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Bart M.N. Smets

Applied Mathematician

Eindhoven University of Technology

Biography

I am a postdoctoral researcher in applied mathematics at the TU Eindhoven in the Geometric Learning and Differential Geometry group of dr.ir. R. Duits. I have a keen interest in both abstract mathematics and its application to new techniques in machine learning and image processing.

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.

Interests

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

Education

  • PhD in Applied Mathematics, 2024

    TU Eindhoven

  • MSc in Applied Mathematics, 2019

    TU Eindhoven

  • BSc in Applied Mathematics, 2017

    TU Eindhoven

Publications

Roto-Translation Invariant Metrics on Position-Orientation Space

Riemannian metrics on the position-orientation space M(3) that are roto-translation group SE(3) invariant play a key role in image …
Preprint DOI

Universal Collection of Euclidean Invariants between Pairs of Position-Orientations

Euclidean E(3) equivariant neural networks that employ scalar fields on position-orientation space M(3) have been effectively applied …
Preprint DOI

Flow Matching on Lie Groups

Flow Matching (FM) is a recent generative modelling technique: we aim to learn how to sample from distribution 𝔛1 by flowing samples …
Preprint DOI

PDE-CNNs: Axiomatic Derivations and Applications

PDE-based group convolutional neural networks (PDE-G-CNNs) use solvers of evolution PDEs as substitutes for the conventional components …
PDF Project DOI Journal for Mathematical Imaging and Vision

Partial Differential Equations in Deep Learning & Image Processing

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Talks

Geometric Invariants on Position-Orientation Space with Application in Equivariant Machine Learning

We present an overview of the use of geometric invariants in designing Euclidean-invariant neural networks for predicting scalar …
Apr 16, 2025 16:20 Conferentiecentrum Eindhoven
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Geometric Learning with Lie Groups and PDEs

We present an overview of geometric learning in the context of Lie groups with the aid of PDEs.
Feb 5, 2025 09:20 Philipps Universität Marburg
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An Introduction to Transformers

I present an overview of the ’transformer’ neural network architecture and how it interacts with text and image modalities.
Apr 26, 2024 16:20 TU/e
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