Interpretable Neural Network Analyses for Understanding Complex Physical Interactions in Engineering Design

Abstract In engineering design, global sensitivity analysis (GSA) is used for analyzing the effects of the system inputs on the model response. Common GSA methods use analytical or surrogate models to study the relationships between model inputs and outputs. However, the accuracy of such system models depends on the complete conformance to all model assumptions. Even so, they are not flexible and fail to capture nonlinear behaviors in complex systems. Besides these GSA approaches, interpretable machine learning would also identify the relationships between system variables, eliminating the disadvantages of common GSA implementations. Apart from studying the independent variables individually, the evaluation of groups of them is likewise valuable. One example motivation in engineering design for performing GSA with groups of input variables would be managing the design space complexity in programmable material systems (PMS) development. In this article, we employ a flexible, interpretable artificial neural network model to uncover individual as well as grouped global sensitivity indices for understanding complex physical interactions in engineering design. The employed model allows the investigation of the feature importance of the main effects and pairwise interaction effects in GSA according to functional analysis of variance (ANOVA) decomposition. To draw a higher-level understanding, we further use a subset decomposition method to analyze the significance of the groups of input variables. Using PMS as an example, we demonstrate the use of our approach for understanding the impact of material, architecture, and stimulus variables as well as their interactions for a programmable photonic metasurface system. This information lays the foundation for deriving design guidelines for PMS development.