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"

50 / 77 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
Open-Source High-Speed Flight Surrogate Modeling Framework Tyler E. Korenyi-Both Nathan J. Falkiewicz Matthew C. Jones AI4CE 61 0 0 06 Nov 2024
GFN: A graph feedforward network for resolution-invariant reduced operator learning in multifidelity applications Oisín M. Morrison F. Pichi J. Hesthaven AI4CE 72 6 0 05 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
Reconstructing Blood Flow in Data-Poor Regimes: A Vasculature Network Kernel for Gaussian Process Regression S. Z. Ashtiani Mohammad Sarabian K. Laksari H. Babaee 52 4 0 14 Mar 2024
PINN-BO: A Black-box Optimization Algorithm using Physics-Informed Neural Networks Dat Phan-Trong Hung The Tran A. Shilton Sunil R. Gupta 81 0 0 05 Feb 2024
A comprehensive framework for multi-fidelity surrogate modeling with noisy data: a gray-box perspective Katerina Giannoukou S. Marelli Bruno Sudret AI4CE 33 1 0 12 Jan 2024
A spectrum of physics-informed Gaussian processes for regression in engineering E. Cross T. Rogers D. J. Pitchforth S. Gibson Matthew R. Jones 61 9 0 19 Sep 2023
Multi-fidelity reduced-order surrogate modeling Paolo Conti Mengwu Guo Andrea Manzoni A. Frangi Steven L. Brunton N. Kutz AI4CE 93 28 0 01 Sep 2023
Bayesian Reasoning for Physics Informed Neural Networks K. Graczyk Kornel Witkowski 87 0 0 25 Aug 2023
Physics-informed Gaussian process model for Euler-Bernoulli beam elements Gledson Rodrigo Tondo Sebastian Rau I. Kavrakov Guido Morgenthal 39 5 0 05 Aug 2023
Data-Driven Identification of Quadratic Representations for Nonlinear Hamiltonian Systems using Weakly Symplectic Liftings Süleyman Yıldız P. Goyal Thomas Bendokat P. Benner 64 10 0 02 Aug 2023
Machine learning with data assimilation and uncertainty quantification for dynamical systems: a review Sibo Cheng César Quilodrán-Casas Said Ouala A. Farchi Che Liu ... Weiping Ding Yike Guo A. Carrassi Marc Bocquet Rossella Arcucci AI4CE 81 135 0 18 Mar 2023
A DeepONet multi-fidelity approach for residual learning in reduced order modeling N. Demo M. Tezzele G. Rozza 79 21 0 24 Feb 2023
Physics Informed Neural Network for Dynamic Stress Prediction H. Bolandi Gautam Sreekumar Xuyang Li N. Lajnef Vishnu Boddeti AI4CE 48 23 0 28 Nov 2022
Multi-fidelity Monte Carlo: a pseudo-marginal approach Diana Cai Ryan P. Adams 60 6 0 04 Oct 2022
Modelling of physical systems with a Hopf bifurcation using mechanistic models and machine learning K. H. Lee David A.W. Barton L. Renson 69 12 0 07 Sep 2022
Domain-aware Control-oriented Neural Models for Autonomous Underwater Vehicles Wenceslao Shaw-Cortez Soumya Vasisht Aaron Tuor Ján Drgoňa D. Vrabie AI4CE 32 0 0 15 Aug 2022
Multi-fidelity wavelet neural operator with application to uncertainty quantification A. Thakur Tapas Tripura S. Chakraborty 76 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 72 0 0 07 Aug 2022
Physically Consistent Learning of Conservative Lagrangian Systems with Gaussian Processes G. Evangelisti Sandra Hirche 51 15 0 24 Jun 2022
A hybrid data driven-physics constrained Gaussian process regression framework with deep kernel for uncertainty quantification Che-Chia Chang T. Zeng GP 50 6 0 13 May 2022
Quantum Extremal Learning Savvas Varsamopoulos E. Philip H. Vlijmen Sairam Menon Ann Vos N. Dyubankova B. Torfs Anthony Rowe V. Elfving 52 6 0 05 May 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 42 29 0 09 Apr 2022
PAGP: A physics-assisted Gaussian process framework with active learning for forward and inverse problems of partial differential equations Jiahao Zhang Shiqi Zhang Guang Lin 81 3 0 06 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 102 42 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 134 1,293 0 14 Jan 2022
Subspace Decomposition based DNN algorithm for elliptic type multi-scale PDEs Xi-An Li Z. Xu Lei Zhang 60 28 0 10 Dec 2021
Learning Free-Surface Flow with Physics-Informed Neural Networks Raphael Leiteritz Marcel Hurler Dirk Pflüger PINN AI4CE 53 7 0 17 Nov 2021
Computational Graph Completion H. Owhadi 82 25 0 20 Oct 2021
Physics-Coupled Spatio-Temporal Active Learning for Dynamical Systems Yu Huang Yufei Tang Xingquan Zhu Min Shi Ali Muhamed Ali H. Zhuang Laurent Chérubin AI4CE 57 3 0 11 Aug 2021
Long-time integration of parametric evolution equations with physics-informed DeepONets Sizhuang He P. Perdikaris AI4CE 89 122 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 66 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 81 21 0 04 Mar 2021
Multi-fidelity regression using artificial neural networks: efficient approximation of parameter-dependent output quantities Mengwu Guo Andrea Manzoni Maurice Amendt Paolo Conti J. Hesthaven 184 97 0 26 Feb 2021
Multi-fidelity Bayesian Neural Networks: Algorithms and Applications Xuhui Meng H. Babaee George Karniadakis 59 132 0 19 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 79 85 0 18 Dec 2020
Multi-fidelity data fusion for the approximation of scalar functions with low intrinsic dimensionality through active subspaces F. Romor M. Tezzele G. Rozza 48 4 0 16 Oct 2020
Symplectic Gaussian Process Regression of Hamiltonian Flow Maps K. Rath C. Albert B. Bischl U. Toussaint 50 29 0 11 Sep 2020
RoeNets: Predicting Discontinuity of Hyperbolic Systems from Continuous Data S. Xiong Xingzhe He Yunjin Tong Runze Liu Bo Zhu AI4CE 8 4 0 07 Jun 2020
A probabilistic generative model for semi-supervised training of coarse-grained surrogates and enforcing physical constraints through virtual observables Maximilian Rixner P. Koutsourelakis AI4CE 85 22 0 02 Jun 2020
Physics-informed Neural Networks for Solving Inverse Problems of Nonlinear Biot's Equations: Batch Training T. Kadeethum T. Jørgensen H. Nick PINN AI4CE 147 20 0 18 May 2020
Efficient Characterization of Dynamic Response Variation Using Multi-Fidelity Data Fusion through Composite Neural Network K. Zhou Jiong Tang AI4CE 156 18 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 152 52 0 02 May 2020
Bayesian differential programming for robust systems identification under uncertainty Yibo Yang Mohamed Aziz Bhouri P. Perdikaris OOD 121 32 0 15 Apr 2020
B-PINNs: Bayesian Physics-Informed Neural Networks for Forward and Inverse PDE Problems with Noisy Data Liu Yang Xuhui Meng George Karniadakis PINN 245 794 0 13 Mar 2020
Physics-informed Neural Networks for Solving Nonlinear Diffusivity and Biot's equations T. Kadeethum T. Jørgensen H. Nick PINN AI4CE 108 110 0 19 Feb 2020
Hamiltonian neural networks for solving equations of motion M. Mattheakis David Sondak Akshunna S. Dogra P. Protopapas 97 59 0 29 Jan 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 107 214 0 28 Jan 2020
SympNets: Intrinsic structure-preserving symplectic networks for identifying Hamiltonian systems Pengzhan Jin Zhen Zhang Aiqing Zhu Yifa Tang George Karniadakis 105 21 0 11 Jan 2020