Error Analysis of Kernel/GP Methods for Nonlinear and Parametric PDEs

Error Analysis of Kernel/GP Methods for Nonlinear and Parametric PDEs

8 May 2023

Bamdad Hosseini

Andrew M. Stuart

Papers citing "Error Analysis of Kernel/GP Methods for Nonlinear and Parametric PDEs"

15 / 15 papers shown

Title
Solving Nonlinear PDEs with Sparse Radial Basis Function Networks Zihan Shao Konstantin Pieper Xiaochuan Tian 24 0 0 12 May 2025
Data-Efficient Kernel Methods for Learning Differential Equations and Their Solution Operators: Algorithms and Error Analysis Yasamin Jalalian Juan Felipe Osorio Ramirez Alexander W. Hsu Bamdad Hosseini H. Owhadi 39 0 0 02 Mar 2025
Reduced Order Models and Conditional Expectation -- Analysing Parametric Low-Order Approximations Hermann G. Matthies 42 0 0 17 Feb 2025
Kernel Methods for the Approximation of the Eigenfunctions of the Koopman Operator Jonghyeon Lee B. Hamzi Boya Hou H. Owhadi G. Santin Umesh Vaidya 70 1 0 21 Dec 2024
Toward Efficient Kernel-Based Solvers for Nonlinear PDEs Zhitong Xu Da Long Yiming Xu Guang Yang Shandian Zhe Houman Owhadi 30 0 0 15 Oct 2024
Physics-informed kernel learning Nathan Doumèche Francis Bach Gérard Biau Claire Boyer PINN 29 2 0 20 Sep 2024
Gaussian process learning of nonlinear dynamics Dongwei Ye Mengwu Guo 16 4 0 19 Dec 2023
Computational Hypergraph Discovery, a Gaussian Process framework for connecting the dots Théo Bourdais Pau Batlle Xianjin Yang Ricardo Baptista Nicolas Rouquette H. Owhadi 16 0 0 28 Nov 2023
Coupling parameter and particle dynamics for adaptive sampling in Neural Galerkin schemes Yuxiao Wen Eric Vanden-Eijnden Benjamin Peherstorfer 8 12 0 27 Jun 2023
Sparse Cholesky Factorization for Solving Nonlinear PDEs via Gaussian Processes Yifan Chen H. Owhadi F. Schafer 24 30 0 03 Apr 2023
The ADMM-PINNs Algorithmic Framework for Nonsmooth PDE-Constrained Optimization: A Deep Learning Approach Yongcun Song Xiaoming Yuan Hangrui Yue PINN 19 6 0 16 Feb 2023
A Kernel Approach for PDE Discovery and Operator Learning D. Long Nicole Mrvaljević Shandian Zhe Bamdad Hosseini 13 7 0 14 Oct 2022
One-Shot Learning of Stochastic Differential Equations with Data Adapted Kernels Matthieu Darcy B. Hamzi Giulia Livieri H. Owhadi P. Tavallali 20 25 0 24 Sep 2022
Bayesian Numerical Methods for Nonlinear Partial Differential Equations Junyang Wang Jon Cockayne O. Chkrebtii T. Sullivan Chris J. Oates 38 19 0 22 Apr 2021
Fourier Neural Operator for Parametric Partial Differential Equations Zong-Yi Li Nikola B. Kovachki Kamyar Azizzadenesheli Burigede Liu K. Bhattacharya Andrew M. Stuart Anima Anandkumar AI4CE 203 2,272 0 18 Oct 2020