In this paper, a novel surrogate model based on the Grassmannian diffusion maps (GDMaps) and utilizing geometric harmonics is developed for predicting response of engineering systems complex physical phenomena. The method utilizes GDMaps to obtain low-dimensional representation underlying behavior physical/mathematical with respect uncertainties in input parameters. Using representation, harmon...

Metocean conditions during hurricanes are defined by multiple parameters (e.g., significant wave height and surge height) that vary in time with auto- cross-correlation. In many cases, the nature of variation these characteristics is important to design assess risk offshore structures, but a persistent problem measurements sparse history simulations using metocean models computationally onerous...

The aircraft conceptual design step requires a substantial number of aerodynamic configuration evaluations. Since the wing is main lifting element, focus on solving direct and reverse problems. former could be solved using low-cost computational model, but latter unlikely, even for these models. Surrogate modeling technique simplifying complex models that reduces time. In this work, surrogate b...

Abstract We introduce a method for the nonlinear dimension reduction of high-dimensional function $u:{\mathbb{R}}^d\rightarrow{\mathbb{R}}$, $d\gg 1$. Our objective is to identify feature map $g:{\mathbb{R}}^d\rightarrow{\mathbb{R}}^m$, with prescribed intermediate $m\ll d$, so that $u$ can be well approximated by $f\circ g$ some profile $f:{\mathbb{R}}^m\rightarrow{\mathbb{R}}$. propose build ...

Gaussian process (GP) surrogate modeling for large computer experiments is limited by cubic runtimes, especially with data from stochastic simulations input-dependent noise. A popular workaround to reduce computational complexity involves local approximation (e.g., LAGP). However, LAGP has only been vetted in deterministic settings. recent variation utilizing inducing points (LIGP) additional s...