9 citations · 10 across the 9 of their papers we have counts for
9 papers · 1 filter
Rational neural networks for tracking complex singularities of nonlinear PDEs
Nadiia Derevianko, Hans-Joachim Bungartz, Felix Dietrich
We present a neural network-based method for numerical analytic continuation of solutions of nonlinear partial differential equations (PDEs) and detection of their complex singular…
Neural network-based singularity detection and applications
Nadiia Derevianko, Ioannis G. Kevrekidis, Felix Dietrich
We present a method for constructing a special type of shallow neural network that learns univariate meromorphic functions with pole-type singularities. Our method is based on usin…
Parameter estimation for multivariate exponential sums via iterative rational approximation
Nadiia Derevianko, Lennart Aljoscha Hübner
We present two new methods for multivariate exponential analysis. In [7], we developed a new algorithm for reconstruction of univariate exponential sums by exploiting the rational…
Recovery of rational functions via Hankel pencil method and sensitivities of the poles
Nadiia Derevianko
In this paper, we introduce a new approach for the recovery of rational functions. The concept we propose is based on using the exponential structure of the Fourier coefficients of…
Differential approximation of the Gaussian by short cosine sums with exponential error decay
Nadiia Derevianko, Gerlind Plonka
In this paper, we propose a method to approximate the Gaussian function on by a short cosine sum. We generalise and extend the differential approximation method propo…
ESPRIT versus ESPIRA for reconstruction of short cosine sums and its application
Nadiia Derevianko, Gerlind Plonka, Raha Razavi
In this paper we introduce two new algorithms for stable approximation with and recovery of short cosine sums. The used signal model contains cosine terms with arbitrary real posit…
From ESPRIT to ESPIRA: Estimation of Signal Parameters by Iterative Rational Approximation
Nadiia Derevianko, Gerlind Plonka, Markus Petz
We introduce a new method for Estimation of Signal Parameters based on Iterative Rational Approximation (ESPIRA) for sparse exponential sums. Our algorithm uses the AAA algorithm f…
Exact Reconstruction of Extended Exponential Sums using Rational Approximation of their Fourier Coefficients
Nadiia Derevianko, Gerlind Plonka
In this paper we derive a new recovery procedure for the reconstruction of extended exponential sums of the form $y(t) = \sum_{j=1}^{M} \left( \sum_{m=0}^{n_j} \, γ_{j,m} \, t^{m}…
Exact Reconstruction of Sparse Non-Harmonic Signals from Fourier Coefficients
Markus Petz, Gerlind Plonka, Nadiia Derevianko
In this paper, we derive a new reconstruction method for real non-harmonic Fourier sums, i.e., real signals which can be represented as sparse exponential sums of the form $f(t) =…