Natural gradients and kernel methods for Physics Informed Neural Networks (PINNs)

This dissertation addresses limitations in Physics-Informed Neural Networks (PINNs) through two complementary approaches. Algorithmically, it develops improved training schemes combining kernel methods and natural gradients. Theoretically, it grounds PINNs in rigorous mathematics using Reproducing Kernel Hilbert Spaces (RKHS) and spectral analysis.

Supervisor: Cyril Furtlehner (TAU Team, INRIA Saclay – A&O–LISN–Paris-Saclay University–CNRS)

Download PDF

BibTeX:

@PHDTHESIS{schwe2025,
  url = "https://theses.fr/2025UPASG087",
  title = "Natural gradients and kernel methods for Physics Informed Neural Networks (PINNs)",
  author = "Schwencke, Nilo",
  year = "2025",
  doi = {https://doi.org/10.70675/3e34b77bz4f26z4c40z9839z8333757a7300},
  note = "Thèse de doctorat dirigée par Furtlehner, Cyril Informatique université Paris-Saclay 2025",
  url = "https://theses.fr/2025UPASG087/document",
}

Recommended citation: Nilo Schwencke, "Natural gradients and kernel methods for Physics Informed Neural Networks (PINNs)." PhD thesis, Université Paris-Saclay, 2025.
Download Paper