CHONKNORIS: Operator Learning at Machine Precision

Python code for the paper "Operator learning at machine precision" implementing the CHONKNORIS method (Cholesky Newton--Kantorovich Neural Operator Residual Iterative System).

@article{BACHO2026CHONKNORIS,
  title = {Operator learning at machine precision},
  journal = {Journal of Computational Physics},
  volume = {566},
  pages = {115240},
  year = {2026},
  issn = {0021-9991},
  doi = {https://doi.org/10.1016/j.jcp.2026.115240},
  url = {https://www.sciencedirect.com/science/article/pii/S0021999126005917},
  author = {Aras Bacho and Aleksei G. Sorokin and Xianjin Yang and Théo Bourdais and Edoardo Calvello and Matthieu Darcy and Alexander W. Hsu and Bamdad Hosseini and Houman Owhadi},
  keywords = {Operator learning, Scientific machine learning, Digital Twins Modeling, Newton-kantorovich method, Forward and inverse problems},
}

Installation

Run the following command to install all packages necessary to run files in this repo.

pip install -e .

Main Directory Structure

• forward_problems
  • burgers_1d
  • darcy_2d
  • elliptic_1d
• foundation_modeling_FONKNORIS foundation modeling with CHONKNORIS
• inverse_problems
  • Calderon
  • full_waveform_inversion
  • inverse_scattering
• paper_plots
  • forward_problems
  • inverse_problems
• classic_operator_learning_gp_benchmarks
  • FNO_TNO: Fourier Neural Operators (FNOs) and Transformer Neural Operators (TNOs)
  • GP: Gaussian processes (GPs)
• chonknoris: utilities for running problems

Accessing Pre-generated Datasets and Models

Various datasets and models are stored when running the different problems. As some of these computations are quite expensive, pre-generated datasets and models are available upon requests to the lead author of the problem, see above.