ResearchTrend.AI
  • Communities
  • Connect sessions
  • AI calendar
  • Organizations
  • Join Slack
  • Contact Sales
Papers
Communities
Social Events
Terms and Conditions
Pricing
Contact Sales
Parameter LabParameter LabTwitterGitHubLinkedInBlueskyYoutube

© 2026 ResearchTrend.AI, All rights reserved.

  1. Home
  2. Papers
  3. 2103.10974
  4. Cited By
Learning the solution operator of parametric partial differential
  equations with physics-informed DeepOnets

Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets

Science Advances (Sci Adv), 2021
19 March 2021
Sizhuang He
Hanwen Wang
P. Perdikaris
    AI4CE
ArXiv (abs)PDFHTMLGithub (342★)

Papers citing "Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets"

50 / 379 papers shown
Pontryagin Neural Operator for Solving Parametric General-Sum
  Differential Games
Pontryagin Neural Operator for Solving Parametric General-Sum Differential GamesConference on Learning for Dynamics & Control (L4DC), 2024
Lei Zhang
Mukesh Ghimire
Zhenni Xu
Wenlong Zhang
Yi Ren
205
4
0
03 Jan 2024
DiffHybrid-UQ: Uncertainty Quantification for Differentiable Hybrid
  Neural Modeling
DiffHybrid-UQ: Uncertainty Quantification for Differentiable Hybrid Neural Modeling
Deepak Akhare
Tengfei Luo
Jian-Xun Wang
222
9
0
30 Dec 2023
Operator learning for hyperbolic partial differential equations
Operator learning for hyperbolic partial differential equations
Christopher Wang
Alex Townsend
362
6
0
29 Dec 2023
HyperDeepONet: learning operator with complex target function space
  using the limited resources via hypernetwork
HyperDeepONet: learning operator with complex target function space using the limited resources via hypernetwork
Jae Yong Lee
S. Cho
H. Hwang
255
30
0
26 Dec 2023
A Mathematical Guide to Operator Learning
A Mathematical Guide to Operator Learning
Nicolas Boullé
Alex Townsend
297
68
0
22 Dec 2023
Harnessing the Power of Neural Operators with Automatically Encoded
  Conservation Laws
Harnessing the Power of Neural Operators with Automatically Encoded Conservation Laws
Ning Liu
Yiming Fan
Xianyi Zeng
Milan Klöwer
Lu Zhang
Yue Yu
AI4CE
398
16
0
18 Dec 2023
An approximate operator-based learning method for the numerical
  solutions of stochastic differential equations
An approximate operator-based learning method for the numerical solutions of stochastic differential equations
Jingyuan Li
Wei Liu
135
2
0
13 Dec 2023
NVFi: Neural Velocity Fields for 3D Physics Learning from Dynamic Videos
NVFi: Neural Velocity Fields for 3D Physics Learning from Dynamic Videos
Jinxi Li
Ziyang Song
Bo Yang
3DH
165
28
0
11 Dec 2023
Rethinking materials simulations: Blending direct numerical simulations
  with neural operators
Rethinking materials simulations: Blending direct numerical simulations with neural operatorsnpj Computational Materials (npj Comput Mater), 2023
Vivek Oommen
K. Shukla
Saaketh Desai
Rémi Dingreville
George Karniadakis
AI4CE
231
33
0
08 Dec 2023
Data-efficient operator learning for solving high Mach number fluid flow
  problems
Data-efficient operator learning for solving high Mach number fluid flow problems
Noah Ford
Victor J. Leon
Honest Mrema
Jeffrey Gilbert
Alexander New
AI4CE
219
0
0
28 Nov 2023
B-LSTM-MIONet: Bayesian LSTM-based Neural Operators for Learning the
  Response of Complex Dynamical Systems to Length-Variant Multiple Input
  Functions
B-LSTM-MIONet: Bayesian LSTM-based Neural Operators for Learning the Response of Complex Dynamical Systems to Length-Variant Multiple Input Functions
Zhihao Kong
Amirhossein Mollaali
Christian Moya
Na Lu
Guang Lin
264
3
0
28 Nov 2023
Operator Learning for Continuous Spatial-Temporal Model with
  Gradient-Based and Derivative-Free Optimization Methods
Operator Learning for Continuous Spatial-Temporal Model with Gradient-Based and Derivative-Free Optimization Methods
Chuanqi Chen
Jin-Long Wu
AI4CE
290
13
0
20 Nov 2023
Uncertainty quantification for noisy inputs-outputs in physics-informed
  neural networks and neural operators
Uncertainty quantification for noisy inputs-outputs in physics-informed neural networks and neural operators
Zongren Zou
Xuhui Meng
George Karniadakis
AI4CE
272
35
0
19 Nov 2023
Accurate and Fast Fischer-Tropsch Reaction Microkinetics using PINNs
Accurate and Fast Fischer-Tropsch Reaction Microkinetics using PINNs
Harshil Patel
Aniruddha Panda
T. Nikolaienko
Stanislav Jaso
Alejandro Lopez
Kaushic Kalyanaraman
150
2
0
17 Nov 2023
Stacked networks improve physics-informed training: applications to
  neural networks and deep operator networks
Stacked networks improve physics-informed training: applications to neural networks and deep operator networksFoundations of Data Science (FDS), 2023
Amanda A. Howard
Sarah H. Murphy
Shady E. Ahmed
P. Stinis
AI4CE
293
28
0
11 Nov 2023
Lie Point Symmetry and Physics Informed Networks
Lie Point Symmetry and Physics Informed Networks
Tara Akhound-Sadegh
Laurence Perreault Levasseur
Johannes Brandstetter
Max Welling
Siamak Ravanbakhsh
PINN
188
21
0
07 Nov 2023
A Physics-Guided Bi-Fidelity Fourier-Featured Operator Learning
  Framework for Predicting Time Evolution of Drag and Lift Coefficients
A Physics-Guided Bi-Fidelity Fourier-Featured Operator Learning Framework for Predicting Time Evolution of Drag and Lift CoefficientsFluids (Fluids), 2023
Amirhossein Mollaali
Izzet Sahin
Iqrar Raza
Christian Moya
Guillermo Paniagua
Guang Lin
184
3
0
07 Nov 2023
D2NO: Efficient Handling of Heterogeneous Input Function Spaces with
  Distributed Deep Neural Operators
D2NO: Efficient Handling of Heterogeneous Input Function Spaces with Distributed Deep Neural OperatorsComputer Methods in Applied Mechanics and Engineering (CMAME), 2023
Zecheng Zhang
Christian Moya
Lu Lu
Guang Lin
Hayden Schaeffer
346
20
0
29 Oct 2023
A foundational neural operator that continuously learns without
  forgetting
A foundational neural operator that continuously learns without forgetting
Tapas Tripura
Souvik Chakraborty
CLL
197
10
0
29 Oct 2023
Efficient kernel surrogates for neural network-based regression
Efficient kernel surrogates for neural network-based regression
S. Qadeer
A. Engel
Amanda A. Howard
Adam Tsou
Max Vargas
P. Stinis
Tony Chiang
258
5
0
28 Oct 2023
An operator preconditioning perspective on training in physics-informed
  machine learning
An operator preconditioning perspective on training in physics-informed machine learningInternational Conference on Learning Representations (ICLR), 2023
Tim De Ryck
Florent Bonnet
Siddhartha Mishra
Emmanuel de Bezenac
AI4CE
335
22
0
09 Oct 2023
Physics-aware Machine Learning Revolutionizes Scientific Paradigm for
  Machine Learning and Process-based Hydrology
Physics-aware Machine Learning Revolutionizes Scientific Paradigm for Machine Learning and Process-based Hydrology
Qingsong Xu
Yilei Shi
Jonathan Bamber
Ye Tuo
Ralf Ludwig
Xiao Xiang Zhu
AI4CE
853
19
0
08 Oct 2023
Investigating the Ability of PINNs To Solve Burgers' PDE Near
  Finite-Time BlowUp
Investigating the Ability of PINNs To Solve Burgers' PDE Near Finite-Time BlowUp
Dibyakanti Kumar
Anirbit Mukherjee
240
3
0
08 Oct 2023
Spectral operator learning for parametric PDEs without data reliance
Spectral operator learning for parametric PDEs without data relianceComputer Methods in Applied Mechanics and Engineering (CMAME), 2023
Junho Choi
Taehyun Yun
Namjung Kim
Youngjoon Hong
192
16
0
03 Oct 2023
Deep Learning in Deterministic Computational Mechanics
Deep Learning in Deterministic Computational Mechanics
L. Herrmann
Stefan Kollmannsberger
AI4CEPINN
307
1
0
27 Sep 2023
Neural Operators for Accelerating Scientific Simulations and Design
Neural Operators for Accelerating Scientific Simulations and DesignNature Reviews Physics (Nat. Rev. Phys.), 2023
Kamyar Azzizadenesheli
Nikola B. Kovachki
Zong-Yi Li
Miguel Liu-Schiaffini
Jean Kossaifi
Anima Anandkumar
AI4CE
645
263
0
27 Sep 2023
CFDBench: A Large-Scale Benchmark for Machine Learning Methods in Fluid
  Dynamics
CFDBench: A Large-Scale Benchmark for Machine Learning Methods in Fluid Dynamics
Yining Luo
Yingfa Chen
Zhen Zhang
AI4CE
244
17
0
13 Sep 2023
Physics-informed machine learning of the correlation functions in bulk
  fluids
Physics-informed machine learning of the correlation functions in bulk fluidsThe Physics of Fluids (Phys. Fluids), 2023
Wenqian Chen
Peiyuan Gao
P. Stinis
114
8
0
02 Sep 2023
Scattering with Neural Operators
Scattering with Neural Operators
Sebastian Mizera
AI4CE
275
14
0
28 Aug 2023
Breaking Boundaries: Distributed Domain Decomposition with Scalable
  Physics-Informed Neural PDE Solvers
Breaking Boundaries: Distributed Domain Decomposition with Scalable Physics-Informed Neural PDE SolversInternational Conference for High Performance Computing, Networking, Storage and Analysis (SC), 2023
Arthur Feeney
Zitong Li
Ramin Bostanabad
Aparna Chandramowlishwaran
AI4CE
176
4
0
28 Aug 2023
Learning Only On Boundaries: a Physics-Informed Neural operator for
  Solving Parametric Partial Differential Equations in Complex Geometries
Learning Only On Boundaries: a Physics-Informed Neural operator for Solving Parametric Partial Differential Equations in Complex GeometriesNeural Computation (Neural Comput.), 2023
Z. Fang
Sizhuang He
P. Perdikaris
AI4CE
216
15
0
24 Aug 2023
Adaptive Uncertainty-Guided Model Selection for Data-Driven PDE
  Discovery
Adaptive Uncertainty-Guided Model Selection for Data-Driven PDE DiscoveryIEEE Access (IEEE Access), 2023
Pongpisit Thanasutives
Takashi Morita
M. Numao
Ken-ichi Fukui
269
5
0
20 Aug 2023
On the Approximation of Bi-Lipschitz Maps by Invertible Neural Networks
On the Approximation of Bi-Lipschitz Maps by Invertible Neural NetworksNeural Networks (Neural Netw.), 2023
Bangti Jin
Zehui Zhou
Jun Zou
267
4
0
18 Aug 2023
Physics-Informed Deep Learning to Reduce the Bias in Joint Prediction of
  Nitrogen Oxides
Physics-Informed Deep Learning to Reduce the Bias in Joint Prediction of Nitrogen Oxides
Lianfa Li
Roxana Khalili
F. Lurmann
N. Pavlovic
Jun Wu
...
M. Franklin
T. Bastain
S. Farzan
C. Breton
R. Habre
AI4CE
139
7
0
14 Aug 2023
Fourier neural operator for learning solutions to macroscopic traffic
  flow models: Application to the forward and inverse problems
Fourier neural operator for learning solutions to macroscopic traffic flow models: Application to the forward and inverse problemsTransportation Research Part C: Emerging Technologies (TRC), 2023
Bilal Thonnam Thodi
Sai Venkata Ramana Ambadipudi
Saif Eddin Jabari
AI4CE
348
18
0
14 Aug 2023
PDE-Refiner: Achieving Accurate Long Rollouts with Neural PDE Solvers
PDE-Refiner: Achieving Accurate Long Rollouts with Neural PDE SolversNeural Information Processing Systems (NeurIPS), 2023
Phillip Lippe
Bastiaan S. Veeling
P. Perdikaris
Richard Turner
Johannes Brandstetter
DiffMAI4CE
399
142
0
10 Aug 2023
Fine-Tune Language Models as Multi-Modal Differential Equation Solvers
Fine-Tune Language Models as Multi-Modal Differential Equation SolversNeural Networks (Neural Netw.), 2023
Liu Yang
Siting Liu
Stanley J. Osher
290
0
0
09 Aug 2023
Sound propagation in realistic interactive 3D scenes with parameterized
  sources using deep neural operators
Sound propagation in realistic interactive 3D scenes with parameterized sources using deep neural operatorsProceedings of the National Academy of Sciences of the United States of America (PNAS), 2023
N. Borrel-Jensen
S. Goswami
A. Engsig-Karup
George Karniadakis
C. Jeong
AI4CE
311
26
0
09 Aug 2023
Comparison of Neural FEM and Neural Operator Methods for applications in
  Solid Mechanics
Comparison of Neural FEM and Neural Operator Methods for applications in Solid Mechanics
Stefan Hildebrand
Sandra Klinge
AI4CE
163
7
0
04 Jul 2023
Learning Generic Solutions for Multiphase Transport in Porous Media via
  the Flux Functions Operator
Learning Generic Solutions for Multiphase Transport in Porous Media via the Flux Functions OperatorAdvances in Water Resources (AWR), 2023
W. Diab
Omar Chaabi
Shayma Alkobaisi
A. Awotunde
M. A. Kobaisi
AI4CE
167
10
0
03 Jul 2023
Accelerated primal-dual methods with enlarged step sizes and operator
  learning for nonsmooth optimal control problems
Accelerated primal-dual methods with enlarged step sizes and operator learning for nonsmooth optimal control problems
Yongcun Song
Xiaoming Yuan
Hangrui Yue
AI4CE
232
4
0
01 Jul 2023
Hyena Neural Operator for Partial Differential Equations
Hyena Neural Operator for Partial Differential EquationsAPL Machine Learning (AML), 2023
Saurabh Patil
Zijie Li
Amir Barati Farimani
AI4CE
137
4
0
28 Jun 2023
Capturing the Diffusive Behavior of the Multiscale Linear Transport
  Equations by Asymptotic-Preserving Convolutional DeepONets
Capturing the Diffusive Behavior of the Multiscale Linear Transport Equations by Asymptotic-Preserving Convolutional DeepONetsComputer Methods in Applied Mechanics and Engineering (CMAME), 2023
Keke Wu
Xiongbin Yan
Shi Jin
Zheng Ma
293
8
0
28 Jun 2023
Residual-Based Error Corrector Operator to Enhance Accuracy and
  Reliability of Neural Operator Surrogates of Nonlinear Variational
  Boundary-Value Problems
Residual-Based Error Corrector Operator to Enhance Accuracy and Reliability of Neural Operator Surrogates of Nonlinear Variational Boundary-Value ProblemsComputer Methods in Applied Mechanics and Engineering (CMAME), 2023
Prashant K. Jha
288
8
0
21 Jun 2023
Towards a Machine-Learned Poisson Solver for Low-Temperature Plasma
  Simulations in Complex Geometries
Towards a Machine-Learned Poisson Solver for Low-Temperature Plasma Simulations in Complex Geometries
Ihda Chaerony Siffa
M. Becker
K. Weltmann
J. Trieschmann
138
3
0
13 Jun 2023
Group Equivariant Fourier Neural Operators for Partial Differential
  Equations
Group Equivariant Fourier Neural Operators for Partial Differential EquationsInternational Conference on Machine Learning (ICML), 2023
Jacob Helwig
Xuan Zhang
Cong Fu
Jerry Kurtin
Stephan Wojtowytsch
Shuiwang Ji
AI4CE
260
42
0
09 Jun 2023
An enrichment approach for enhancing the expressivity of neural
  operators with applications to seismology
An enrichment approach for enhancing the expressivity of neural operators with applications to seismology
E. Haghighat
U. Waheed
George Karniadakis
139
0
0
07 Jun 2023
Data driven localized wave solution of the Fokas-Lenells equation using
  modified PINN
Data driven localized wave solution of the Fokas-Lenells equation using modified PINN
G. K. Saharia
Sagardeep Talukdar
Riki Dutta
S. Nandy
104
1
0
03 Jun 2023
CS4ML: A general framework for active learning with arbitrary data based
  on Christoffel functions
CS4ML: A general framework for active learning with arbitrary data based on Christoffel functionsNeural Information Processing Systems (NeurIPS), 2023
Ben Adcock
Juan M. Cardenas
N. Dexter
378
8
0
01 Jun 2023
Scalable Transformer for PDE Surrogate Modeling
Scalable Transformer for PDE Surrogate ModelingNeural Information Processing Systems (NeurIPS), 2023
Zijie Li
Dule Shu
A. Farimani
352
118
0
27 May 2023
Previous
12345678
Next