# Matthieu Darcy

## PhD student in Computing and Mathematical Sciences

## California Institute of Technology

I am a third year PhD student in the Computing and Mathematical Sciences Department at Caltech, working under the supervision of Houman Owhadi. I am broadly interested in scientific machine learning, specifically in the applications of Gaussian processes, kernel methods, and wavelets to the inference and predictions of stochastic (partial) differential equations and dynamical systems.

My current research includes

Inference of Stochastic Differential Equations.

Numerical Methods for Stochastic Partial Differential Equations.

Operator Learning for non-linear PDEs and integro-differential functional equations.

Learning Dynamical Systems.

## Recent news:

My paper on kernel methods for operator learning is now out in the Journal of Computational Physics. Read it here: https://authors.elsevier.com/a/1i2RS508HwOFl

I gave a talk on "Kernel methods are competitive for Operator Learning" at the 10th International Congress on Industrial and Applied Mathematics - August 22nd 2023 (slides).

I gave a talk on kernel methods for operator learning at the Argonne National Lab LANS Seminar - August 2nd 2023 (slides).

I gave a talk on kernel methods for learnings SDEs at the SIAM conference on dynamical systems - May 18th 2023 (slides).

My new paper on kernel methods for operator learning is now available: https://arxiv.org/abs/2304.13202 - April 27th 2023.

I gave a talk on "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) .

I gave a talk in the DataSig Rough Path Interest Group on "Kernel methods are competitive for Operator Learning" - March 28th 2023

I gave a presentation on learning stochastic differential equations at the SIAM CSE 2023 in Amsterdam, Netherlands- February 28th 2023 (slides).

My paper on "One-shot learning of stochastic differential equations with data adapted kernels" was accepted in Physica D - November 2023.