Fast surrogate modeling using dimensionality reduction in model inputs and field output: Application to additive manufacturing
Manav Vohra, Paromita Nath, Sankaran Mahadevan, Yung-Tsun T. Lee
A novel approach to surrogate modeling motivated by recent advancements in parameter dimension reduction isproposed. Specifically, the approach aims to speed-up surrogate modeling for mapping multiple input variablesto 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, andthe active subspace (AS) methodology is used to capture their relationship in a low-dimensional subspace in theinput domain. Thus, the PCAS method accomplishes dimension reduction in the input as well as the output. Themethod is demonstrated on a realistic problem pertaining to variability in residual stress in an additivelymanufactured component due to the stochastic nature of the process variables and material properties. Theresulting surrogate model is exploited for uncertainty propagation, and identification of stress hotspots in thepart. Additionally, the surrogate model is used for global sensitivity analysis to quantify relative contributions ofthe uncertain inputs to stress variability. Our findings based on the considered application are indicative ofenormous potential for computational gains in such analyses, especially in generating training data, and en-abling advancements in control and optimization of additive manufacturing processes.