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:
I gave a talk at SIAM Uncertainty Quantification 2024 on kernel methods for rough partial differential equations (slides).
I gave a talk at the International Conference: Differential Equations for Data Science on the inference of SDEs with kernel methods (slides)
My paper "Kernel methods are competitive for operator learning" is now out in the Journal of Computational Physics.
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).
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 in the DataSig Rough Path Interest Group on "Kernel methods are competitive for Operator Learning" - March 28th 2023
My paper on "One-shot learning of stochastic differential equations with data adapted kernels" was accepted in Physica D - November 2023.
