33 citations · 157 across the 27 of their papers we have counts for
32 papers
OmniPoser: Flexible Human Motion Recovery in the Wild with Masked Flow Matching
Minghao Liu, Tutian Tang
Recovering 3D human motion from sparse wearable sensors is challenging due to the inherent noise, occlusion, and instability of real-world tracking signals. Existing approaches are…
Learning solution operators of PDEs with sparse approximation methods
Sebastian Neumayer, Daniel Potts, Fabian Taubert
We investigate the approximation of solution operators for partial differential equations (PDEs) using sparse high-dimensional techniques. Building on a dimension-incremental frame…
Optimal density compensation factors for the reconstruction of the Fourier transform of bandlimited functions
Melanie Kircheis, Daniel Potts
An inverse nonequispaced fast Fourier transform (iNFFT) is a fast algorithm to compute the Fourier coefficients of a trigonometric polynomial from nonequispaced sampling data. Howe…
On numerical realizations of Shannon's sampling theorem
Melanie Kircheis, Daniel Potts, Manfred Tasche
In this paper, we discuss some numerical realizations of Shannon's sampling theorem. First we show the poor convergence of classical Shannon sampling sums by presenting sharp upper…
ANOVA approximation with mixed tensor product basis on scattered points
Daniel Potts, Pascal Schröter
In this paper we consider an orthonormal basis, generated by a tensor product of Fourier basis functions, half period cosine basis functions, and the Chebyshev basis functions. We…
Fast and direct inversion methods for the multivariate nonequispaced fast Fourier transform
Melanie Kircheis, Daniel Potts
The well-known discrete Fourier transform (DFT) can easily be generalized to arbitrary nodes in the spatial domain. The fast procedure for this generalization is referred to as non…
Nonlinear approximation in bounded orthonormal product bases
Lutz Kämmerer, Daniel Potts, Fabian Taubert
We present a dimension-incremental algorithm for the nonlinear approximation of high-dimensional functions in an arbitrary bounded orthonormal product basis. Our goal is to detect…
On the reconstruction of functions from values at subsampled quadrature points
Felix Bartel, Lutz Kämmerer, Daniel Potts +1
This paper is concerned with function reconstruction from samples. The sampling points used in several approaches are (1) structured points connected with fast algorithms or (2) un…
Variable Transformations in combination with Wavelets and ANOVA for high-dimensional approximation
Daniel Potts, Laura Weidensager
We use hyperbolic wavelet regression for the fast reconstruction of high-dimensional functions having only low dimensional variable interactions. Compactly supported periodic Chui-…
On regularized Shannon sampling formulas with localized sampling
Melanie Kircheis, Daniel Potts, Manfred Tasche
In this paper we present new regularized Shannon sampling formulas which use localized sampling with special window functions, namely Gaussian, B-spline, and sinh-type window funct…
Nonequispaced Fast Fourier Transform Boost for the Sinkhorn Algorithm
Rajmadan Lakshmanan, Alois Pichler, Daniel Potts
This contribution features an accelerated computation of the Sinkhorn's algorithm, which approximates the Wasserstein transportation distance, by employing nonequispaced fast Fouri…
Interpretable transformed ANOVA approximation on the example of the prevention of forest fires
Daniel Potts, Michael Schmischke
The distribution of data points is a key component in machine learning. In most cases, one uses min-max normalization to obtain nodes in or Z-score normalization for standa…
The uniform sparse FFT with application to PDEs with random coefficients
Lutz Kämmerer, Daniel Potts, Fabian Taubert
We develop the uniform sparse Fast Fourier Transform (usFFT), an efficient, non-intrusive, adaptive algorithm for the solution of elliptic partial differential equations with rando…
Fast Hyperbolic Wavelet Regression meets ANOVA
Laura Lippert, Daniel Potts, Tino Ullrich
We use hyperbolic wavelet regression for the fast reconstruction of high-dimensional functions having only low dimensional variable interactions. Compactly supported periodic Chui-…
Nonuniform fast Fourier transforms with nonequispaced spatial and frequency data and fast sinc transforms
Melanie Kircheis, Daniel Potts, Manfred Tasche
In this paper we study the nonuniform fast Fourier transform with nonequispaced spatial and frequency data (NNFFT) and the fast sinc transform as its application. The computation o…
Interpretable Approximation of High-Dimensional Data
Daniel Potts, Michael Schmischke
In this paper we apply the previously introduced approximation method based on the ANOVA (analysis of variance) decomposition and Grouped Transformations to synthetic and real data…
A note on transformed Fourier systems for the approximation of non-periodic signals
Robert Nasdala, Daniel Potts
A variety of techniques have been developed for the approximation of non-periodic functions. In particular, there are approximation techniques based on rank- lattices and transf…
Grouped Transformations and Regularization in High-Dimensional Explainable ANOVA Approximation
Felix Bartel, Daniel Potts, Michael Schmischke
In this paper we propose a tool for high-dimensional approximation based on trigonometric polynomials where we allow only low-dimensional interactions of variables. In a general hi…
Continuous window functions for NFFT
Daniel Potts, Manfred Tasche
In this paper, we study the error behavior of the nonequispaced fast Fourier transform (NFFT). This approximate algorithm is mainly based on the convenient choice of a compactly su…
Uniform error estimates for nonequispaced fast Fourier transforms
Daniel Potts, Manfred Tasche
In this paper, we study the error behavior of the nonequispaced fast Fourier transform (NFFT). This approximate algorithm is mainly based on the convenient choice of a compactly su…
Learning multivariate functions with low-dimensional structures using polynomial bases
Daniel Potts, Michael Schmischke
In this paper we propose a method for the approximation of high-dimensional functions over finite intervals with respect to complete orthonormal systems of polynomials. An importan…
Efficient multivariate approximation on the cube
Robert Nasdala, Daniel Potts
We combine a periodization strategy for weighted -integrands with efficient approximation methods in order to approximate multivariate non-periodic functions on the high-dim…
Approximation of high-dimensional periodic functions with Fourier-based methods
Daniel Potts, Michael Schmischke
In this paper we propose an approximation method for high-dimensional -periodic functions based on the multivariate ANOVA decomposition. We provide an analysis on the classical…
Fast Cross-validation in Harmonic Approximation
Felix Bartel, Ralf Hielscher, Daniel Potts
Finding a good regularization parameter for Tikhonov regularization problems is a though yet often asked question. One approach is to use leave-one-out cross-validation scores to i…