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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
Pau Batlle
Yifan Chen
Bamdad Hosseini
H. Owhadi
Andrew M. Stuart
ArXivPDFHTML

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
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
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
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
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
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
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
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
Computational Hypergraph Discovery, a Gaussian Process framework for connecting the dots
Théo Bourdais
Pau Batlle
Xianjin Yang
Ricardo Baptista
Nicolas Rouquette
H. Owhadi
13
0
0
28 Nov 2023
Coupling parameter and particle dynamics for adaptive sampling in Neural
  Galerkin schemes
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
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
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
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
One-Shot Learning of Stochastic Differential Equations with Data Adapted Kernels
Matthieu Darcy
B. Hamzi
Giulia Livieri
H. Owhadi
P. Tavallali
18
25
0
24 Sep 2022
Bayesian Numerical Methods for Nonlinear Partial Differential Equations
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
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
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