18 citations · 23 across the 4 of their papers we have counts for
4 papers
Discovery of slow variables in a class of multiscale stochastic systems via neural networks
Przemyslaw Zielinski, Jan S. Hesthaven
Finding a reduction of complex, high-dimensional dynamics to its essential, low-dimensional "heart" remains a challenging yet necessary prerequisite for designing efficient numeric…
A micro-macro acceleration method for the Monte Carlo simulation of stochastic differential equations
Kristian Debrabant, Giovanni Samaey, Przemysław Zieliński
We present and analyse a micro-macro acceleration method for the Monte Carlo simulation of stochastic differential equations with separation between the (fast) time-scale of indivi…
Spectral and topological methods in the study of solvability of semilinear equations in Hilbert spaces
Przemysław Zieliński
The main goal of this dissertation is to find conditions which will guarantee the existence of solutions in the Hilbert space of semilinear equation \[ L u+N(u)=h \] where …
Solvability of semilinear equations with zero on the boundary of spectral gap and applications to nonlinear Schrödinger equation
Przemysław Zieliński
We study the existence of solutions in Hilbert space of the semilinear equation \[ L u+N(u)=h, \] where is linear self-adjoint, is a nonlinear operator and . We…