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Uncertainty Quantification, Dimension Reduction and Domain Decomposition for High Dimensional Stochastic Partial Differential Equations

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Virtual Event

Thursday, February 17, 2022 4 pm

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ME-EM Graduate Seminar Speaker Series

proudly presents

Ramakrishna Tipireddy, PhD

Pacific Northwest National Laboratory

Abstract

This talk will present a brief introduction to polynomial chaos (PC) based uncertainty quantification (UQ) methods for high dimensional stochastic partial differential equations (SPDEs) and introduce stochastic dimension reduction and spatial domain decomposition methods. This talk also presents conditional Gaussian process (GP) models for uncertainty reduction. In this approach, the PDE coefficient is represented as a log-normal random field, with the corresponding Gaussian part modeled as a zero-mean Gaussian process (GP) with appropriate covariance function. The reduction in uncertainty is achieved by conditioning the GP model on observations of the coefficient at a few spatial locations. The resulting conditional GP model is then discretized using truncated Karhunen-Loève (KL) expansion and the stochastic solution of the PDE is computed using Monte Carlo and sparse-grid collocation methods. Uncertainty in the system is further reduced by adaptively selecting additional observation locations using two active learning criteria. The talk will feature several applications in computational mechanics such as random eigenvalue analysis for stability of a wind turbine blade with random Young’s modulus, plate with a hole subjected to internal pressure.

Bio

Ramakrishna Tipireddy is a Research Scientist in the Physical and Computational Sciences Directorate at the Pacific Northwest National Laboratory. His research interests include uncertainty quantification, computational mechanics, and development of reduced order models for complex stochastic systems. Tipireddy received his PhD in civil engineering from University of Southern California.

Invited by: Susanta Ghosh

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