High-Dimensional Stochastic Design Optimization by Spline Dimensional Decomposition

Sponsor:                          U.S. National Science Foundation

Project No.:                      CMMI-1933114

Duration:                         September 2019 – August 2022

Principal Investigator:    Professor Sharif Rahman

Graduate Students:        Steven Dixler and Dongjin Lee

 

SUMMARY

This research will establish a sound mathematical foundation, create robust numerical algorithms, and build practical computational tools for design optimization of high-dimensional complex systems in the presence of uncertainty.  The proposed effort will involve: (1) new multivariate orthonormal basis splines (B-splines) and non-uniform rational B-splines (NURBS), leading to a new spline dimensional decomposition (SDD) method; (2) new formulae and scalable algorithms of the SDD method for calculating the statistical moments, including estimation of design sensitivities of moments from score functions; and (3) new computationally expedient robust design optimization (RDO) algorithms comprising a single or at most a few stochastic simulations.  The research is novel, debuting the stochastic version of B-splines and NURBS for the very first time.  New formulae and scalable algorithms generated for estimating the statistical moments will account for discontinuous or nonsmooth stochastic responses.  The integration with score functions will concurrently determine both the stochastic response characteristics and design sensitivities from the same computational effort, thereby solving RDO problems from a few stochastic simulations.  As a consequence, the speed of design process will be substantially enhanced, producing rare or potentially unprecedented solutions to large-scale stochastic design optimization problems.