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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2017
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/1710.10919 |
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| _version_ | 1866913696990625792 |
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| author | Héas, Patrick Herzet, Cédric Combès, Benoit |
| author_facet | Héas, Patrick Herzet, Cédric Combès, Benoit |
| contents | Reduced modeling of a computationally demanding dynamical system aims at approximating its trajectories, while optimizing the trade-off between accuracy and computational complexity. In this work, we propose to achieve such an approximation by first embedding the trajectories in a reproducing kernel Hilbert space (RKHS), which exhibits appealing approximation and computational capabilities, and then solving the associated reduced model problem. More specifically, we propose a new efficient algorithm for data-driven reduced modeling of non-linear dynamics based on linear approximations in a RKHS. This algorithm takes advantage of the closed-form solution of a low-rank constraint optimization problem while exploiting advantageously kernel-based computations. Reduced modeling with this algorithm reveals a gain in approximation accuracy, as shown by numerical simulations, and in complexity with respect to existing approaches. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1710_10919 |
| institution | arXiv |
| publishDate | 2017 |
| record_format | arxiv |
| spellingShingle | Non-linear reduced modeling of dynamical systems using kernel methods and low-rank approximation Héas, Patrick Herzet, Cédric Combès, Benoit Machine Learning Reduced modeling of a computationally demanding dynamical system aims at approximating its trajectories, while optimizing the trade-off between accuracy and computational complexity. In this work, we propose to achieve such an approximation by first embedding the trajectories in a reproducing kernel Hilbert space (RKHS), which exhibits appealing approximation and computational capabilities, and then solving the associated reduced model problem. More specifically, we propose a new efficient algorithm for data-driven reduced modeling of non-linear dynamics based on linear approximations in a RKHS. This algorithm takes advantage of the closed-form solution of a low-rank constraint optimization problem while exploiting advantageously kernel-based computations. Reduced modeling with this algorithm reveals a gain in approximation accuracy, as shown by numerical simulations, and in complexity with respect to existing approaches. |
| title | Non-linear reduced modeling of dynamical systems using kernel methods and low-rank approximation |
| topic | Machine Learning |
| url | https://arxiv.org/abs/1710.10919 |