dc.contributor.author Kiessling, Jonas dc.contributor.author Ström, Emanuel dc.contributor.author Tempone, Raul dc.date.accessioned 2021-02-17T12:20:16Z dc.date.available 2021-02-17T12:20:16Z dc.date.issued 2021-02-04 dc.identifier.uri http://hdl.handle.net/10754/667500 dc.description.abstract 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 to a set of benchmark methods including Kriging and Inverse distance weighting. Random Fourier features is a linear model $\beta(\pmb x) = \sum_{k=1}^K \beta_k e^{i\omega_k \pmb x}$ approximating the velocity field, with frequencies $\omega_k$ randomly sampled and amplitudes $\beta_k$ trained to minimize a loss function. We include a physically motivated divergence penalty term $|\nabla \cdot \beta(\pmb x)|^2$, as well as a penalty on the Sobolev norm. We derive a bound on the generalization error and derive a sampling density that minimizes the bound. Following (arXiv:2007.10683 [math.NA]), we 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. dc.publisher arXiv dc.relation.url https://arxiv.org/pdf/2102.02365 dc.rights Archived with thanks to arXiv dc.title Wind Field Reconstruction with Adaptive Random Fourier Features dc.type Preprint dc.contributor.department Applied Mathematics and Computational Science Program dc.contributor.department Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division dc.contributor.department Stochastic Numerics Research Group dc.eprint.version Pre-print dc.identifier.arxivid 2102.02365 kaust.person Tempone, Raul refterms.dateFOA 2021-02-17T12:23:08Z
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