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Gradient-Enhanced Uncertainty Propagation

Wednesday, October 26, 1:30PM – 3PM
ACE 6.304

Mihai Anitescu, Argonne National Labs

In this work we discuss an approach for uncertainty propagation through computationally expensive physics simulation codes. Our approach incorporates gradient information information to provide a higher quality surrogate with fewer simulation results compared with derivative-free approaches.

We use this information in two ways: we fit a polynomial or Gaussian process model ("surrogate") of the system response. In a third approach we hybridize the techniques where a Gaussian process with polynomial mean is fit resulting in an improvement of both techniques. The surrogate coupled with input uncertainty information provides a complete uncertainty approach when the physics simulation code can be run at only a small number of times. We discuss various algorithmic choices such as polynomial basis and covariance kernel. We demonstrate our findings on synthetic functions as well as nuclear reactor models.

Biosketch: Dr. Anitescu has obtained his Engineer (M.Sc.) Diploma in electrical engineering from the University "Politehnica" of Bucharest in 1992 and his Ph.D. degree in applied mathematical and computational sciences from the University of Iowa in 1997. Between 1997 and 1999 he was the Wilkinson fellow in computational science in the Mathematics and Computer Science Division at Argonne National Laboratory. Between 1999 and 2002 he was an assistant professor of mathematics at the University of Pittsburgh. Since 2002, he has been a Computational Mathematician in the Mathematics and Computer Science Division at Argonne National Laboratory. Since 2009, he is a professor (part-time) in the Department of Statistics at the University of Chicago. Dr. Anitescu is a Senior Editor for Optimization Methods and Software and a member of the editorial boards of Mathematical Programming series A, Mathematical Programming series B, SIAM Journal on Optimization and SIAM Journal on Scientific Computing. He is the vice-president of the SIAM Activity Group in Optimization. He is a past organizer of the SIAM Annual Meeting and International Symposium on Mathematical Programming. He is the author of more than 80 papers in scholarly journals and conference proceedings, on numerical optimization, numerical analysis, computational mathematics and their applications.

His current research interests include nonlinear programming, scalable stochastic programming, uncertainty quantification, scalable Gaussian Process analysis, differential variational inequalities, and their application to climate, materials science, nuclear engineering, and the power grid.

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