5 papers
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…
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…
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…
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…
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…