Research

Bold indicates first author contribution.

Publications

• Batlle, P., Darcy, M., Hosseini, B., & Owhadi, H. (2023). Kernel Methods are Competitive for Operator Learning (Journal, Arxiv)

• Darcy, M., Hamzi, B., Livieri, G., Owhadi, H., & Tavallali, P. (2023). One-shot learning of stochastic differential equations with data adapted kernels. Physica D: Nonlinear Phenomena, 444, 133583. (Journal, Arxiv).

• M. Darcy, B.Hamzi, J. Susiluoto, A. Braverman, H. Owhadi. (2021). Learning dynamical systems from data: a simple cross-validation perspective, part II: nonparametric kernel flows.  Physica D: Nonlinear Phenomena, Volume 476, 2025. (Journal).

Preprints

• R. Baptista, E. Calvello, M. Darcy, H. Owhadi, A. M. Stuart, and X. Yang, Solving roughly forced nonlinear PDEs via misspecified kernel methods and neural networks, 2025. arXiv: 2501.17110.

Talks and presentations

• Talk: "Solving Roughly Forced Nonlinear PDEs via Misspecified Kernel Methods and Neural Networks" Workshop on Kernel Methods in Uncertainty Quantification and Experimental Design at the Institute for Mathematical and Statistical Innovation (IMSI) - April 3rd 2025.

• Talk: "Solving Roughly Forced Nonlinear PDEs via Misspecified Kernel Methods and Neural Networks" SIAM Conference on Computational Science and Engineering - March 7th, 2025

• Poster: "Solving Roughly Forced Nonlinear PDEs via Misspecified Kernel Methods and Neural Networks" Workshop on Dynamical Systems and Machine Learning, Tokyo - February 17th, 2025.

• Talk: "Solving Roughly Forced Nonlinear PDEs via Misspecified Kernel Methods and Neural Networks" - Workshop on Differential Equations for Data Science, Kyoto - February 11th, 2025.

• Talk: "Kernel methods are competitive for operator learning" SIAM Mathematics of Data Science - October 24th, 2024.

• Talk: "Kernel methods and PINNs for rough partial differential equations"  Digital Twins for inverse problems in Earth sciences (CIRM) - July 22nd, 2024.

• Talk: "Kernel methods and PINNs for rough partial differential equations" SciCADE, National University of Singapore, Singapore, July 15th, 2024. 

• Talk: Research overview, Franca Hoffman group meeting - May 31st, 2024.

• Talk: "Kernel methods for rough partial differential equations" Southern California Applied Mathematics Workshop, UC San Diego, USA, April 27th 2024. 

• Talk: "Kernel methods for rough partial differential equations"  SIAM Material sciences - May 20th, 2024. 

• Talk: "Kernel methods for rough partial differential equations" SIAM Uncertainty Quantification 2024 - March 1st 2024 (slides).

• Talk: "One shot learning of SDEs with Gaussian processes" at the International Conference: Differential Equations for Data Science - February 22nd 2024 (slides).

• Talk “Kernel methods for operator learning” at the One World Mathematics of Machine Learning seminar (online), October 18th, 2023 (watch).

• Talk: “Kernel Methods are Competitive for Operator Learning” at the 2nd IACM Mechanistic Machine Learning and Digital Engineering for Computational Science Engineering and Technology, University of El Paso, Texas, USA - September 23rd 2023.  

• Talk: "Kernel Methods are Competitive for Operator Learning" at 10th International Congress on Industrial and Applied Mathematics - August 22nd 2023 (slides).

• Talk: "Kernel Methods are Competitive for Operator Learning" at the Argonne  National Lab LANS Seminar - August 2nd 2023 (slides).

• Talk: "One Shot Learning of Stochastic Differential Equations with Gaussian Processes" at the SIAM conference on the Application of Dynamical Systems- May 18th 2023 (slides). 

• Talk: "Kernel methods are competitive for Operator Learning", DataSig Rough Path Interest Group (online)- May 11th 2023.

• Talk: "Benchmarking Operator Learning with Simple and interpretable Kernel Methods" at the Workshop on Establishing Benchmarks for Data-Driven Modeling of Physical System - April 6th, 2023 (slides).

• Talk:  "One shot learning of stochastic differential equations with Gaussian Processes" - SIAM Computational Sciences and Engineering, Amsterdam - March 6th, 2023.

• Poster - "One shot learning of stochastic differential equations with Gaussian Processes" - Third Symposium on Dynamical Systems and Machine Learning 2022, Fields Institute, Toronto, CA (poster).

• Talk - "One shot learning of stochastic differential equations with Gaussian processes and computational graph completion" - ICCOPT 2022, Lehigh, PA, USA (slides).

• Talk - "Kernel Flows Demystified: Application to Regression" - Second Symposium on Dynamical Systems and Machine Learning 2020, Fields Institute, Toronto, CA (watch).

mdarcy@ caltech.edu