Solving and Learning Nonlinear PDEs with Gaussian Processes

24 March 2021

Papers citing "Solving and Learning Nonlinear PDEs with Gaussian Processes"

29 / 29 papers shown

Title
Solving Nonlinear PDEs with Sparse Radial Basis Function Networks Zihan Shao Konstantin Pieper Xiaochuan Tian 31 0 0 12 May 2025
Gaussian Process Policy Iteration with Additive Schwarz Acceleration for Forward and Inverse HJB and Mean Field Game Problems Xianjin Yang Jingguo Zhang 24 0 0 01 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 43 0 0 02 Mar 2025
Physics-informed kernel learning Nathan Doumèche Francis Bach Gérard Biau Claire Boyer PINN 37 2 0 20 Sep 2024
Linearization Turns Neural Operators into Function-Valued Gaussian Processes Emilia Magnani Marvin Pfortner Tobias Weber Philipp Hennig UQCV 69 1 0 07 Jun 2024
Label Propagation Training Schemes for Physics-Informed Neural Networks and Gaussian Processes Ming Zhong Dehao Liu Raymundo Arroyave U. Braga-Neto AI4CE SSL 26 1 0 08 Apr 2024
Gaussian process learning of nonlinear dynamics Dongwei Ye Mengwu Guo 20 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 21 0 0 28 Nov 2023
Tasks Makyth Models: Machine Learning Assisted Surrogates for Tipping Points Gianluca Fabiani N. Evangelou Tianqi Cui J. M. Bello-Rivas Cristina P. Martin-Linares Constantinos Siettos Ioannis G. Kevrekidis 38 2 0 25 Sep 2023
Error Analysis of Kernel/GP Methods for Nonlinear and Parametric PDEs Pau Batlle Yifan Chen Bamdad Hosseini H. Owhadi Andrew M. Stuart 34 17 0 08 May 2023
Efficient Sampling of Stochastic Differential Equations with Positive Semi-Definite Models Anant Raj Umut Simsekli Alessandro Rudi DiffM 31 1 0 30 Mar 2023
Gradient Flows for Sampling: Mean-Field Models, Gaussian Approximations and Affine Invariance Yifan Chen Daniel Zhengyu Huang Jiaoyang Huang Sebastian Reich Andrew M. Stuart 19 17 0 21 Feb 2023
Physics-informed Information Field Theory for Modeling Physical Systems with Uncertainty Quantification A. Alberts Ilias Bilionis 34 12 0 18 Jan 2023
Parameter Inference based on Gaussian Processes Informed by Nonlinear Partial Differential Equations Zhao-Xia Li Shih-Feng Yang Jeff Wu 11 2 0 22 Dec 2022
Partial Differential Equations Meet Deep Neural Networks: A Survey Shudong Huang Wentao Feng Chenwei Tang Jiancheng Lv AI4CE AIMat 29 18 0 27 Oct 2022
Minimax Optimal Kernel Operator Learning via Multilevel Training Jikai Jin Yiping Lu Jose H. Blanchet Lexing Ying 26 12 0 28 Sep 2022
One-Shot Learning of Stochastic Differential Equations with Data Adapted Kernels Matthieu Darcy B. Hamzi Giulia Livieri H. Owhadi P. Tavallali 36 26 0 24 Sep 2022
Gaussian Process Hydrodynamics H. Owhadi 24 1 0 21 Sep 2022
Monotonic Gaussian process for physics-constrained machine learning with materials science applications Anh Tran Kathryn A. Maupin T. Rodgers PINN AI4CE 21 6 0 31 Aug 2022
Sobolev Acceleration and Statistical Optimality for Learning Elliptic Equations via Gradient Descent Yiping Lu Jose H. Blanchet Lexing Ying 38 7 0 15 May 2022
AutoIP: A United Framework to Integrate Physics into Gaussian Processes D. Long Zihan Wang Aditi S. Krishnapriyan Robert M. Kirby Shandian Zhe Michael W. Mahoney AI4CE 32 14 0 24 Feb 2022
Tutorial on amortized optimization Brandon Amos OffRL 75 43 0 01 Feb 2022
Stochastic Processes Under Linear Differential Constraints : Application to Gaussian Process Regression for the 3 Dimensional Free Space Wave Equation Iain Henderson P. Noble O. Roustant 21 1 0 23 Nov 2021
Learning Partial Differential Equations in Reproducing Kernel Hilbert Spaces George Stepaniants 49 15 0 26 Aug 2021
Long-time integration of parametric evolution equations with physics-informed DeepONets Sizhuang He P. Perdikaris AI4CE 24 117 0 09 Jun 2021
Learning particle swarming models from data with Gaussian processes Jinchao Feng Charles Kulick Yunxiang Ren Sui Tang 26 5 0 04 Jun 2021
Bayesian Numerical Methods for Nonlinear Partial Differential Equations Junyang Wang Jon Cockayne O. Chkrebtii T. Sullivan Chris J. Oates 56 19 0 22 Apr 2021
On the eigenvector bias of Fourier feature networks: From regression to solving multi-scale PDEs with physics-informed neural networks Sizhuang He Hanwen Wang P. Perdikaris 131 439 0 18 Dec 2020
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 238 2,298 0 18 Oct 2020