BESTie Mark Fuge, Assistant Professor at the University of Maryland, College Park) has recently won the NSF CAREER grant of $500,000 for his work on “Learning Design Representations: The Effect of Differential Geometric Manifolds on the Inference of Design Structure”.

Mark received his PhD in 2014 from UC Berkeley. Dissertation title: “Collaborative Design Informatics: Leveraging Big Data to Create Better Designs.”

Abstract: This grant will answer the following question: “When (or under what conditions) does incorporating and merging multiple, known differential geometric manifolds into a learning algorithm significantly improve the sample efficiency of learning a design representation, given data?” Finding useful mathematical representations of designed products and systems is one of the field’s long-standing, fundamental, open research problems. It affects almost every major design task, whether that be optimization, understanding decision making and preferences, manufacturing planning, uncertainty quantification, or studying design cognition, behavior, or creativity, among others. But finding useful representations is difficult, because they must concurrently describe multiple mathematical structures, whose types vary across a design’s shape, behavior, and function. If successful, such learned design representations can: (1) accelerate technological and economic competitiveness ? e.g., by improving optimization convergence ? (2) enable uncertainty quantification for more complex systems than presently possible ? e.g., in systems with chaotic dynamics like Large Eddy Simulation; and (3) permit fast, accurate manufacturing analysis, computer geometry queries, and design synthesis ? e.g., by providing compact search spaces for analysis algorithms.

By combining advances across three novel mathematical areas — Differential Geometry, Statistics, and Machine Learning (ML) ? with Engineering Design, the work will advance the science behind how to infer underlying mathematical representations for complex systems, e.g., by enabling existing design methods to extend from single Euclidean representations to general Differential Geometry. Unlike past approaches to design representation, this approach of using both differential geometry and ML enables the research to answer fundamental questions regarding the practical limits of what is “learnable” about a system’s design in finite samples when multiple, diverse types of representation are needed ? the generated knowledge will answer related questions that arise across other scientific fields. Education and outreach will include: (1) a set of graduate summer programs that experiment with an unconventional part-workshop, part-summer school format for helping translate key results from new areas of mathematics into Engineering Design; (2) open-source, research and teaching infrastructure for broadening access to topics at the intersection of Design and Machine Learning; and (3) cross-cutting education and outreach activities that focus on increasing industrial relevance and participation of underrepresented groups in research and education at the college and K-12 level.