Seminar: Nonlinear and high-dimensional approximation (WS 2026/2027)

Prof. Dr. Markus Bachmayr


Event
Time
Location
SWS
Seminar
Thu, 16:30 - 18:00 Office West (3210 | 377) 2 SWS


News and information

The first meeting including the discussion of topics takes place on October 15 at 16:30, seminar room 377 at Office West.


Topics

In this seminar, we will discuss recent literature and ongoing research on numerical approximation methods for high-dimensional functions, in particular for partial differential equations on high-dimensional domains. For this semester, the main topic will be special numerical techniques that can be used in computer-assisted proofs, including their application to nonlinear approximation methods:

  • Basics of validated numerical analysis
  • Applications to the analysis of dynamical systems
  • Singularities and (non)uniqueness in nonlinear PDEs
  • Spectral geometry and shape optimization
  • Optimal configurations and designs
  • Validation for neural networks
  • Formal verification and software


Registration, organization and credits

The seminar will accommodate talks both by MSc students and by PhD students and postdoctoral researchers. The talks by MSc students will take place at the end of the semester.

If you are interested in participating in the seminar as an MSc student, please contact Prof. Bachmayr directly. Registration is via RWTHonline. If you register for the seminar you will automatically get access to the course room in RWTHmoodle. Further information (including on the first meeting in the first week of the semester) will be provided there.



Literature

Some selected works:

  • Warwick Tucker. Validated Numerics. Princeton University Press, 2011.
  • Warwick Tucker. A Rigorous ODE Solver and Smale’s 14th Problem. Foundations of Computational Mathematics, 2002.
  • Thomas Hales et al. A proof of the Kepler conjecture, Annals of Mathematics, 2005.
  • Joel Dahne, Javier Gómez-Serrano, Joana Pech-Alberich. Monotonicity of the first Dirichlet eigenvalue of regular polygons, arXiv:2601.16285
  • Maxime Breden. A posteriori validation of generalized polynomial chaos expansions, SIAM Journal on Applied Dynamical Systems, 2023.
  • Kai Jia and Martin Rinard. Exploiting verified neural networks via floating point numerical error, SAS 2021.
  • Can Zhou et al. A domain-theoretic framework for robustness analysis of neural networks, Mathematical Structures in Computer Science, 2023.