Publications

2026

1. 

   Solving Roughly Forced Nonlinear PDEs via Misspecified Kernel Methods and Neural Networks

   R. Baptista, E. Calvello, M. Darcy, and 3 more authors

   Mathematics of Computation, 2026

   DOI arXiv Bib

   @article{baptista2026rough,
     title = {Solving Roughly Forced Nonlinear {PDEs} via Misspecified Kernel Methods and Neural Networks},
     author = {Baptista, R. and Calvello, E. and Darcy, M. and Owhadi, H. and Stuart, A. M. and Yang, X.},
     journal = {Mathematics of Computation},
     year = {2026},
     doi = {10.1090/mcom/4219},
   }

2. 

   Solving Functional PDEs with Gaussian Processes and Applications to Functional Renormalization Group Equations

   X. Yang, M. Darcy, M. Hudes, and 3 more authors

   Journal of Computational Physics, 2026

   DOI arXiv Bib

   @article{yang2025functional,
     title = {Solving Functional {PDEs} with {G}aussian Processes and Applications to Functional Renormalization Group Equations},
     author = {Yang, X. and Darcy, M. and Hudes, M. and Alexander, F. J. and Eyink, G. and Owhadi, H.},
     journal = {Journal of Computational Physics},
     volume = {563},
     pages = {115085},
     year = {2026},
     doi = {10.1016/j.jcp.2026.115085},
   }

3. 

   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},
   }

2025

1. Benchmarking Gaussian Processes for Prediction and Data Assimilation of Alzheimer’s Disease Progression

   P. Batlle, M. Darcy, M. Levine, and 6 more authors

   Journal of Alzheimer’s Disease, 2025

   DOI Bib

   @article{batlle2025alzheimer,
     title = {Benchmarking {G}aussian Processes for Prediction and Data Assimilation of {A}lzheimer's Disease Progression},
     author = {Batlle, P. and Darcy, M. and Levine, M. and Hamzi, B. and Owhadi, H. and Bastani, M. and Zhang, Y. and Sarsour, K. and Talamas, F.},
     journal = {Journal of Alzheimer's Disease},
     volume = {109},
     pages = {1137--1141},
     year = {2025},
     doi = {10.1177/13872877251404082},
   }

2. 

   Learning Dynamical Systems from Data: A Simple Cross-Validation Perspective, Part II: Nonparametric Kernel Flows

   M. Darcy, B. Hamzi, J. Susiluoto, and 2 more authors

   Physica D: Nonlinear Phenomena, 2025

   Bib HTML

   @article{darcy2025kernelflows,
     title = {Learning Dynamical Systems from Data: A Simple Cross-Validation Perspective, Part {II}: Nonparametric Kernel Flows},
     author = {Darcy, M. and Hamzi, B. and Susiluoto, J. and Braverman, A. and Owhadi, H.},
     journal = {Physica D: Nonlinear Phenomena},
     volume = {476},
     pages = {134641},
     year = {2025},
   }

2024

1. 

   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},
   }

2023

1. 

   One-Shot Learning of Stochastic Differential Equations with Data Adapted Kernels

   M. Darcy, B. Hamzi, G. Livieri, and 2 more authors

   Physica D: Nonlinear Phenomena, 2023

   DOI arXiv Bib

   @article{darcy2023oneshot,
     title = {One-Shot Learning of Stochastic Differential Equations with Data Adapted Kernels},
     author = {Darcy, M. and Hamzi, B. and Livieri, G. and Owhadi, H. and Tavallali, P.},
     journal = {Physica D: Nonlinear Phenomena},
     volume = {444},
     pages = {133583},
     year = {2023},
     doi = {10.1016/j.physd.2022.133583},
   }