LLMs and GenAI for marketplace design, bidding, and strategic interactions
• User Modeling, Personalization and Recommendation: On-Device user modeling, personalization, and recommendation
• Semantics and Knowledge: Data modeling to support human-machine intelligence, including LLMs agents, intelligent system behavior, explanations, and user-friendly interactions

Abstract

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.

Problem

• Overcoming limited dataset constraints in 3D shape optimization
• Enhancing robustness in geometric learning with limited data
• Achieving versatile multi-objective optimization for mechanical designs

Innovation

• Uses positional encoding for robust learning
• Applies Lipschitz regularization for latent space
• Tailored for limited dataset optimization