Related papers: Wind Field Reconstruction with Adaptive Random Fou…
The method of random Fourier features (RFF), proposed in a seminal paper by Rahimi and Recht (NIPS'07), is a powerful technique to find approximate low-dimensional representations of points in (high-dimensional) kernel space, for…
Wind flow can be highly unpredictable and can suffer substantial fluctuations in speed and direction due to the shape and height of hills, mountains, and valleys, making accurate wind speed (WS) forecasting essential in complex terrain.…
The object of this work is to design an adequate regularization for the problem of recovering missing Fourier coefficients, particularly in some non standard situations were low frequency coefficients are lost. In the framework of non-local…
In this paper, we propose a dimension reduction model for spatially dependent variables. Namely, we investigate an extension of the \emph{inverse regression} method under strong mixing condition. This method is based on estimation of the…
In this article we introduce a broad family of adaptive, linear time-frequency representations termed superposition frames, and show that they admit desirable fast overlap-add reconstruction properties akin to standard short-time Fourier…
In order to measure the radial displacements of facets on surface of a growing spherical Cu_{2-\delta}Se crystal with sub-nanometer resolution, we have investigated the reliability and accuracy of standard method of Fourier analysis of…
We reconstruct the velocity field of incompressible flows given a finite set of measurements. For the spatial approximation, we introduce the Sparse Fourier divergence-free (SFdf) approximation based on a discrete $L^2$ projection. Within…
In this paper, we propose a new trigonometric interpolation algorithm and establish relevant convergent properties. The method adjusts an existing trigonometric interpolation algorithm such that it can better leverage Fast Fourier Transform…
Fourier-encoded implicit neural representations (INRs) have shown strong capability in modeling continuous signals from discrete samples. However, conventional Fourier feature mappings use a fixed set of frequencies over the entire spatial…
Estimates of the generalization error are proved for a residual neural network with $L$ random Fourier features layers $\bar z_{\ell+1}=\bar z_\ell + \mathrm{Re}\sum_{k=1}^K\bar b_{\ell k}e^{\mathrm{i}\omega_{\ell k}\bar z_\ell}+…
We present a regime-switching vector-autoregressive method for very-short-term wind speed forecasting at multiple locations with regimes based on large-scale meteorological phenomena. Statistical methods short-term wind forecasting…
We propose a new class of random feature methods for linearizing softmax and Gaussian kernels called hybrid random features (HRFs) that automatically adapt the quality of kernel estimation to provide most accurate approximation in the…
Feature subsampling is a core component of random forests and other ensemble methods. While recent theory suggests that this randomization acts solely as a variance reduction mechanism analogous to ridge regularization, these results…
With Fourier sensing, it is commonly the case that the field-of-view (FOV), the area of space to be imaged, is known prior to reconstruction. To date, reconstruction algorithms have focused on FOVs with simple geometries: a rectangle or a…
We prove new explicit upper bounds on the leverage scores of Fourier sparse functions under both the Gaussian and Laplace measures. In particular, we study $s$-sparse functions of the form $f(x) = \sum_{j=1}^s a_j e^{i \lambda_j x}$ for…
We develop and analyze a random field model for the reconstruction of turbulent velocity fluctuations from inhomogeneous characteristic flow quantities provided by RANS simulations that is accessible to both a rigorous analytical validation…
Random feature approximation is arguably one of the most widely used techniques for kernel methods in large-scale learning algorithms. In this work, we analyze the generalization properties of random feature methods, extending previous…
This paper proposes a novel structure-aware matrix completion framework assisted by radial basis function (RBF) interpolation for near-field radio map construction in extremely large multiple-input multiple-output (XL-MIMO) systems. Unlike…
The superstatistics concept is a useful statistical method to describe inhomogeneous complex systems for which a system parameter $\beta$ fluctuates on a large spatio-temporal scale. In this paper we analyze a measured time series of wind…
We develop a scalable algorithm for mean field control problems with kernel interactions by combining particle system simulations with random Fourier feature approximations. The method replaces the quadratic-cost kernel evaluations by…