Quantifying the Influence of Continuous and Discrete Design Decisions Using Sensitivities

Early-stage design decisions significantly impact the performance of architectural geometries and structures, especially in the context of high-performance buildings. However, most design problems involve a combination of continuous and discrete variables as decisions, making it challenging to understand their individual contributions to performance. For instance, tradeoffs between geometry (continuous) and material type (discrete) often lead to non-obvious performance behaviors, complicating the inclination to establish “rules of thumb” for low-carbon structural design. In response, we propose a new approach for assessing the influence of mixed variables on performance based on variable sensitivities, with a focus on architectural applications. A conditional variational autoencoder is trained to learn a continuous representation of variables and their relationship to performance, and gradients of the learned model are used to compute the relative influences of variables on performance. Multiple scales of insights are attainable: 1) locally at a design instance of interest, and 2) globally across the whole design space. The method is demonstrated on a case study of designing a structurally feasible gridshell for low embodied carbon.