7 citations · 8 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…
Bilevel optimization for learning hyperparameters: Application to solving PDEs and inverse problems with Gaussian processes
Nicholas H. Nelsen, Houman Owhadi, Andrew M. Stuart +2
Methods for solving scientific computing and inference problems, such as kernel- and neural network-based approaches for partial differential equations (PDEs), inverse problems, an…
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…
Codiscovering graphical structure and functional relationships within data: A Gaussian Process framework for connecting the dots
Théo Bourdais, Pau Batlle, Xianjin Yang +3
Most problems within and beyond the scientific domain can be framed into one of the following three levels of complexity of function approximation. Type 1: Approximate an unknown f…