Investigating the impact of operating parameters on molecular weight distributions using functional regression

Molecular weight distributions (MWDs) are inherently functional observations in which differential weight fraction is expressed as a function of chain length. Conventional approaches for analyzing and predicting MWDs include discretization and treatment as multi-response estimation problems, characterization using moments, and detailed mechanistic modeling to predict fractions for each chain length. However, these approaches can be sensitive to loss of information, complexity and problem conditioning. An alternative is to treat the MWDs as functional observations, and to use techniques from Functional Data Analysis (FDA), notably functional regression. The objective of this paper is to develop and apply empirical modeling techniques based on functional regression for investigating the impact of operating parameters on MWDs.