Inferring solutions of differential equations using noisy multi-fidelity data

16 July 2016

Papers citing "Inferring solutions of differential equations using noisy multi-fidelity data"

36 / 36 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 53 0 0 30 Apr 2025
Reconstructing Blood Flow in Data-Poor Regimes: A Vasculature Network Kernel for Gaussian Process Regression S. Z. Ashtiani Mohammad Sarabian K. Laksari H. Babaee 34 2 0 14 Mar 2024
A DeepONet multi-fidelity approach for residual learning in reduced order modeling N. Demo M. Tezzele G. Rozza 32 19 0 24 Feb 2023
Multi-fidelity Monte Carlo: a pseudo-marginal approach Diana Cai Ryan P. Adams 26 5 0 04 Oct 2022
Domain-aware Control-oriented Neural Models for Autonomous Underwater Vehicles Wenceslao Shaw-Cortez Soumya Vasisht Aaron Tuor Ján Drgoňa D. Vrabie AI4CE 21 0 0 15 Aug 2022
Multi-fidelity wavelet neural operator with application to uncertainty quantification A. Thakur Tapas Tripura S. Chakraborty 38 12 0 11 Aug 2022
Use of BNNM for interference wave solutions of the gBS-like equation and comparison with PINNs S. Vadyala S. N. Betgeri 29 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 25 25 0 09 Apr 2022
Constructing coarse-scale bifurcation diagrams from spatio-temporal observations of microscopic simulations: A parsimonious machine learning approach Evangelos Galaris Gianluca Fabiani I. Gallos Ioannis G. Kevrekidis Constantinos Siettos AI4CE 28 40 0 31 Jan 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
Subspace Decomposition based DNN algorithm for elliptic type multi-scale PDEs Xi-An Li Z. Xu Lei Zhang 27 27 0 10 Dec 2021
Computational Graph Completion H. Owhadi 8 24 0 20 Oct 2021
Long-time integration of parametric evolution equations with physics-informed DeepONets Sizhuang He P. Perdikaris AI4CE 24 117 0 09 Jun 2021
The Discovery of Dynamics via Linear Multistep Methods and Deep Learning: Error Estimation Q. Du Yiqi Gu Haizhao Yang Chao Zhou 26 20 0 21 Mar 2021
Gaussian processes meet NeuralODEs: A Bayesian framework for learning the dynamics of partially observed systems from scarce and noisy data Mohamed Aziz Bhouri P. Perdikaris 28 20 0 04 Mar 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 27 80 0 18 Dec 2020
Symplectic Gaussian Process Regression of Hamiltonian Flow Maps K. Rath C. Albert B. Bischl U. Toussaint 22 29 0 11 Sep 2020
Physics-informed Neural Networks for Solving Inverse Problems of Nonlinear Biot's Equations: Batch Training T. Kadeethum T. Jørgensen H. Nick PINN AI4CE 25 19 0 18 May 2020
Efficient Characterization of Dynamic Response Variation Using Multi-Fidelity Data Fusion through Composite Neural Network K. Zhou Jiong Tang AI4CE 23 17 0 07 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 43 51 0 02 May 2020
Physics-informed Neural Networks for Solving Nonlinear Diffusivity and Biot's equations T. Kadeethum T. Jørgensen H. Nick PINN AI4CE 25 106 0 19 Feb 2020
Physics-Guided Machine Learning for Scientific Discovery: An Application in Simulating Lake Temperature Profiles X. Jia J. Willard Anuj Karpatne J. Read Jacob Aaron Zwart M. Steinbach Vipin Kumar AI4CE PINN 26 207 0 28 Jan 2020
SympNets: Intrinsic structure-preserving symplectic networks for identifying Hamiltonian systems Pengzhan Jin Zhen Zhang Aiqing Zhu Yifa Tang George Karniadakis 21 21 0 11 Jan 2020
Learning the Tangent Space of Dynamical Instabilities from Data Antoine Blanchard T. Sapsis 18 8 0 24 Jul 2019
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
Adversarial Uncertainty Quantification in Physics-Informed Neural Networks Yibo Yang P. Perdikaris AI4CE PINN 32 355 0 09 Nov 2018
Hidden Fluid Mechanics: A Navier-Stokes Informed Deep Learning Framework for Assimilating Flow Visualization Data M. Raissi A. Yazdani George Karniadakis AI4CE PINN 19 158 0 13 Aug 2018
Deep convolutional recurrent autoencoders for learning low-dimensional feature dynamics of fluid systems F. J. Gonzalez Maciej Balajewicz AI4CE 25 138 0 03 Aug 2018
Machine Learning of Space-Fractional Differential Equations Mamikon A. Gulian M. Raissi P. Perdikaris George Karniadakis 38 46 0 02 Aug 2018
Forward-Backward Stochastic Neural Networks: Deep Learning of High-dimensional Partial Differential Equations M. Raissi 31 184 0 19 Apr 2018
Deep Hidden Physics Models: Deep Learning of Nonlinear Partial Differential Equations M. Raissi PINN AI4CE 40 745 0 20 Jan 2018
Multistep Neural Networks for Data-driven Discovery of Nonlinear Dynamical Systems M. Raissi P. Perdikaris George Karniadakis PINN 20 266 0 04 Jan 2018
Inverse modeling of hydrologic systems with adaptive multi-fidelity Markov chain Monte Carlo simulations Jiangjiang Zhang J. Man Guang Lin Laosheng Wu L. Zeng 30 41 0 06 Dec 2017
Physics Informed Deep Learning (Part II): Data-driven Discovery of Nonlinear Partial Differential Equations M. Raissi P. Perdikaris George Karniadakis PINN AI4CE 26 607 0 28 Nov 2017
Bayesian Probabilistic Numerical Methods Jon Cockayne Chris J. Oates T. Sullivan Mark Girolami 24 164 0 13 Feb 2017
Gamblets for opening the complexity-bottleneck of implicit schemes for hyperbolic and parabolic ODEs/PDEs with rough coefficients H. Owhadi Lei Zhang AI4CE 23 69 0 24 Jun 2016