Adaptive surrogate modeling for high dimensional problems using Autoencoder Gaussian Process

High-dimensional surrogate modeling poses significant challenges, particularly when data is limited, as traditional Gaussian Process (GP) models struggle with scalability and computational efficiency. This paper addresses these issues by proposing a framework for optimizing the latent dimension in an Autoencoder-Gaussian Process (AE-GP) model, ensuring both accuracy and scalability. Using 10 representative benchmark functions, the study evaluates the GP’s performance in terms of Mean Squared Error (MSE) under 5-fold cross-validation, with latent dimensions ranging from 1 to 20. The experiments are conducted across varying combinations of dataset dimensions D0 and sample sizes N, identifying the best-performing specific values and ranges of latent dimensions. These optimal dimensions are then applied to high-dimensional case studies with unknown x-y relationships to validate the model’s practical applicability. By proposing an adaptive framework for high-dimensional surrogate modeling, this work provides actionable insights for selecting AE latent dimensions under resource constraints and demonstrates its effectiveness in improving model scalability and accuracy across diverse scenarios.

Name thesis:degree_name

M.S.

Level thesis:degree_level

Thesis

Discipline thesis:degree_discipline

Industrial Engineering

Grantor

University of Illinois at Urbana-Champaign

Year dc:date

2024

Author dc:creator

• Zhao, Jiayi

Contributors dc:contributor

• Wang, Pingfeng

• Surrogate Modeling
• High Dimension
• Autoencoder
• Gaussian Process

Statement dc:rights

• Copyright 2024 Jiayi Zhao

Language dc:language

en, eng

Handle dc:identifier

https://hdl.handle.net/2142/127512

OAI record oai:identifier

https://www.ideals.illinois.edu/oai-pmh?verb=GetRecord&metadataPrefix=etdms&identifier=oai%3Awww.ideals.illinois.edu%3A2142%2F127512