Bayesian Numerical Homogenization

25 June 2014

Papers citing "Bayesian Numerical Homogenization"

23 / 23 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 46 0 0 02 Mar 2025
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
Physics-Guided, Physics-Informed, and Physics-Encoded Neural Networks in Scientific Computing Salah A. Faroughi N. Pawar C. Fernandes Maziar Raissi Subasish Das N. Kalantari S. K. Mahjour PINN AI4CE 27 49 0 14 Nov 2022
Gaussian Process Hydrodynamics H. Owhadi 24 1 0 21 Sep 2022
Use of BNNM for interference wave solutions of the gBS-like equation and comparison with PINNs S. Vadyala S. N. Betgeri 24 0 0 07 Aug 2022
A Deep Learning Approach for Predicting Two-dimensional Soil Consolidation Using Physics-Informed Neural Networks (PINN) Yue Lu Gang Mei F. Piccialli PINN AI4CE 19 25 0 09 Apr 2022
Probabilistic learning inference of boundary value problem with uncertainties based on Kullback-Leibler divergence under implicit constraints Christian Soize 30 5 0 10 Feb 2022
Scientific Machine Learning through Physics-Informed Neural Networks: Where we are and What's next S. Cuomo Vincenzo Schiano Di Cola F. Giampaolo G. Rozza Maizar Raissi F. Piccialli PINN 26 1,190 0 14 Jan 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
Bayesian Numerical Methods for Nonlinear Partial Differential Equations Junyang Wang Jon Cockayne O. Chkrebtii T. Sullivan Chris J. Oates 59 19 0 22 Apr 2021
Data-driven geophysical forecasting: Simple, low-cost, and accurate baselines with kernel methods B. Hamzi R. Maulik H. Owhadi AI4TS 11 28 0 13 Feb 2021
Data-driven rogue waves and parameter discovery in the defocusing NLS equation with a potential using the PINN deep learning Li Wang Zhenya Yan 21 80 0 18 Dec 2020
Symplectic Gaussian Process Regression of Hamiltonian Flow Maps K. Rath C. Albert B. Bischl U. Toussaint 20 29 0 11 Sep 2020
Weak SINDy For Partial Differential Equations Daniel Messenger David M. Bortz 12 169 0 06 Jul 2020
Deep regularization and direct training of the inner layers of Neural Networks with Kernel Flows G. Yoo H. Owhadi 24 21 0 19 Feb 2020
Physics Informed Extreme Learning Machine (PIELM) -- A rapid method for the numerical solution of partial differential equations Vikas Dwivedi Balaji Srinivasan PINN 19 190 0 08 Jul 2019
A Modern Retrospective on Probabilistic Numerics Chris J. Oates T. Sullivan AI4CE 18 64 0 14 Jan 2019
Bayesian Probabilistic Numerical Methods Jon Cockayne Chris J. Oates T. Sullivan Mark Girolami 19 164 0 13 Feb 2017
Probabilistic Numerical Methods for PDE-constrained Bayesian Inverse Problems Jon Cockayne Chris J. Oates T. Sullivan Mark Girolami AI4CE 19 79 0 15 Jan 2017
Inferring solutions of differential equations using noisy multi-fidelity data M. Raissi P. Perdikaris George Karniadakis AI4CE 16 286 0 16 Jul 2016
Gamblets for opening the complexity-bottleneck of implicit schemes for hyperbolic and parabolic ODEs/PDEs with rough coefficients H. Owhadi Lei Zhang AI4CE 21 69 0 24 Jun 2016
Probabilistic Numerical Methods for Partial Differential Equations and Bayesian Inverse Problems Jon Cockayne Chris J. Oates T. Sullivan Mark Girolami 27 45 0 25 May 2016