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 Roughly Forced Nonlinear PDEs via Misspecified Kernel Methods and Neural Networks" at the IMSI 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. 

• 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 in the DataSig Rough Path Interest Group on "Kernel methods are competitive for Operator Learning" - March 28th 2023.

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