Estimating the Topology of Low-Dimensional Data Using Deep Neural Networks

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This project will expand on the superhuman visual capabilities of deep neural networks to allow us to analyse the topology of 3- and 4-dimensional manifolds. While these spaces still count as low-dimensional, 4-dimensional manifolds typically are beyond human visual comprehension. The topology of a manifold describes its essential properties such as the number of connected components, holes, tunnels and cavities of various dimensions. Traditional methods from computational topology fail in large practical applications due to computational restrictions. We propose an approximation that overcomes previous limitations and can open new doors to data analysis in material science, medical imaging, dynamical systems and other applications.