An adaptive RBF-HDMR modeling approach under limited computational budget
The metamodel-based high-dimensional model representation (e.g., RBF-HDMR) has recently been proven to be very promising for modeling high dimensional functions. A frequently encountered scenario in practical engineering problems is the need of building accurate models under limited computational bu...
| Main Authors: | , , , , |
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| Format: | Journal Article |
| Language: | English |
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2020
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| Online Access: | https://hdl.handle.net/10356/139027 |
| _version_ | 1826120058779205632 |
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| author | Liu, Haitao Hervas, Jaime-Rubio Ong, Yew-Soon Cai, Jianfei Wang, Yi |
| author2 | School of Computer Science and Engineering |
| author_facet | School of Computer Science and Engineering Liu, Haitao Hervas, Jaime-Rubio Ong, Yew-Soon Cai, Jianfei Wang, Yi |
| author_sort | Liu, Haitao |
| collection | NTU |
| description | The metamodel-based high-dimensional model representation (e.g., RBF-HDMR) has recently been proven to be very promising for modeling high dimensional functions. A frequently encountered scenario in practical engineering problems is the need of building accurate models under limited computational budget. In this context, the original RBF-HDMR approach may be intractable due to the independent and successive treatment of the component functions, which translates in a lack of knowledge on when the modeling process will stop and how many points (simulations) it will cost. This article proposes an adaptive and tractable RBF-HDMR (ARBF-HDMR) modeling framework. Given a total of Nmax points, it first uses Nini points to build an initial RBF-HDMR model for capturing the characteristics of the target function f, and then keeps adaptively identifying, sampling and modeling the potential cuts with the remaining Nmax − Nini points. For the second-order ARBF-HDMR, Nini ∈ [2n + 2,2n2 + 2] not only depends on the dimensionality n but also on the characteristics of f. Numerical results on nine cases with up to 30 dimensions reveal that the proposed approach provides more accurate predictions than the original RBF-HDMR with the same computational budget, and the version that uses the maximin sampling criterion and the best-model strategy is a recommended choice. Moreover, the second-order ARBF-HDMR model significantly outperforms the first-order model; however, if the computational budget is strictly limited (e.g., 2n + 1 < Nmax ≪ 2n2 + 2), the first-order model becomes a better choice. Finally, it is noteworthy that the proposed modeling framework can work with other metamodeling techniques. |
| first_indexed | 2024-10-01T05:09:59Z |
| format | Journal Article |
| id | ntu-10356/139027 |
| institution | Nanyang Technological University |
| language | English |
| last_indexed | 2024-10-01T05:09:59Z |
| publishDate | 2020 |
| record_format | dspace |
| spelling | ntu-10356/1390272020-05-15T01:35:48Z An adaptive RBF-HDMR modeling approach under limited computational budget Liu, Haitao Hervas, Jaime-Rubio Ong, Yew-Soon Cai, Jianfei Wang, Yi School of Computer Science and Engineering Rolls-Royce@NTU Corporate Laboratory Data Science and Artificial Intelligence Research Center Engineering::Computer science and engineering Metamodeling Adaptive High Dimensional Model Representation The metamodel-based high-dimensional model representation (e.g., RBF-HDMR) has recently been proven to be very promising for modeling high dimensional functions. A frequently encountered scenario in practical engineering problems is the need of building accurate models under limited computational budget. In this context, the original RBF-HDMR approach may be intractable due to the independent and successive treatment of the component functions, which translates in a lack of knowledge on when the modeling process will stop and how many points (simulations) it will cost. This article proposes an adaptive and tractable RBF-HDMR (ARBF-HDMR) modeling framework. Given a total of Nmax points, it first uses Nini points to build an initial RBF-HDMR model for capturing the characteristics of the target function f, and then keeps adaptively identifying, sampling and modeling the potential cuts with the remaining Nmax − Nini points. For the second-order ARBF-HDMR, Nini ∈ [2n + 2,2n2 + 2] not only depends on the dimensionality n but also on the characteristics of f. Numerical results on nine cases with up to 30 dimensions reveal that the proposed approach provides more accurate predictions than the original RBF-HDMR with the same computational budget, and the version that uses the maximin sampling criterion and the best-model strategy is a recommended choice. Moreover, the second-order ARBF-HDMR model significantly outperforms the first-order model; however, if the computational budget is strictly limited (e.g., 2n + 1 < Nmax ≪ 2n2 + 2), the first-order model becomes a better choice. Finally, it is noteworthy that the proposed modeling framework can work with other metamodeling techniques. NRF (Natl Research Foundation, S’pore) 2020-05-15T01:35:48Z 2020-05-15T01:35:48Z 2017 Journal Article Liu, H., Hervas, J.-R., Ong, Y.-S., Cai, J., & Wang, Y. (2018). An adaptive RBF-HDMR modeling approach under limited computational budget. Structural and Multidisciplinary Optimization, 57(3), 1233-1250. doi:10.1007/s00158-017-1807-0 1615-147X https://hdl.handle.net/10356/139027 10.1007/s00158-017-1807-0 2-s2.0-85029810679 3 57 1233 1250 en Structural and Multidisciplinary Optimization © 2017 Springer-Verlag GmbH Germany. All rights reserved. |
| spellingShingle | Engineering::Computer science and engineering Metamodeling Adaptive High Dimensional Model Representation Liu, Haitao Hervas, Jaime-Rubio Ong, Yew-Soon Cai, Jianfei Wang, Yi An adaptive RBF-HDMR modeling approach under limited computational budget |
| title | An adaptive RBF-HDMR modeling approach under limited computational budget |
| title_full | An adaptive RBF-HDMR modeling approach under limited computational budget |
| title_fullStr | An adaptive RBF-HDMR modeling approach under limited computational budget |
| title_full_unstemmed | An adaptive RBF-HDMR modeling approach under limited computational budget |
| title_short | An adaptive RBF-HDMR modeling approach under limited computational budget |
| title_sort | adaptive rbf hdmr modeling approach under limited computational budget |
| topic | Engineering::Computer science and engineering Metamodeling Adaptive High Dimensional Model Representation |
| url | https://hdl.handle.net/10356/139027 |
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