National Institute of Aerospace | ECS Lecture by Sastry Isukapalli

ECS Lecture by Sastry Isukapalli

Date: March 4, 2005
Time: 10:30am
Location: NIA, Rm 404
Speaker: Sastry Isukapalli with the Computational Chemodynamics Laboratory
Subject: "Stochastic Response Surface Method, Automatic Differentiation, and Bayesian Approaches for Uncertainty Propagation and Parameter Estimation"
Additional Information: Presentation (PDF) Webcast

Uncertainty propagation in complex, nested computational models is often resource intensive. Traditional techniques such as Monte Carlo analysis and Latin Hypercube Sampling require large number of model simulations in order to estimate the probability distributions of model outputs. Furthermore, estimating contributions of uncertainties in individual inputs towards the uncertainties in model outputs sometimes requires even more simulations. The Stochastic Response Surface Method (SRSM) facilitates computationally efficient uncertainty propagation via a representation of random inputs and outputs in terms of a set of "standard random variables" (srvs). In the SRSM, uncertain model inputs are expressed as functions of the srvs via simple transformations, and a polynomial functional form for outputs (a "polynomial chaos expansion") is assumed. Based on model outputs at a set of sample points from the model input space, the parameters of the output approximation are estimated, thus providing a simple expression for output uncertainties; this approach requires substantially fewer model simulations than traditional methods. Further improvements in computational efficiency of the SRSM are achieved by coupling the SRSM with automated source code differentiation tools, which produce code for partial derivatives with respect to model inputs and parameters. One such combination is the SRSM-ADIFOR, a combination of SRSM with the Automatic DIfferentiation of FORtran (ADIFOR). ADIFOR provides estimates of multiple partial derivatives from a single model run, and the partial derivative information has been used in the estimation of the coefficients of the polynomial chaos expansions.are obtained by coupling the SRSM with an automatic differentiation technique, ADIFOR (Automatic Differentiation of FORTRAN). The approach of SRSM-ADIFOR is simple, and is applicable to other forms of functional approximations, and can be coupled with other local sensitivity models including automated differentiation techniques for other programming languages (e.g. Matlab and C/C++). Applications of the SRSM include uncertainty propagation in numerical models simulating environmental and biological systems, and in the field of electric motor design. The SRSM has also been applied with Bayesian Markov Chain Monte Carlo (MCMC) to provide an approximate model to be used in parameter estimation.

The presentation provides a brief introduction of the SRSM and SRSM-ADIFOR, and discusses some case studies involving biological and environmental models, including the application of SRSM with Bayesian MCMC techniques. The presentation will also discuss ongoing improvements to the SRSM.