Wind field reconstruction with adaptive random Fourier features

Proceedings of the Royal Society A Mathematical Physical and Engineering Sciences, vol. 477, pp. 20210236

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 with a set of benchmark methods including kriging and inverse distance weighting. Random Fourier features is a linear model β ( x ) = ∑ k = 1 K β k e i ω k x approximating the velocity field, with randomly sampled frequencies ω k and amplitudes β k 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.

Authors 3

1. Jonas Kiessling

   KTH Royal Institute of Technology

   Affiliation as printed

   H-Ai AB, Stockholm, Sweden

   KTH Royal Institute of Technology, Stockholm, Sweden

2. Emanuel Ström corresponding

   KTH Royal Institute of Technology

   Affiliation as printed

   KTH Royal Institute of Technology, Stockholm, Sweden

   KTH Royal Institute of Technology,, Stockholm, Sweden

3. Raul F. Tempone Aachen

   RWTH Aachen University · King Abdullah University of Science and Technology

   Affiliation as printed

   KAUST, Thuwal, Saudi Arabia

   RWTH Aachen University, Aachen, Germany