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Neural-net-induced Gaussian process regression for function
  approximation and PDE solution

Neural-net-induced Gaussian process regression for function approximation and PDE solution

22 June 2018
G. Pang
Liu Yang
George Karniadakis
ArXiv (abs)PDFHTML

Papers citing "Neural-net-induced Gaussian process regression for function approximation and PDE solution"

22 / 22 papers shown
Title
A general physics-constrained method for the modelling of equation's closure terms with sparse data
A general physics-constrained method for the modelling of equation's closure terms with sparse data
Tian Chen
Shengping Liu
Li Liu
Heng Yong
PINNAI4CE
78
0
0
30 Apr 2025
Muti-Fidelity Prediction and Uncertainty Quantification with Laplace Neural Operators for Parametric Partial Differential Equations
Muti-Fidelity Prediction and Uncertainty Quantification with Laplace Neural Operators for Parametric Partial Differential Equations
Haoyang Zheng
Guang Lin
AI4CE
84
0
0
01 Feb 2025
Gaussian Process Priors for Systems of Linear Partial Differential
  Equations with Constant Coefficients
Gaussian Process Priors for Systems of Linear Partial Differential Equations with Constant Coefficients
Marc Härkönen
Markus Lange-Hegermann
Bogdan Raiță
138
16
0
29 Dec 2022
Learning Skills from Demonstrations: A Trend from Motion Primitives to
  Experience Abstraction
Learning Skills from Demonstrations: A Trend from Motion Primitives to Experience Abstraction
Mehrdad Tavassoli
S. Katyara
Maria Pozzi
Nikhil Deshpande
D. Caldwell
D. Prattichizzo
89
13
0
14 Oct 2022
Spiking Neural Operators for Scientific Machine Learning
Spiking Neural Operators for Scientific Machine Learning
Adar Kahana
Qian Zhang
Leonard Gleyzer
George Karniadakis
65
9
0
17 May 2022
MultiAuto-DeepONet: A Multi-resolution Autoencoder DeepONet for
  Nonlinear Dimension Reduction, Uncertainty Quantification and Operator
  Learning of Forward and Inverse Stochastic Problems
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
PINNAI4CE
64
63
0
16 Mar 2022
On the Correspondence between Gaussian Processes and Geometric Harmonics
On the Correspondence between Gaussian Processes and Geometric Harmonics
Felix Dietrich
J. M. Bello-Rivas
Ioannis G. Kevrekidis
56
3
0
05 Oct 2021
Neural Network Gaussian Processes by Increasing Depth
Neural Network Gaussian Processes by Increasing Depth
Shao-Qun Zhang
Fei Wang
Feng-lei Fan
66
7
0
29 Aug 2021
Interpretable Machine Learning: Fundamental Principles and 10 Grand
  Challenges
Interpretable Machine Learning: Fundamental Principles and 10 Grand Challenges
Cynthia Rudin
Chaofan Chen
Zhi Chen
Haiyang Huang
Lesia Semenova
Chudi Zhong
FaMLAI4CELRM
240
675
0
20 Mar 2021
Learning elliptic partial differential equations with randomized linear
  algebra
Learning elliptic partial differential equations with randomized linear algebra
Nicolas Boullé
Alex Townsend
40
43
0
31 Jan 2021
Multi-fidelity Bayesian Neural Networks: Algorithms and Applications
Multi-fidelity Bayesian Neural Networks: Algorithms and Applications
Xuhui Meng
H. Babaee
George Karniadakis
59
132
0
19 Dec 2020
Neural Network Gaussian Process Considering Input Uncertainty for
  Composite Structures Assembly
Neural Network Gaussian Process Considering Input Uncertainty for Composite Structures Assembly
Cheolhei Lee
Jianguo Wu
Wei Cao
Xiaowei Yue
52
19
0
21 Nov 2020
B-PINNs: Bayesian Physics-Informed Neural Networks for Forward and
  Inverse PDE Problems with Noisy Data
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
SympNets: Intrinsic structure-preserving symplectic networks for
  identifying Hamiltonian systems
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
Constraint-Aware Neural Networks for Riemann Problems
Constraint-Aware Neural Networks for Riemann Problems
Jim Magiera
Deep Ray
J. Hesthaven
C. Rohde
AI4CEPINN
65
60
0
29 Apr 2019
Linking Gaussian Process regression with data-driven manifold embeddings
  for nonlinear data fusion
Linking Gaussian Process regression with data-driven manifold embeddings for nonlinear data fusion
Seungjoon Lee
Felix Dietrich
George Karniadakis
Ioannis G. Kevrekidis
41
38
0
16 Dec 2018
Physics-Informed CoKriging: A Gaussian-Process-Regression-Based
  Multifidelity Method for Data-Model Convergence
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
Physics-Informed Generative Adversarial Networks for Stochastic
  Differential Equations
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
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
Deep Learning of Vortex Induced Vibrations
Deep Learning of Vortex Induced Vibrations
M. Raissi
Zhicheng Wang
M. Triantafyllou
George Karniadakis
AI4CE
81
378
0
26 Aug 2018
Parametric Gaussian Process Regression for Big Data
Parametric Gaussian Process Regression for Big Data
M. Raissi
99
39
0
11 Apr 2017
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