Numerical Gaussian Processes for Time-dependent and Non-linear Partial Differential Equations

29 March 2017

Papers citing "Numerical Gaussian Processes for Time-dependent and Non-linear Partial Differential Equations"

50 / 63 papers shown

Title
A general physics-constrained method for the modelling of equation's closure terms with sparse data Tian Chen Shengping Liu Li Liu Heng Yong PINN AI4CE 78 0 0 30 Apr 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 174 0 0 02 Mar 2025
Gaussian Process Port-Hamiltonian Systems: Bayesian Learning with Physics Prior Thomas Beckers Jacob H. Seidman P. Perdikaris George J. Pappas PINN 82 17 0 15 May 2023
$Laplace-fPINNs: Laplace-based fractional physics-informed neural networks for solving forward and inverse problems of subdiffusion$ Laplace-fPINNs: Laplace-based fractional physics-informed neural networks for solving forward and inverse problems of subdiffusion Xiongbin Yan Zhi-Qin John Xu Zheng Ma 65 2 0 03 Apr 2023
Gaussian Process Priors for Systems of Linear Partial Differential Equations with Constant Coefficients Marc Härkönen Markus Lange-Hegermann Bogdan Raiță 133 16 0 29 Dec 2022
High Precision Differentiation Techniques for Data-Driven Solution of Nonlinear PDEs by Physics-Informed Neural Networks M. Mukhametzhanov 28 1 0 02 Oct 2022
Use of BNNM for interference wave solutions of the gBS-like equation and comparison with PINNs S. Vadyala S. N. Betgeri 72 0 0 07 Aug 2022
Scalable algorithms for physics-informed neural and graph networks K. Shukla Mengjia Xu N. Trask George Karniadakis PINN AI4CE 131 41 0 16 May 2022
Neural Implicit Representations for Physical Parameter Inference from a Single Video Florian Hofherr Lukas Koestler Florian Bernard Daniel Cremers AI4CE 114 10 0 29 Apr 2022
MultiAuto-DeepONet: A Multi-resolution Autoencoder DeepONet for Nonlinear Dimension Reduction, Uncertainty Quantification and Operator Learning of Forward and Inverse Stochastic Problems Jiahao Zhang Shiqi Zhang Guang Lin 95 15 0 07 Apr 2022
$Monte Carlo PINNs: deep learning approach for forward and inverse problems involving high dimensional fractional partial differential equations$ Monte Carlo PINNs: deep learning approach for forward and inverse problems involving high dimensional fractional partial differential equations Ling Guo Hao Wu Xiao-Jun Yu Tao Zhou PINN AI4CE 64 63 0 16 Mar 2022
Incorporating Sum Constraints into Multitask Gaussian Processes Philipp Pilar Carl Jidling Thomas B. Schon Niklas Wahlström TPM 44 3 0 03 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 123 1,293 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 47 1 0 23 Nov 2021
Learning Free-Surface Flow with Physics-Informed Neural Networks Raphael Leiteritz Marcel Hurler Dirk Pflüger PINN AI4CE 53 7 0 17 Nov 2021
Recipes for when Physics Fails: Recovering Robust Learning of Physics Informed Neural Networks Minh Nguyen Luke McLennan T. Andeen Avik Roy PINN 59 29 0 26 Oct 2021
Probabilistic Numerical Method of Lines for Time-Dependent Partial Differential Equations Nicholas Kramer Jonathan Schmidt Philipp Hennig 73 19 0 22 Oct 2021
Wasserstein Generative Adversarial Uncertainty Quantification in Physics-Informed Neural Networks Yihang Gao Michael K. Ng 78 30 0 30 Aug 2021
Normalizing field flows: Solving forward and inverse stochastic differential equations using physics-informed flow models Ling Guo Hao Wu Tao Zhou AI4CE 77 48 0 30 Aug 2021
Physics-informed neural networks (PINNs) for fluid mechanics: A review Shengze Cai Zhiping Mao Zhicheng Wang Minglang Yin George Karniadakis PINN AI4CE 96 1,213 0 20 May 2021
Dominant motion identification of multi-particle system using deep learning from video Yayati Jadhav Amir Barati Farimani 116 5 0 26 Apr 2021
Bayesian Numerical Methods for Nonlinear Partial Differential Equations Junyang Wang Jon Cockayne O. Chkrebtii T. Sullivan Chris J. Oates 111 19 0 22 Apr 2021
Solving and Learning Nonlinear PDEs with Gaussian Processes Yifan Chen Bamdad Hosseini H. Owhadi Andrew M. Stuart 82 157 0 24 Mar 2021
A Deep Collocation Method for the Bending Analysis of Kirchhoff Plate Hongwei Guo X. Zhuang Timon Rabczuk AI4CE 60 439 0 04 Feb 2021
An overview on deep learning-based approximation methods for partial differential equations C. Beck Martin Hutzenthaler Arnulf Jentzen Benno Kuckuck 117 153 0 22 Dec 2020
APIK: Active Physics-Informed Kriging Model with Partial Differential Equations Jialei Chen Zhehui Chen Chuck Zhang C. F. J. Wu 99 15 0 22 Dec 2020
Data-driven rogue waves and parameter discovery in the defocusing NLS equation with a potential using the PINN deep learning Li Wang Zhenya Yan 76 85 0 18 Dec 2020
System Identification Through Lipschitz Regularized Deep Neural Networks Elisa Negrini G. Citti L. Capogna 38 12 0 07 Sep 2020
A Survey of Constrained Gaussian Process Regression: Approaches and Implementation Challenges L. Swiler Mamikon A. Gulian A. Frankel Cosmin Safta J. Jakeman GP AI4CE 104 106 0 16 Jun 2020
Hybrid Scheme of Kinematic Analysis and Lagrangian Koopman Operator Analysis for Short-term Precipitation Forecasting Shitao Zheng T. Miyamoto K. Iwanami S. Shimizu Ryohei Kato 65 3 0 03 Jun 2020
When Machine Learning Meets Multiscale Modeling in Chemical Reactions Wuyue Yang Liangrong Peng Yi Zhu L. Hong AI4CE 20 12 0 01 Jun 2020
SciANN: A Keras/Tensorflow wrapper for scientific computations and physics-informed deep learning using artificial neural networks E. Haghighat R. Juanes AI4CE PINN 123 21 0 11 May 2020
Active Training of Physics-Informed Neural Networks to Aggregate and Interpolate Parametric Solutions to the Navier-Stokes Equations Christopher J. Arthurs A. King PINN 152 52 0 02 May 2020
Nonnegativity-Enforced Gaussian Process Regression Andrew Pensoneault Xiu Yang Xueyu Zhu 69 28 0 07 Apr 2020
Discovery of Dynamics Using Linear Multistep Methods Rachael Keller Q. Du 83 36 0 29 Dec 2019
Sparse Polynomial Chaos expansions using Variational Relevance Vector Machines Panagiotis Tsilifis I. Papaioannou D. Štraub F. Nobile 119 19 0 23 Dec 2019
Numerical Gaussian process Kalman filtering Armin Küper S. Waldherr 131 3 0 03 Dec 2019
Physics Informed Extreme Learning Machine (PIELM) -- A rapid method for the numerical solution of partial differential equations Vikas Dwivedi Balaji Srinivasan PINN 79 194 0 08 Jul 2019
SNODE: Spectral Discretization of Neural ODEs for System Identification A. Quaglino Marco Gallieri Jonathan Masci Jan Koutník AI4TS 106 48 0 17 Jun 2019
Enforcing constraints for time series prediction in supervised, unsupervised and reinforcement learning P. Stinis AI4TS AI4CE 71 11 0 17 May 2019
Fleet Prognosis with Physics-informed Recurrent Neural Networks R. Nascimento F. Viana 25 52 0 16 Jan 2019
Physics-Informed CoKriging: A Gaussian-Process-Regression-Based Multifidelity Method for Data-Model Convergence Xiu Yang D. Barajas-Solano G. Tartakovsky A. Tartakovsky 73 78 0 24 Nov 2018
Adversarial Uncertainty Quantification in Physics-Informed Neural Networks Yibo Yang P. Perdikaris AI4CE PINN 142 361 0 09 Nov 2018
Physics-Informed Generative Adversarial Networks for Stochastic Differential Equations Siyu Dai Shawn Schaffert Andreas G. Hofmann 134 367 0 05 Nov 2018
Quantifying total uncertainty in physics-informed neural networks for solving forward and inverse stochastic problems Dongkun Zhang Lu Lu Ling Guo George Karniadakis UQCV 124 412 0 21 Sep 2018
Data-driven discovery of PDEs in complex datasets Jens Berg K. Nystrom AI4CE PINN 71 141 0 31 Aug 2018
Deep Learning of Vortex Induced Vibrations M. Raissi Zhicheng Wang M. Triantafyllou George Karniadakis AI4CE 79 378 0 26 Aug 2018
Hidden Fluid Mechanics: A Navier-Stokes Informed Deep Learning Framework for Assimilating Flow Visualization Data M. Raissi A. Yazdani George Karniadakis AI4CE PINN 99 161 0 13 Aug 2018
Machine Learning of Space-Fractional Differential Equations Mamikon A. Gulian M. Raissi P. Perdikaris George Karniadakis 109 47 0 02 Aug 2018
Neural-net-induced Gaussian process regression for function approximation and PDE solution G. Pang Liu Yang George Karniadakis 70 73 0 22 Jun 2018