Bayesian Numerical Methods for Nonlinear Partial Differential Equations

Bayesian Numerical Methods for Nonlinear Partial Differential Equations

22 April 2021

Papers citing "Bayesian Numerical Methods for Nonlinear Partial Differential Equations"

14 / 14 papers shown

Title
Flexible and Efficient Probabilistic PDE Solvers through Gaussian Markov Random Fields Tim Weiland Marvin Pfortner Philipp Hennig AI4CE 40 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 41 0 0 02 Mar 2025
Toward Efficient Kernel-Based Solvers for Nonlinear PDEs Zhitong Xu Da Long Yiming Xu Guang Yang Shandian Zhe Houman Owhadi 30 0 0 15 Oct 2024
Scaling up Probabilistic PDE Simulators with Structured Volumetric Information Tim Weiland Marvin Pfortner Philipp Hennig AI4CE 21 2 0 07 Jun 2024
Gaussian Measures Conditioned on Nonlinear Observations: Consistency, MAP Estimators, and Simulation Yifan Chen Bamdad Hosseini H. Owhadi Andrew M. Stuart 44 1 0 21 May 2024
Probabilistic Numeric SMC Sampling for Bayesian Nonlinear System Identification in Continuous Time Joe D. Longbottom M.D. Champneys T. J. Rogers 30 1 0 19 Apr 2024
Sample Path Regularity of Gaussian Processes from the Covariance Kernel Nathael Da Costa Marvin Pfortner Lancelot Da Costa Philipp Hennig GP 16 10 0 22 Dec 2023
Solving High Frequency and Multi-Scale PDEs with Gaussian Processes Shikai Fang Madison Cooley Da Long Shibo Li R. Kirby Shandian Zhe 22 4 0 08 Nov 2023
Error Analysis of Kernel/GP Methods for Nonlinear and Parametric PDEs Pau Batlle Yifan Chen Bamdad Hosseini H. Owhadi Andrew M. Stuart 24 17 0 08 May 2023
Physics-Informed Gaussian Process Regression Generalizes Linear PDE Solvers Marvin Pfortner Ingo Steinwart Philipp Hennig Jonathan Wenger AI4CE 28 26 0 23 Dec 2022
Probabilistic Numerical Method of Lines for Time-Dependent Partial Differential Equations Nicholas Kramer Jonathan Schmidt Philipp Hennig 19 18 0 22 Oct 2021
GaussED: A Probabilistic Programming Language for Sequential Experimental Design Matthew A. Fisher Onur Teymur Chris J. Oates 24 1 0 15 Oct 2021
Black Box Probabilistic Numerics Onur Teymur Christopher N. Foley Philip G. Breen Toni Karvonen Chris J. Oates 19 5 0 15 Jun 2021
Stable Implementation of Probabilistic ODE Solvers Nicholas Kramer Philipp Hennig 86 20 0 18 Dec 2020