3 papers
math.NA2026
A Primer on the Karhunen-Loève Expansion
Alen Alexanderian
This article provides a primer on the spectral representation of random fields via the Karhunen-Loève Expansion (KLE). The goal is to bridge the gap between the theoretical founda…
math.ST2026
A new kernel-based approach for the global sensitivity analysis of models with correlated inputs
Troy Larsen, Alen Alexanderian
We present an HSIC-based approach for global sensitivity analysis of broad classes of models with correlated and possibly function-valued inputs and outputs. To this end, we define…
math.NA2025
Robust optimal design of large-scale Bayesian nonlinear inverse problems
Abhijit Chowdhary, Ahmed Attia, Alen Alexanderian
We consider robust optimal experimental design (ROED) for nonlinear Bayesian inverse problems governed by partial differential equations (PDEs). An optimal design is one that maxim…