Probabilistic Numerical Methods for PDE-constrained Bayesian Inverse Problems

15 January 2017

Papers citing "Probabilistic Numerical Methods for PDE-constrained Bayesian Inverse Problems"

26 / 26 papers shown

Title
Are Statistical Methods Obsolete in the Era of Deep Learning? Skyler Wu Shihao Yang S. C. Kou 12 0 0 27 May 2025
Flexible and Efficient Probabilistic PDE Solvers through Gaussian Markov Random Fields Tim Weiland Marvin Pfortner Philipp Hennig AI4CE 79 0 0 11 Mar 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 176 0 0 02 Mar 2025
Physics-Informed Variational State-Space Gaussian Processes Oliver Hamelijnck Arno Solin Theodoros Damoulas 64 1 0 20 Sep 2024
Scaling up Probabilistic PDE Simulators with Structured Volumetric Information Tim Weiland Marvin Pfortner Philipp Hennig AI4CE 79 3 0 07 Jun 2024
Gaussian Measures Conditioned on Nonlinear Observations: Consistency, MAP Estimators, and Simulation Yifan Chen Bamdad Hosseini H. Owhadi Andrew M. Stuart 106 1 0 21 May 2024
Solving High Frequency and Multi-Scale PDEs with Gaussian Processes Shikai Fang Madison Cooley Da Long Shibo Li R. Kirby Shandian Zhe 77 4 0 08 Nov 2023
Gaussian processes for Bayesian inverse problems associated with linear partial differential equations Tianming Bai A. Teckentrup K. Zygalakis 68 13 0 17 Jul 2023
Error Analysis of Kernel/GP Methods for Nonlinear and Parametric PDEs Pau Batlle Yifan Chen Bamdad Hosseini H. Owhadi Andrew M. Stuart 80 18 0 08 May 2023
Images of Gaussian and other stochastic processes under closed, densely-defined, unbounded linear operators T. Matsumoto T. Sullivan 70 3 0 05 May 2023
Introduction To Gaussian Process Regression In Bayesian Inverse Problems, With New ResultsOn Experimental Design For Weighted Error Measures T. Helin Andrew M. Stuart A. Teckentrup K. Zygalakis 62 5 0 09 Feb 2023
Gaussian Process Priors for Systems of Linear Partial Differential Equations with Constant Coefficients Marc Härkönen Markus Lange-Hegermann Bogdan Raiță 140 16 0 29 Dec 2022
Physics-Informed Gaussian Process Regression Generalizes Linear PDE Solvers Marvin Pfortner Ingo Steinwart Philipp Hennig Jonathan Wenger AI4CE 119 29 0 23 Dec 2022
Parameter Inference based on Gaussian Processes Informed by Nonlinear Partial Differential Equations Zhao-Xia Li Shih-Feng Yang Jeff Wu 102 2 0 22 Dec 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 47 1 0 23 Nov 2021
Probabilistic Numerical Method of Lines for Time-Dependent Partial Differential Equations Nicholas Kramer Jonathan Schmidt Philipp Hennig 73 19 0 22 Oct 2021
Black Box Probabilistic Numerics Onur Teymur Christopher N. Foley Philip G. Breen Toni Karvonen Chris J. Oates 55 5 0 15 Jun 2021
Solving and Learning Nonlinear PDEs with Gaussian Processes Yifan Chen Bamdad Hosseini H. Owhadi Andrew M. Stuart 82 157 0 24 Mar 2021
Differentiable Likelihoods for Fast Inversion of 'Likelihood-Free' Dynamical Systems Hans Kersting N. Krämer Martin Schiegg Christian Daniel Michael Tiemann Philipp Hennig 70 21 0 21 Feb 2020
Comments on the article "A Bayesian conjugate gradient method" T. Sullivan 18 0 0 24 Jun 2019
A Modern Retrospective on Probabilistic Numerics Chris J. Oates T. Sullivan AI4CE 101 64 0 14 Jan 2019
Rejoinder for "Probabilistic Integration: A Role in Statistical Computation?" François‐Xavier Briol Chris J. Oates Mark Girolami Michael A. Osborne Dino Sejdinovic 49 9 0 26 Nov 2018
Bayesian Quadrature for Multiple Related Integrals Xiaoyue Xi François‐Xavier Briol Mark Girolami 108 39 0 12 Jan 2018
Bayesian Probabilistic Numerical Methods Jon Cockayne Chris J. Oates T. Sullivan Mark Girolami 106 166 0 13 Feb 2017
Machine Learning of Linear Differential Equations using Gaussian Processes M. Raissi George Karniadakis 85 553 0 10 Jan 2017
Convergence Rates for a Class of Estimators Based on Stein's Method Chris J. Oates Jon Cockayne F. Briol Mark Girolami 83 57 0 10 Mar 2016