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…
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…
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…