30 citations · 30 across the 4 of their papers we have counts for
5 papers
Solving Functional PDEs with Gaussian Processes and Applications to Functional Renormalization Group Equations
Xianjin Yang, Matthieu Darcy, Matthew Hudes +3
We present an operator learning framework for solving non-perturbative functional renormalization group equations, which are integro-differential equations defined on functionals.…
Operator Learning at Machine Precision
Aras Bacho, Aleksei G. Sorokin, Xianjin Yang +6
Neural operator learning methods have garnered significant attention in scientific computing for their ability to approximate infinite-dimensional operators. However, increasing th…
Solving Roughly Forced Nonlinear PDEs via Misspecified Kernel Methods and Neural Networks
Ricardo Baptista, Edoardo Calvello, Matthieu Darcy +3
We consider the use of Gaussian Processes (GPs) or Neural Networks (NNs) to numerically approximate the solutions to nonlinear partial differential equations (PDEs) with rough forc…
Kernel Methods are Competitive for Operator Learning
Pau Batlle, Matthieu Darcy, Bamdad Hosseini +1
We present a general kernel-based framework for learning operators between Banach spaces along with a priori error analysis and comprehensive numerical comparisons with popular neu…
One-Shot Learning of Stochastic Differential Equations with Data Adapted Kernels
Matthieu Darcy, Boumediene Hamzi, Giulia Livieri +2
We consider the problem of learning Stochastic Differential Equations of the form from one sample trajectory. This problem is more challenging than le…