Past Event: PhD Dissertation Defense

Derivative-informed Surrogate Models for PDE-constrained Optimization under Uncertainty

Dingcheng Luo, Ph.D. Candidate, Oden Institute

Abstract

Design optimization using computational models is a key technology that enables practitioners to develop performant and cost-effective designs for a wide range of engineering systems.
In many instances, it is critical for the optimization procedure to explicitly account for system uncertainties to ensure robustness of the design solutions, leading to a class of problems known as optimization under uncertainty (OUU). In this setting, optimization objectives and constraints are often formulated in terms of risk measures---scalar functionals summarizing the distribution of a quantity of interest (QoI)---whose estimation via sampling or deterministic quadrature can require a large number of model evaluations. This leads to a computationally challenging task due to the need to simultaneously explore the vast design and uncertainty spaces, especially when the underlying model is expensive to evaluate.

In this dissertation, we investigate novel approaches for the construction of surrogate models for the optimization of systems governed by partial differential equations (PDEs) under uncertain model parameters, exploring both their theoretical and computational aspects. Specifically, we are interested in fast surrogate models that can replace, to some extent, the high-fidelity PDE model in order to accelerate the estimation of risk measures, and hence enable efficient OUU. We focus on high-dimensional uncertain parameters that arise from the discretization of random fields, 
which requires that the surrogates are scalable with respect to the parameter dimension. As a theme, our approaches leverage information provided by the derivatives of the underlying mappings to improve accuracy and reduce construction costs.

Biography

Dingcheng is a PhD Student in the Center for Optimization, Inversion, Machine Learning, and Uncertainty for Complex Systems, supervised by Prof. Omar Ghattas and Prof. Peng Chen. His research interests are in developing computational methods to enable risk-informed decision making for physical systems. Prior to the Oden Institute, he obtained his B.E. (Hons) in civil engineering from the University of Canterbury.