Design Manifolds Capture the Intrinsic Complexity and Dimension of Design Spaces Wei Chen ∗ Department of Mechanical Engineering University of Maryland College Park, MD 20742 Email: wchen459@umd.edu Mark Fuge Department of Mechanical Engineering University of Maryland College Park, MD 20742 Email: fuge@umd.edu Jonah Chazan Department of Computer Science University of Maryland College Park, MD 20742 Email: jchazan@umd.edu ABSTRACT This paper shows how to measure the intrinsic complexity and dimensionality of a design space. It assumes that high-dimensional design parameters actually lie in a much lower-dimensional space that represents semantic attributes—a design manifold. Past work has shown how to embed designs using techniques like autoencoders; in contrast, the method proposed in this paper first captures the inherent properties of a design space and then chooses appropriate embeddings based on the captured properties. We demonstrate this with both synthetic shapes of controllable complexity (using a generalization of the ellipse called the superformula) and real-world designs (glassware and airfoils). We evaluate multiple embeddings by measuring shape reconstruction error, pairwise dis- tance preservation, and captured semantic attributes. By generating fundamental knowledge about the inherent complexity of a design space and how designs differ from one another, our approach allows us to improve de- sign optimization, consumer preference learning, geometric modeling, and other design applications that rely on navigating complex design spaces. Ultimately, this deepens our understanding of design complexity in general. ∗ Corresponding author. MD-16-1647 W. Chen, M. Fuge, and J. Chazan 1