1. holds a Ph. D. in tropical meteorology, M. Tech
holds a Ph.D. in tropical meteorology, M.Tech. Degree in Atmospheric Science and M.S. Degree in Meteorology.
Hurricane Weather Research and Forecast (HWRF) modeling system.
Solution of Direct and Inverse Problems with Limited Forward Solver Evaluations: A Bayesian Perspective
Uncertainty propagation in physical processes is a challenging problem due to the high-dimensionality of the random property fields and the computational complexity of the models that are involved. The usual approach is to construct a surrogate response surface and then use it instead of the expensive model to carry out the uncertainty propagation task. However, the construction of the surrogate surface is hampered by various aspects such as the limited number of model evaluations that one can afford, the curse of dimensionality, multi-variate responses with non-trivial correlations, localized features of the response and/or discontinuities.
In the first part of the presentation, we expand upon the concept of the Multi-output Gaussian Process (MGP) to effectively deal with these difficulties in forward uncertainty propagation. This non-trivial extension involves an infinite mixture of MGP’s that is trained using variational Bayesian inference. Prior to observing any data, a Dirichlet process is used to generate the components of the MGP mixture. The Bayesian nature of the model allows for the quantification of the uncertainties due to the limited number of simulations. The automatic detection of the mixture components by the variational inference algorithm is able to capture discontinuities and localized features without adhering to ad hoc constructions. Finally, correlations between the components of multi-variate responses are captured.
  In the second part of the presentation, we briefly discuss a reformulation of the solution of the corresponding inverse problem when the expensive forward model is replaced by a set of simulations. We derive approximations of the reformulated solution with increasing complexity and fidelity. We demonstrate numerically that the proposed approximations capture the epistemic uncertainty of the solution of the inverse problem induced by the fact that the forward model is replaced by a finite amount of data. Examples will be shown from flows in random heterogeneous media.
Prof. Nicholas Zabaras
Viola D. Hank Professor Computational Science and Engineering
Department of Aerospace and Mechanical Engineering
Notre Dame University
Tuesday, November 8, :00-12:15 PM DeBartolo
Nicholas Zabaras joined Notre Dame's College of Engineering after serving as founding director of the Warwick Centre for Predictive Modeling at the University of Warwick and the Hans Fisher Senior Fellow with the Institute for Advanced Study at the Technical University of Munich. Earlier he spent twenty three years serving in all academic ranks of the faculty of the Sibley School of Mechanical and Aerospace Engineering at Cornell University where he was the director of the Materials Process Design and Control Laboratory. He received his PhD in Theoretical and Applied Mechanics at Cornell University, after which he started his academic career at the faculty of the University of Minnesota. He received his Ph.D. in Theoretical and Applied Mechanics from Cornell in 1987, after which he joined the faculty of the University of Minnesota.