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Gaussian process surrogate model with composite kernel learning for engineering design
Palar P.S.a, Zuhal L.R.a, Shimoyama K.b
a Faculty of Mechanical and Aerospace Engineering, Bandung Institute of Technology, Bandung, 40132, Indonesia
b Institute of Fluid Science, Tohoku University, Sendai, 980-8577, Japan
[vc_row][vc_column][vc_row_inner][vc_column_inner][vc_separator css=”.vc_custom_1624529070653{padding-top: 30px !important;padding-bottom: 30px !important;}”][/vc_column_inner][/vc_row_inner][vc_row_inner layout=”boxed”][vc_column_inner width=”3/4″ css=”.vc_custom_1624695412187{border-right-width: 1px !important;border-right-color: #dddddd !important;border-right-style: solid !important;border-radius: 1px !important;}”][vc_empty_space][megatron_heading title=”Abstract” size=”size-sm” text_align=”text-left”][vc_column_text]© 2020 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved.The composite kernel learning (CKL) method is introduced to efficiently construct composite kernels for Gaussian process (GP) surrogate models with applications in engineering design. The mixture of kernel functions is cast as a weighted-sum model in which the weights are treated as extra hyperparameters to yield a higher optimum likelihood. The CKL framework aims to improve the accuracy of the GP and relieves the difficulty of kernel selection. In this paper, the combination of five kernel functions are studied, namely, Gaussian, Matérn-3/2, Matérn-5/2, exponential, and cubic, with each kernel sharing the same length scale. Numerical studies were performed on a set of engineering problems to assess the approximation capability ofGP-CKL. The results show that, in general,GP-CKLyields a lower approximation error and higher robustness as compared to GP models with single kernel and model selection methods. Numerical experiments show that it is worth using the GP-CKL method for achieving higher accuracy with extra burdens on the number of hyperparameters and a longer training time. Besides, experiments were also performed with variable length scales for each kernel and each variable.However, this variant ofCKLis not suggested because it is prone to overfitting and is significantly more expensive than the other GP variants.[/vc_column_text][vc_empty_space][vc_separator css=”.vc_custom_1624528584150{padding-top: 25px !important;padding-bottom: 25px !important;}”][vc_empty_space][megatron_heading title=”Author keywords” size=”size-sm” text_align=”text-left”][vc_column_text]Approximation capabilities,Engineering design,Engineering problems,Gaussian Processes,Lower approximation,Model selection methods,Numerical experiments,Weighted sum model[/vc_column_text][vc_empty_space][vc_separator css=”.vc_custom_1624528584150{padding-top: 25px !important;padding-bottom: 25px !important;}”][vc_empty_space][megatron_heading title=”Indexed keywords” size=”size-sm” text_align=”text-left”][vc_column_text][/vc_column_text][vc_empty_space][vc_separator css=”.vc_custom_1624528584150{padding-top: 25px !important;padding-bottom: 25px !important;}”][vc_empty_space][megatron_heading title=”Funding details” size=”size-sm” text_align=”text-left”][vc_column_text]Pramudita Satria Palar and Lavi Rizki Zuhal were funded in part through Program Riset Institut Teknologi Bandung 2019 Kategori A (Award No: 0109/I1.B04.1/PL/2019). Part of the work was also carried out under Collaborative Research Project 2019 of the Institute of Fluid Science, Tohoku University (project number J19I014).[/vc_column_text][vc_empty_space][vc_separator css=”.vc_custom_1624528584150{padding-top: 25px !important;padding-bottom: 25px !important;}”][vc_empty_space][megatron_heading title=”DOI” size=”size-sm” text_align=”text-left”][vc_column_text]https://doi.org/10.2514/1.J058807[/vc_column_text][/vc_column_inner][vc_column_inner width=”1/4″][vc_column_text]Widget Plumx[/vc_column_text][/vc_column_inner][/vc_row_inner][/vc_column][/vc_row][vc_row][vc_column][vc_separator css=”.vc_custom_1624528584150{padding-top: 25px !important;padding-bottom: 25px !important;}”][/vc_column][/vc_row]