Wind Field Reconstruction with Adaptive Random Fourier Features

• URL: http://arxiv.org/abs/2102.02365v1
• Date: Thu, 4 Feb 2021 01:42:08 GMT
• Title: Wind Field Reconstruction with Adaptive Random Fourier Features
• Authors: Jonas Kiessling, Emanuel Str\"om and Ra\'ul Tempone
• Abstract summary: We investigate the use of spatial methods for reconstructing the horizontal near-surface wind field given a sparse set of measurements. We include a physically motivated divergence penalty term $|nabla cdot beta(pmb x)|2$, as well as a penalty on the Sobolev norm. We devise an adaptive-Hastings algorithm for sampling the frequencies of the optimal distribution.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• 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.

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