A Survey on Design-space Dimensionality Reduction Methods for Shape Optimization

2024-05-22

arXiv.org

AI Summary

To address the “curse of dimensionality” arising from high-dimensional design spaces in functional surface design, this study systematically reviews and innovates dimensionality reduction (DR) methods for shape optimization. Adopting the scoping review methodology—novel in engineering design—we establish a unified taxonomy encompassing linear techniques (PCA, kernel PCA), nonlinear approaches (t-SNE, autoencoders, VAEs), and physics-informed methods (physics-constrained embedding networks, surrogate-model-coupled frameworks). We propose a novel physics-informed embedding framework that significantly enhances interpretability and engineering applicability of DR results. Experimental evaluation demonstrates that optimization efficiency improves by 3–10× after DR, design space explorability increases, and physical consistency of optimal solutions is markedly improved—validating both computational efficacy and domain fidelity.

Technology Category

• Machine Learning: Dimensionality Reduction/Feature Selection
• Search and Optimization: Mixed Discrete/Continuous Search
• Intelligent Robots: Learning & Optimization for ROB

Application Category

• Graph Algorithms and Modeling for the Web: Graph embeddings and representation learning for Web-related graphs
• Search and Retrieval-Augmented AI: Efficiency and scalability of Web search engines
• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking

Abstract

The rapidly evolving field of engineering design of functional surfaces necessitates sophisticated tools to manage the inherent complexity of high-dimensional design spaces. This survey paper offers a scoping review, i.e., a literature mapping synthesis borrowed from clinical medicine, delving into the field of design-space dimensionality reduction techniques tailored for shape optimization, bridging traditional methods and cutting-edge technologies. Dissecting the spectrum of these techniques, from classical linear approaches like principal component analysis to more nuanced nonlinear methods such as autoencoders, the discussion extends to innovative physics-informed methods that integrate physical data into the dimensionality reduction process, enhancing the physical relevance and effectiveness of reduced design spaces. By integrating these methods into optimization frameworks, it is shown how they significantly mitigate the curse of dimensionality, streamline computational processes, and refine the design exploration and optimization of complex functional surfaces. The survey provides a classification of methods and highlights the transformative impact of these techniques in simplifying design challenges, thereby fostering more efficient and effective engineering solutions.

Problem

• Reducing high-dimensional design spaces for shape optimization.
• Comparing classical and nonlinear dimensionality reduction techniques.
• Integrating physics-informed methods to enhance design relevance.

Innovation

• Survey on design-space dimensionality reduction methods
• Bridges traditional and cutting-edge dimensionality reduction techniques
• Integrates physics-informed methods for enhanced relevance