### ### Thursday, October 27th, 2016 | 12:00 PM* | 37-212

### Thursday, October 27th, 2016 | 12:00 PM* | 37-212

**A NONPARAMETRIC PROBABILISTIC APPROACH FOR QUANTIFYING UNCERTAINTIES IN LOW- AND HIGH-DIMENSIONAL NONLINEAR MODELS **

*Charbel Farhat *

A. Bos^1 and C. Farhat^{1,2,3}

^1 Department of Aeronautics and Astronautics

^2 Department of Mechanical Engineering

^3 Institute for Computational and Mathematical Engineering

Stanford University, Stanford, CA 94305, USA

C. Soize

Laboratoire Mod\'elisation et Simulation Multi Echelle

MSME UMR 8208 CNRS, Universit\'e Paris-Est, 5 bd Descartes

77454 Marne-la-Vallee, France

A nonparametric probabilistic approach for modeling uncertainties in projection-based, nonlinear, reduced-order models is presented. When experimental data is available, this approach can also quantify uncertainties in the associated high-dimensional models.

The main underlying idea is two-fold. First, to substitute the deterministic Reduced-Order Basis (ROB) with a stochastic counterpart. Second, to construct the probability measure of the Stochastic Reduced-Order Basis (SROB) on a subset of a compact Stiefel manifold in order to preserve some important properties of a ROB. The stochastic modeling is performed so that the probability distribution of the constructed SROB depends on a small number of hyperparameters. These are determined by solving a reduced-order statistical inverse problem.

The proposed nonparametric probabilistic approach for taking into account model form uncertainties can be interpreted as a stochastic-based method for extracting fundamental information or knowledge from test or High-Dimensional Model (HDM) data that is not captured by a deterministic HDM or ROM, respectively. In this approach, one essentially parameterizes the approximation basis in order to capture the variabilities instead of parameterizing the governing equations. Its mathematical properties are analyzed through theoretical developments and numerical simulations. Its potential is demonstrated through several example problems from nonlinear computational structural dynamics.

* Lunch available at 11:45

### ### Thursday, December 8th, 2016 | 12:00 PM* | 37-212

### Thursday, December 8th, 2016 | 12:00 PM* | 37-212

*Antonio Huerta *

* Lunch provided at 11:45

### ### Thursday, March 23rd 2017 | 12:00 PM* | 37-212

### Thursday, March 23rd 2017 | 12:00 PM* | 37-212

*Serkan Gugerin *

* Lunch available at 11:45

### ### Thursday, April 27th 2017 | 12:00 PM* | 37-212

### Thursday, April 27th 2017 | 12:00 PM* | 37-212

*Misha Kilmer *

* Lunch provided at 11:45