Research

My research lies at the intersection of dynamical systems, approximation theory, machine learning and control theory.

Journal Articles

• Analysis of the Geometric Structure of Neural Networks and Neural ODEs via Morse Functions
  Christian Kuehn, Sara-Viola Kuntz
  Advances in Computational Mathematics 52(9), 2026 (arXiv)

• Geometric Blow-Up for Folded Limit Cycle Manifolds in Three Time-Scale Systems
  Samuel Jelbart, Christian Kuehn, Sara-Viola Kuntz
  Journal of Nonlinear Science 34(17), 2024 (arXiv)

Book Chapters

• A Dynamical Systems Perspective on the Analysis of Neural Networks
  Dennis Chemnitz, Maximilian Engel, Christian Kuehn, Sara-Viola Kuntz
  In: Bülte et al. (eds.), Theoretical Foundations of Deep Learning, Springer, to appear 2027 (arXiv)

Preprints

• Universal Approximation Constraints of Narrow ResNets: The Tunnel Effect
  Christian Kuehn, Sara-Viola Kuntz, Tobias Wöhrer
  arXiv:2603.28591, 2026

• The Influence of the Memory Capacity of Neural DDEs on the Universal Approximation Property
  Christian Kuehn, Sara-Viola Kuntz
  arXiv:2505.07244, 2025

• Embedding Capabilities of Neural ODEs
  Christian Kuehn, Sara-Viola Kuntz
  arXiv:2308.01213, 2023

Blog Posts

• DeepNets: Dynamics of Deep Neural Networks
  MDSI Science Blog, Munich Data Science Institute, 2025