We investigate the use of spatial interpolation methods for reconstructing the horizontal near-surface wind field given a sparse set of measurements. In particular, random Fourier features is compared with a set of benchmark methods including kriging and inverse distance weighting. Random Fourier features is a linear model β(x)=∑Kk=1βk eiωkx approximating the velocity field, with randomly sampled frequencies ωk and amplitudes βk trained to minimize a loss function. We include a physically motivated divergence penalty |∇⋅β(x)|2, as well as a penalty on the Sobolev norm of β. We derive a bound on the generalization error and a sampling density that minimizes the bound. We then devise an adaptive Metropolis–Hastings algorithm for sampling the frequencies of the optimal distribution. In our experiments, our random Fourier features model outperforms the benchmark models.
|Original language||English (US)|
|Journal||Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences|
|State||Published - Nov 17 2021|
Bibliographical noteKAUST Repository Item: Exported on 2021-11-22
Acknowledged KAUST grant number(s): OSR-2019-CRG8-4033, OSR-2019-CRG8-4033.2
Acknowledgements: J.K. and R.T. were partially supported by the KAUST Office of Sponsored Research (OSR) under Award numbers OSR-2019-CRG8-4033 and OSR-2019-CRG8-4033.2, and the Alexander von Humboldt Foundation, through the Alexander von Humboldt Professorship award. E.S. was supported by the KAUST Visiting Student Research Program (VSRP).
ASJC Scopus subject areas
- Physics and Astronomy(all)