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math.NA2026
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…
math.NA2024
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-…
math.NA2024
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…