Raphaël Gautier
(Advisor: Prof. Mavris)

will defend a doctoral thesis entitled

Bayesian And Multi-Fidelity Supervised Dimension Reduction Methods
For Surrogate Modeling Of Expensive Analyses With High-Dimensional Inputs

On

Monday, April 4 at 1:30 p.m.

In the

Collaborative Visualization Environment (CoVE)
Weber Space Science and Technology Building (SST II)

And
https://bluejeans.com/154734862/5227

Abstract
Modern approaches to engineering design rely on decision-support tools such as design space exploration, engineering optimization, or uncertainty quantification, to make better-informed design decisions. Such approaches typically rely on physics-based analyses that model the aspects of the system-of-interest that are relevant to the design task. As they operate by repeatedly evaluating their underlying analyses, carrying out these so-called ``many-query applications'' may become prohibitively expensive. Surrogate models act as enablers by replacing the online cost of evaluating analyses with a smaller offline cost spent to gather data used to train a cheap-to-evaluate mathematical model. Two current trends however make the generation of surrogate models more challenging and may therefore hinder the application of modern approaches. First, analyses of higher fidelity and greater computational cost are increasingly used to gather more detailed and accurate design knowledge early on in the design process, leading to the availability of fewer training observations under a constant analysis budget. Second, higher-dimensional parameter spaces are being considered, for example motivated by a more thorough exploration of the design space, the investigation of novel vehicle configurations, or the desire to retain design freedom longer, leading to surrogate models with high-dimensional inputs whose training suffers from the curse of dimensionality. In this thesis, we propose to investigate methods that address the impacts of these two trends on the generation of surrogate models: we seek new methods better suited for the creation of surrogate models with high-dimensional inputs and using only relatively few training observations. In particular, we focus on three surrogate modeling scenarios that map to the three research areas structuring this thesis: 1) single-fidelity surrogate modeling, 2) multi-fidelity surrogate modeling, and 3) active sampling in the multi-fidelity context.

The methods proposed in this thesis rely on approximation by ridge functions to alleviate the curse of dimensionality. It consists in first projecting the original high-dimensional inputs onto a low-dimensional feature space, followed by a traditional regression. Accordingly, training such approximations consists in 1) determining a relevant projection, and 2) training the regression model. Multiple contributions are made in this thesis, starting in the single-fidelity context with a fully Bayesian and gradient-free formulation of approximation by ridge functions. Compared to existing approaches, the proposed method enables a full quantification of epistemic uncertainty due to limited training data, in both the regression parameters and the low-dimensional projection. Through a thorough study conducted on multiple datasets originating from science and engineering applications, it is shown to outperform existing state-of-the-art methods. Alternate methods for determining the dimension of the low-dimensional feature space, that aim to address shortcomings of existing methods, are then proposed and assessed. These advancements are then brought to the multi-fidelity context by altering a deep multi-fidelity Gaussian process model to include an initial projection of its inputs and a fully Bayesian approach to its training. Under certain conditions, this approach is shown to make better use of a given analysis budget compared to relying on a single fidelity. The relationship between the projections used for the low- and high-fidelity parts of the model is then investigated. Two approaches to sampling leveraging the feature space are formulated and assessed. The proposed approach to experimental design for selecting the location of high-fidelity observations is shown to outperform a traditional design of experiments in the original input space, but the proposed active sampling approach does not yield any additional improvement. Finally, a coherent approach to multi-fidelity modeling is assembled, that leverages the knowledge of the low-dimensional feature space to assist the selection of expensive, high-fidelity observations and is shown to outperform the state-of-the-art deep multi-fidelity Gaussian process method.

Committee

• Prof. Dimitri Mavris – School of Aerospace Engineering (advisor)
• Prof. Lakshmi Sankar – School of Aerospace Engineering
•  
• Prof. Graeme Kennedy – School of Aerospace Engineering
•  
• Dr. Sayan Ghosh – GE Research
•  
• Dr. Chung Lee – School of Aerospace Engineering
•