Bart M.N. Smets

Applied Mathematician

Eindhoven University of Technology


I am a PhD student in applied mathematics at the TU Eindhoven under the supervision of dr.ir. R. Duits. I have a keen interest in both abstract mathematics and new techniques in the field of machine learning.

In my research I try to bridge neural networks with classic mathematical ideas from geometry and analysis, such as in the PDE-based G-CNN paper. Implementations of techniques I have developed are available as an open source extension to the popular PyTorch deep learning framework, named LieTorch.


  • Differential Geometry
  • Mathematical Image Analysis
  • Probability Theory
  • Machine Learning
  • Applied Analysis
  • Motorsport
  • History


  • MSc in Applied Mathematics, 2019

    TU Eindhoven

  • BSc in Applied Mathematics, 2017

    TU Eindhoven


Geodesic Tracking of Retinal Vascular Trees with Optical and TV-Flow Enhancement in SE(2)

Retinal images are often used to examine the vascular system in a non-invasive way. Studying the behavior of the vasculature on the …

Analysis of (sub-)Riemannian PDE-G-CNNs

Group equivariant convolutional neural networks (G-CNNs) have been successfully applied in geometric deep learning. Typically, G-CNNs …

Geodesic Tracking via New Data-driven Connections of Cartan Type for Vascular Tree Tracking

We introduce a data-driven version of the plus Cartan connection on the 3D homogeneous space $\mathbb{M}_2$ of 2D positions and …

PDE-based Group Equivariant Convolutional Neural Networks

We present a PDE-based framework that generalizes Group equivariant Convolutional Neural Networks (G-CNNs). In this framework, a …

Total Variation and Mean Curvature PDEs on the Homogeneous Space of Positions and Orientations (JMIV)

Two key ideas have greatly improved techniques for image enhancement and denoising: the lifting of image data to multi-orientation …


PDE-based CNNs with Morphological Convolutions

Convolutional neural networks have found wide adoption and great success in image processing yet have drawbacks such as needing huge …