Matthieu Darcy

I am a fourth 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 learning and predicting stochastic (partial) differential equations and stochastic time-series. 

My current research includes

• Inference and Numerical Methods for Stochastic (Partial) Differential Equations.

• Operator Learning.

• Learning Dynamical Systems.

• Generative models for multiscale systems.

CV

Recent news:

• I gave a talk on solving rough PDEs with kernels and neural networks at the Early Career Pioneers in Uncertainty Quantification and AI for Science workshop (Isaac Newton Institute, University of Cambridge).

• I gave a talk on operator learning at  the Mathematical foundations of digital twins worksop (Centre International de Rencontres Mathématiques, Marseille) (slides).

• I gave a talk on "Solving Roughly Forced Nonlinear PDEs via Misspecified Kernel Methods and Neural Networks" at the IMSI (University of Chicago) Workshop on Kernel Methods in Uncertainty Quantification and Experimental Design and at DEDS Kyoto (slides).

• I gave a talk on Kernel methods for operator learning at SIAM Mathematics of Data Science.

• Our new preprint on "Solving Roughly Forced Nonlinear PDEs via Misspecified Kernel Methods and Neural Networks" is now available on the ArXiv.

• I gave a talk at CIRM ( in Marseille) and SciCADE (at NUS) on kernel methods and PINNS for rough partial differential equations (slides).

• 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)

• Our paper "Kernel methods are competitive for operator learning" is now out in the Journal of Computational Physics.