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dc.contributor.authorKiessling, Jonas
dc.contributor.authorStröm, Emanuel
dc.contributor.authorTempone, Raul
dc.date.accessioned2021-02-17T12:20:16Z
dc.date.available2021-02-17T12:20:16Z
dc.date.issued2021-02-04
dc.identifier.urihttp://hdl.handle.net/10754/667500
dc.description.abstractWe 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.publisherarXiv
dc.relation.urlhttps://arxiv.org/pdf/2102.02365
dc.rightsArchived with thanks to arXiv
dc.titleWind Field Reconstruction with Adaptive Random Fourier Features
dc.typePreprint
dc.contributor.departmentApplied Mathematics and Computational Science Program
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
dc.contributor.departmentStochastic Numerics Research Group
dc.eprint.versionPre-print
dc.identifier.arxivid2102.02365
kaust.personTempone, Raul
refterms.dateFOA2021-02-17T12:23:08Z


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