TY - GEN
T1 - Gaussian process emulation for big data in data-driven metamaterials design
AU - Bostanabad, Ramin
AU - Chan, Yu Chin
AU - Wang, Liwei
AU - Zhu, Ping
AU - Chen, Wei
N1 - Funding Information:
The authors are grateful to Prof. K. Svanberg, from Royal Institute of Technology, Sweden, for providing a copy of the MMA code for metamaterial designs. Support from NSF grants (ACI 1640840 and OAC 1835782) and AFOSR FA9550-18-1-0381 are greatly appreciated. Ms. Yu-Chin Chan would like to acknowledge the NSF Graduate Research Fellowship Program under grant DGE-1842165.
Publisher Copyright:
Copyright © 2019 ASME.
PY - 2019
Y1 - 2019
N2 - Our main contribution is to introduce a novel method for Gaussian process (GP) modeling of massive datasets. The key idea is to build an ensemble of independent GPs that use the same hyperparameters but distribute the entire training dataset among themselves. This is motivated by our observation that estimates of the GP hyperparameters change negligibly as the size of the training data exceeds a certain level, which can be found in a systematic way. For inference, the predictions from all GPs in the ensemble are pooled to efficiently exploit the entire training dataset for prediction. We name our modeling approach globally approximate Gaussian process (GAGP), which, unlike most largescale supervised learners such as neural networks and trees, is easy to fit and can interpret the model behavior. These features make it particularly useful in engineering design with big data. We use analytical examples to demonstrate that GAGP achieves very high predictive power that matches or exceeds 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 design where it is used to link reduced-dimension geometrical descriptors of unit cells and their properties. Searching for new unit cell designs with desired properties is then accomplished by employing GAGP in inverse optimization.
AB - Our main contribution is to introduce a novel method for Gaussian process (GP) modeling of massive datasets. The key idea is to build an ensemble of independent GPs that use the same hyperparameters but distribute the entire training dataset among themselves. This is motivated by our observation that estimates of the GP hyperparameters change negligibly as the size of the training data exceeds a certain level, which can be found in a systematic way. For inference, the predictions from all GPs in the ensemble are pooled to efficiently exploit the entire training dataset for prediction. We name our modeling approach globally approximate Gaussian process (GAGP), which, unlike most largescale supervised learners such as neural networks and trees, is easy to fit and can interpret the model behavior. These features make it particularly useful in engineering design with big data. We use analytical examples to demonstrate that GAGP achieves very high predictive power that matches or exceeds 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 design where it is used to link reduced-dimension geometrical descriptors of unit cells and their properties. Searching for new unit cell designs with desired properties is then accomplished by employing GAGP in inverse optimization.
KW - Big data
KW - Gaussian processes
KW - Metamaterials
KW - Supervised learning
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U2 - 10.1115/DETC2019-98027
DO - 10.1115/DETC2019-98027
M3 - Conference contribution
AN - SCOPUS:85076460427
T3 - Proceedings of the ASME Design Engineering Technical Conference
BT - 45th Design Automation Conference
PB - American Society of Mechanical Engineers (ASME)
T2 - ASME 2019 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, IDETC-CIE 2019
Y2 - 18 August 2019 through 21 August 2019
ER -