Matthieu Darcy

New York, NY

I am a machine learning research scientist at the Basis Research Institute in New York.

I obtained my PhD in Computing and Mathematical Sciences from Caltech, where I was advised by Houman Owhadi.

CV · Google Scholar

Research areas

Dynamical Systems

Simulation, learning and control in dynamical systems.

SDEsKernel FlowsData Assimilation

Input and output fields of a learned operator

Operator Learning

Learning maps between infinite-dimensional spaces.

Gaussian ProcessesKernel MethodsNeural Operators

Predicted solution of a roughly forced PDE, as a surface and a heatmap

PDEs & Numerical Analysis

Principled algorithms for PDEs with rough forcing or in infinite dimensions.

Rough PDEsKernel SolversError Analysis

news

Nov 10, 2026	We released Dynestyx, an open-source probabilistic programming library for dynamical systems. Read the blog post and the documentation.
Nov 03, 2026	I gave a talk on Dynestyx at the workshop Mathematical and Computational Foundations of Digital Twins at the Institut d’Études Scientifiques de Cargèse (IESC) (slides).
Jul 01, 2026	I joined the Basis Research Institute as a Machine Learning Research Scientist.
May 05, 2026	I successfully defended my PhD thesis.
Mar 24, 2026	I gave a talk “Gaussian Processes for Operator Learning: from Surrogates to Machine Precision” at SIAM UQ 2026.
Feb 17, 2026	I gave a talk on machine learning for partial differential equations and operator learning in Youssef Marzouk’s group at MIT.
Feb 15, 2026	Our paper on solving rough PDEs was accepted in AMS Mathematics of Computation.
Jan 20, 2026	I gave a talk and a tutorial on operator learning at the Institute of Mathematical Statistics and Actuarial Science at the University of Bern, hosted by Prof. David Ginsbourger.
Jan 08, 2026	I gave a talk on machine learning for partial differential equations and operator learning at PLATON - INRIA and Polytechnique, hosted by Pietro Congedo and Olivier Le Maître.

selected publications

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},
}

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},
}

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},
}

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},
}