Solving and Learning Nonlinear PDEs with Gaussian Processes

24 March 2021

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

26 / 76 papers shown

Title
Partial Differential Equations Meet Deep Neural Networks: A Survey Shudong Huang Wentao Feng Chenwei Tang Jiancheng Lv AI4CE AIMat 34 18 0 27 Oct 2022
Mitigating spectral bias for the multiscale operator learning Xinliang Liu Bo Xu Shuhao Cao Lei Zhang AI4CE 38 26 0 19 Oct 2022
Minimax Optimal Kernel Operator Learning via Multilevel Training Jikai Jin Yiping Lu Jose H. Blanchet Lexing Ying 33 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 43 27 0 24 Sep 2022
Gaussian Process Hydrodynamics H. Owhadi 42 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 29 6 0 31 Aug 2022
Data-driven Control of Agent-based Models: an Equation/Variable-free Machine Learning Approach Dimitrios G. Patsatzis Lucia Russo Ioannis G. Kevrekidis Constantinos Siettos 26 15 0 12 Jul 2022
Learning "best" kernels from data in Gaussian process regression. With application to aerodynamics J. Akian L. Bonnet H. Owhadi Éric Savin 11 24 0 03 Jun 2022
Learning black- and gray-box chemotactic PDEs/closures from agent based Monte Carlo simulation data Seungjoon Lee Y. M. Psarellis Constantinos Siettos Ioannis G. Kevrekidis AI4CE 21 27 0 26 May 2022
Sobolev Acceleration and Statistical Optimality for Learning Elliptic Equations via Gradient Descent Yiping Lu Jose H. Blanchet Lexing Ying 43 7 0 15 May 2022
Parsimonious Physics-Informed Random Projection Neural Networks for Initial-Value Problems of ODEs and index-1 DAEs Gianluca Fabiani Evangelos Galaris L. Russo Constantinos Siettos 19 29 0 10 Mar 2022
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 39 14 0 24 Feb 2022
Tutorial on amortized optimization Brandon Amos OffRL 78 43 0 01 Feb 2022
Learning dynamical systems from data: A simple cross-validation perspective, part III: Irregularly-Sampled Time Series Jonghyeon Lee E. Brouwer B. Hamzi H. Owhadi AI4TS 21 19 0 25 Nov 2021
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
Recipes for when Physics Fails: Recovering Robust Learning of Physics Informed Neural Networks Minh Nguyen Luke McLennan T. Andeen Avik Roy PINN 31 27 0 26 Oct 2021
Probabilistic Numerical Method of Lines for Time-Dependent Partial Differential Equations Nicholas Kramer Jonathan Schmidt Philipp Hennig 32 18 0 22 Oct 2021
Computational Graph Completion H. Owhadi 29 24 0 20 Oct 2021
Learning Partial Differential Equations in Reproducing Kernel Hilbert Spaces George Stepaniants 51 15 0 26 Aug 2021
A Framework for Machine Learning of Model Error in Dynamical Systems Matthew E. Levine Andrew M. Stuart 32 67 0 14 Jul 2021
Long-time integration of parametric evolution equations with physics-informed DeepONets Sizhuang He P. Perdikaris AI4CE 26 117 0 09 Jun 2021
Learning particle swarming models from data with Gaussian processes Jinchao Feng Charles Kulick Yunxiang Ren Sui Tang 31 5 0 04 Jun 2021
Bayesian Numerical Methods for Nonlinear Partial Differential Equations Junyang Wang Jon Cockayne O. Chkrebtii T. Sullivan Chris J. Oates 63 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 135 442 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 271 2,315 0 18 Oct 2020
Do ideas have shape? Idea registration as the continuous limit of artificial neural networks H. Owhadi 98 14 0 10 Aug 2020