Operator learning | Matthieu Darcy

I study methods for learning maps between infinite-dimensional function spaces, such as the solution operators of PDEs. These models serve as fast surrogates for expensive simulations in engineering and the sciences, from design and uncertainty quantification to many-query and real-time settings.

Relevant research

Kernel Methods are Competitive for Operator Learning

P. Batlle, M. Darcy, B. Hosseini, and 1 more author

Journal of Computational Physics, 2024

arXiv Bib HTML

@article{batlle2024kernel,
  title = {Kernel Methods are Competitive for Operator Learning},
  author = {Batlle, P. and Darcy, M. and Hosseini, B. and Owhadi, H.},
  journal = {Journal of Computational Physics},
  volume = {496},
  pages = {112549},
  year = {2024},
}

Tutorial: Kernels and FNO for operator learning

Gaussian processes and Fourier neural operators applied to Burgers' equation and to an elliptic coefficient-to-solution map.

Code Slides

Operator Learning at Machine Precision

A. Bacho, A. Sorokin, X. Yang, and 6 more authors

Journal of Computational Physics, 2026

DOI arXiv Bib

@article{bacho2025machine,
  title = {Operator Learning at Machine Precision},
  author = {Bacho, A. and Sorokin, A. and Yang, X. and Bourdais, T. and Calvello, E. and Darcy, M. and Hsu, A. and Hosseini, B. and Owhadi, H.},
  journal = {Journal of Computational Physics},
  volume = {566},
  pages = {115240},
  year = {2026},
  doi = {10.1016/j.jcp.2026.115240},
}