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research-article

Globally Approximate Gaussian Processes for Big Data with Application to Data-Driven Metamaterials Design (IDETC2019-98027)

[+] Author and Article Information
Ramin Bostanabad

2145 Sheridan Road Evanston, IL 60208 bostanabad@u.northwestern.edu

Yu-Chin Chan

2145 Sheridan Road Evanston, IL 60208 ychan@u.northwestern.edu

Liwei Wang

800 Dongchuan Road Shanghai, 200240 China iridescence@sjtu.edu.cn

Ping Zhu

School of Mechanical Engineering, Shanghai Jiao Tong University, Shanghai 200240 Shanghai, Shanghai 200240 China pzhu@sjtu.edu.cn

Wei Chen

2145 Sheridan Rd Evanston, IL 60208-3111 editor@asmejmd.org

1Corresponding author.

Contributed by the Design Automation Committee of ASME for publication in the Journal of Mechanical Design. Manuscript received March 1, 2019; final manuscript received July 11, 2019; published online xx xx, xxxx. Assoc. Editor: Samy Missoum.

ASME doi:10.1115/1.4044257 History: Received March 01, 2019; Accepted July 12, 2019

Abstract

We introduce a novel method for Gaussian process (GP) modeling of massive datasets called globally approximate Gaussian process (GAGP). Unlike most largescale supervised learners such as neural networks and trees, GAGP is easy to fit and can interpret the model behavior, making it particularly useful in engineering design with big data. The key idea of GAGP is to build a collection of independent GPs that use the same hyperparameters but randomly distribute the entire training dataset among themselves. This is based on the observation that the GP hyperparameter approximations change negligibly as the size of the training data exceeds a certain level that can be systematically estimated. For inference, the predictions from all GPs in the collection are pooled, allowing the entire training dataset to be efficiently exploited for prediction. Through analytical examples, we demonstrate that GAGP achieves very high predictive power matching (and in some cases exceeding) that of state-of-the-art machine learning methods. We illustrate the application of GAGP in engineering design with a problem on data-driven metamaterials, using it to link reduced-dimension geometrical descriptors of unit cells and their properties. Searching for new unit cell designs with desired properties is then achieved by employing GAGP in inverse optimization.

Copyright © 2019 by ASME
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