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

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

19 / 19 papers shown

Title
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 169 0 0 02 Mar 2025
Reduced Order Models and Conditional Expectation -- Analysing Parametric Low-Order Approximations Hermann G. Matthies 91 0 0 17 Feb 2025
Kernel Methods are Competitive for Operator Learning Pau Batlle Matthieu Darcy Bamdad Hosseini H. Owhadi 68 40 0 26 Apr 2023
Can Physics-Informed Neural Networks beat the Finite Element Method? T. G. Grossmann Urszula Julia Komorowska J. Latz Carola-Bibiane Schönlieb PINN AI4CE 89 91 0 08 Feb 2023
AutoIP: A United Framework to Integrate Physics into Gaussian Processes D. Long Ziyi Wang Aditi S. Krishnapriyan Robert M. Kirby Shandian Zhe Michael W. Mahoney AI4CE 83 15 0 24 Feb 2022
Bayesian Numerical Methods for Nonlinear Partial Differential Equations Junyang Wang Jon Cockayne O. Chkrebtii T. Sullivan Chris J. Oates 97 19 0 22 Apr 2021
Solving and Learning Nonlinear PDEs with Gaussian Processes Yifan Chen Bamdad Hosseini H. Owhadi Andrew M. Stuart 69 156 0 24 Mar 2021
Solving high-dimensional parabolic PDEs using the tensor train format Lorenz Richter Leon Sallandt Nikolas Nusken 65 50 0 23 Feb 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 500 2,444 0 18 Oct 2020
A Survey of Constrained Gaussian Process Regression: Approaches and Implementation Challenges L. Swiler Mamikon A. Gulian A. Frankel Cosmin Safta J. Jakeman GP AI4CE 73 106 0 16 Jun 2020
Consistency of Empirical Bayes And Kernel Flow For Hierarchical Parameter Estimation Yifan Chen H. Owhadi Andrew M. Stuart 77 31 0 22 May 2020
Sparse Cholesky factorization by Kullback-Leibler minimization Florian Schäfer Matthias Katzfuss H. Owhadi 72 94 0 29 Apr 2020
DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operators Lu Lu Pengzhan Jin George Karniadakis 248 2,150 0 08 Oct 2019
Kernel Flows: from learning kernels from data into the abyss H. Owhadi G. Yoo 73 90 0 13 Aug 2018
Deep Neural Networks as Gaussian Processes Jaehoon Lee Yasaman Bahri Roman Novak S. Schoenholz Jeffrey Pennington Jascha Narain Sohl-Dickstein UQCV BDL 131 1,097 0 01 Nov 2017
The Deep Ritz method: A deep learning-based numerical algorithm for solving variational problems E. Weinan Ting Yu 123 1,387 0 30 Sep 2017
Bayesian Probabilistic Numerical Methods Jon Cockayne Chris J. Oates T. Sullivan Mark Girolami 77 166 0 13 Feb 2017
Probabilistic Numerical Methods for PDE-constrained Bayesian Inverse Problems Jon Cockayne Chris J. Oates T. Sullivan Mark Girolami AI4CE 62 80 0 15 Jan 2017
Deep Kernel Learning A. Wilson Zhiting Hu Ruslan Salakhutdinov Eric Xing BDL 248 888 0 06 Nov 2015