# Wind Field Reconstruction with Adaptive Random Fourier Features

arXiv: https://arxiv.org/abs/2102.02365 · HTML: https://mlsanity.com/paper/2102.02365/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 1 of its 41 references that are in the map.
- First posted on arXiv 4 Feb 2021.

## Builds on (most cited first, 1 of 1)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)

## Built on by (most cited first, 3 of 3)

- [Comparing Spectral Bias and Robustness For Two-Layer Neural Networks: SGD vs Adaptive Random Fourier Features](https://mlsanity.com/paper/2402.00332/) (2024)
- [Adaptive Random Fourier Features Training Stabilized By Resampling With Applications in Image Regression](https://mlsanity.com/paper/2410.06399/) (2024)
- [Error Estimation for Random Fourier Features](https://mlsanity.com/paper/2302.11174/) (2023)

## Abstract (arXiv)

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 β(pmb x) = sumk=1K βk eiωk pmb x approximating the velocity field, with frequencies ωk randomly sampled and amplitudes βk trained to minimize a loss function. We include a physically motivated divergence penalty term |nabla · β(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.