194 citations · 637 across the 38 of their papers we have counts for
42 papers
Topological Characteristics for the Analysis of Vector Fields. New stable characteristics for discrete and continuous dynamical systems
Marta Marszewska, Justyna Signerska, Paweł Dłotko
The qualitative analysis of nonlinear dynamical systems relies on identifying geometric and topological structures that govern phase-space organization. We develop a computational…
Transferable 3D Convolutional Neural Networks for Elastic Constants Prediction in Nanoporous Metals
Sergei Zorkaltsev, Rafał Topolnicki, Tal-El Carmon +4
The topology of nanoporous metals is crucial for determining their mechanical response. In this work, we generated 6,000 gold and 422 silver nanoporous structures and calculated th…
Physics-informed convolutional neural networks for fluid flow through porous media
Rafał Topolnicki, Paweł Dłotko, Maciej Matyka
Accurate simulation of fluid flow in porous media is challenging due to complex pore-space geometries and the computational cost of solving the Navier-Stokes equations. This diffic…
Topological cell-openness index for porous materials
Michał Bogdan, Paweł Dłotko
We propose a method of estimating and parametrising the proportion of open and closed cells in a porous material based on measuring Betti numbers on the structures. We define a cel…
Direction-aware topological descriptors for elastic stiffness tensor prediction in porous materials
Rafał Topolnicki, Michał Bogdan, Jakub Malinowski +3
Classical topological descriptors used in topological data analysis (TDA) are invariant under permutations of spatial axes and therefore cannot represent the loading direction, whi…
Understanding the geometry of deep learning with decision boundary volume
Matthew Burfitt, Jacek Brodzki, Pawel Dłotko
For classification tasks, the performance of a deep neural network is determined by the structure of its decision boundary, whose geometry directly affects essential properties of…