Fast surrogate modeling using dimensionality reduction in model inputs and field output: Application to additive manufacturing

A novel approach to surrogate modeling motivated by recent advancements in parameter dimension reduction is proposed. Specifically, the approach aims to speed-up surrogate modeling for mapping multiple input variables to a field quantity of interest. Computational efficiency is accomplished by first identifying principal components (PC) and corresponding features in the output field data. A map from inputs to each feature is considered, and the active subspace (AS) methodology is used to capture their relationship in a low-dimensional subspace in the input domain. Thus, the PCAS method accomplishes dimension reduction in the input as well as the output. The method is demonstrated on a realistic problem pertaining to variability in residual stress in an additively manufactured component due to the stochastic nature of the process variables and material properties. The resulting surrogate model is exploited for uncertainty propagation, and identification of stress hotspots in the part. Additionally, the surrogate model is used for global sensitivity analysis to quantify relative contributions of the uncertain inputs to stress variability. Our findings based on the considered application are indicative of enormous potential for computational gains in such analyses, especially in generating training data, and enabling advancements in control and optimization of additive manufacturing processes.