output
19992022
most citedSolving high-dimensional partial differential equations using deep learning

1.8k citations

researchers with a paper here

Counting papers with at most 25 authors, so collaboration author lists do not stand in for the people here.

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5 papers · 1 filter

math.FA2022★ 3 cited

On the connection between uniqueness from samples and stability in Gabor phase retrieval

Rima Alaifari, Francesca Bartolucci, Stefan Steinerberger +1

Gabor phase retrieval is the problem of reconstructing a signal from only the magnitudes of its Gabor transform. Previous findings suggest a possible link between unique solvabilit…

math.FA2020★ 21 cited

Phase retrieval from sampled Gabor transform magnitudes: Counterexamples

Rima Alaifari, Matthias Wellershoff

We consider the recovery of square-integrable signals from discrete, equidistant samples of their Gabor transform magnitude and show that, in general, signals can not be recovered…

math.FA2020★ 14 cited

Phase retrieval of bandlimited functions for the wavelet transform

Rima Alaifari, Francesca Bartolucci, Matthias Wellershoff

We study the recovery of square-integrable signals from the absolute values of their wavelet transforms, also called wavelet phase retrieval. We present a new uniqueness result for…

math.FA2018★ 97 cited

DNN Expression Rate Analysis of High-dimensional PDEs: Application to Option Pricing

Dennis Elbrächter, Philipp Grohs, Arnulf Jentzen +1

We analyze approximation rates by deep ReLU networks of a class of multi-variate solutions of Kolmogorov equations which arise in option pricing. Key technical devices are deep ReL…

math.FA2009★ 4 cited

Continuous Shearlet Frames and Resolution of the Wavefront Set

Philipp Grohs

In recent years directional multiscale transformations like the curvelet- or shearlet transformation have gained considerable attention. The reason for this is that these transform…