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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
Principled Approaches for Extending Neural Architectures to Function Spaces for Operator Learning
Principled Approaches for Extending Neural Architectures to Function Spaces for Operator Learning
Julius Berner
Miguel Liu-Schiaffini
Jean Kossaifi
Valentin Duruisseaux
Boris Bonev
Kamyar Azizzadenesheli
A. Anandkumar
AI4CE
382
4
0
12 Jun 2025
FunDiff: Diffusion Models over Function Spaces for Physics-Informed Generative Modeling
FunDiff: Diffusion Models over Function Spaces for Physics-Informed Generative Modeling
Sifan Wang
Zehao Dou
Tong-Rui Liu
Lu Lu
Lu Lu
DiffM
283
11
0
09 Jun 2025
PMNO: A novel physics guided multi-step neural operator predictor for partial differential equations
PMNO: A novel physics guided multi-step neural operator predictor for partial differential equations
Jin Song
Kenji Kawaguchi
Zhenya Yan
AI4CE
268
0
0
02 Jun 2025
Neuro-Symbolic Operator for Interpretable and Generalizable Characterization of Complex Piezoelectric Systems
Neuro-Symbolic Operator for Interpretable and Generalizable Characterization of Complex Piezoelectric Systems
Abhishek Chandra
Taniya Kapoor
M. Curti
K. Tiels
E. Lomonova
186
0
0
30 May 2025
Toward Knowledge-Guided AI for Inverse Design in Manufacturing: A Perspective on Domain, Physics, and Human-AI Synergy
Toward Knowledge-Guided AI for Inverse Design in Manufacturing: A Perspective on Domain, Physics, and Human-AI Synergy
Hugon Lee
Hyeonbin Moon
Junhyeong Lee
Seunghwa RYu
AI4CE
99
2
0
29 May 2025
DeepRTE: Pre-trained Attention-based Neural Network for Radiative Transfer
DeepRTE: Pre-trained Attention-based Neural Network for Radiative Transfer
Yekun Zhu
Min Tang
Zheng Ma
403
0
0
29 May 2025
Dual Natural Gradient Descent for Scalable Training of Physics-Informed Neural Networks
Dual Natural Gradient Descent for Scalable Training of Physics-Informed Neural Networks
Anas Jnini
Flavio Vella
282
2
0
27 May 2025
Spectral-inspired Operator Learning with Limited Data and Unknown Physics
Spectral-inspired Operator Learning with Limited Data and Unknown Physics
Han Wan
Rui Zhang
Hao Sun
AI4CE
374
0
0
27 May 2025
MMET: A Multi-Input and Multi-Scale Transformer for Efficient PDEs Solving
MMET: A Multi-Input and Multi-Scale Transformer for Efficient PDEs SolvingInternational Joint Conference on Artificial Intelligence (IJCAI), 2025
Yichen Luo
Jia Wang
Dapeng Lan
Yu Liu
Zhibo Pang
AI4CE
155
1
0
24 May 2025
Hierarchical-embedding autoencoder with a predictor (HEAP) as efficient architecture for learning long-term evolution of complex multi-scale physical systems
Hierarchical-embedding autoencoder with a predictor (HEAP) as efficient architecture for learning long-term evolution of complex multi-scale physical systems
Alexander Khrabry
Edward Startsev
Andrew Powis
Igor Kaganovich
AI4CE
301
1
0
24 May 2025
Continuum Transformers Perform In-Context Learning by Operator Gradient Descent
Continuum Transformers Perform In-Context Learning by Operator Gradient Descent
Abhiti Mishra
Yash Patel
Ambuj Tewari
301
0
0
23 May 2025
Hamiltonian Neural PDE Solvers through Functional Approximation
Hamiltonian Neural PDE Solvers through Functional Approximation
Anthony Zhou
Amir Barati Farimani
AI4CE
248
0
0
19 May 2025
Beyond Accuracy: EcoL2 Metric for Sustainable Neural PDE Solvers
Beyond Accuracy: EcoL2 Metric for Sustainable Neural PDE Solvers
Taniya Kapoor
Abhishek Chandra
Anastasios Stamou
Stephen J Roberts
255
2
0
18 May 2025
Reinforcement Learning Closures for Underresolved Partial Differential Equations using Synthetic Data
Reinforcement Learning Closures for Underresolved Partial Differential Equations using Synthetic Data
Lothar Heimbach
Sebastian Kaltenbach
Petr Karnakov
Francis J. Alexander
Petros Koumoutsakos
AI4CE
353
1
0
16 May 2025
Spatiotemporal Field Generation Based on Hybrid Mamba-Transformer with Physics-informed Fine-tuning
Spatiotemporal Field Generation Based on Hybrid Mamba-Transformer with Physics-informed Fine-tuning
Peimian Du
Jiabin Liu
Xiaowei Jin
Mengwang Zuo
Hui Li
AI4CE
478
0
0
16 May 2025
Crack Path Prediction with Operator Learning using Discrete Particle System data Generation
Crack Path Prediction with Operator Learning using Discrete Particle System data Generation
Elham Kiyani
Venkatesh Ananchaperumal
Ahmad Peyvan
Mahendaran Uchimali
Gang Li
George Karniadakis
AI4CE
211
0
0
15 May 2025
Sensitivity-Constrained Fourier Neural Operators for Forward and Inverse Problems in Parametric Differential Equations
Sensitivity-Constrained Fourier Neural Operators for Forward and Inverse Problems in Parametric Differential EquationsInternational Conference on Learning Representations (ICLR), 2025
Abdolmehdi Behroozi
Chaopeng Shen and
Daniel Kifer
AI4CE
414
4
0
13 May 2025
Compression, Regularity, Randomness and Emergent Structure: Rethinking Physical Complexity in the Data-Driven Era
Compression, Regularity, Randomness and Emergent Structure: Rethinking Physical Complexity in the Data-Driven Era
Nima Dehghani
AI4CE
382
0
0
12 May 2025
Physics-informed Multiple-Input Operators for efficient dynamic response prediction of structures
Physics-informed Multiple-Input Operators for efficient dynamic response prediction of structuresEngineering applications of artificial intelligence (EAAI), 2025
Bilal Ahmed
Yuqing Qiu
Diab W. Abueidda
Waleed El-Sekelly
Tarek Abdoun
M. Mobasher
AI4CE
217
0
0
11 May 2025
Physics-Informed DeepONets for drift-diffusion on metric graphs: simulation and parameter identification
Physics-Informed DeepONets for drift-diffusion on metric graphs: simulation and parameter identification
J. Blechschmidt
Tom-Christian Riemer
M. Winkler
Martin Stoll
Jan-F. Pietschmann
223
0
0
07 May 2025
Anant-Net: Breaking the Curse of Dimensionality with Scalable and Interpretable Neural Surrogate for High-Dimensional PDEs
Anant-Net: Breaking the Curse of Dimensionality with Scalable and Interpretable Neural Surrogate for High-Dimensional PDEsComputer Methods in Applied Mechanics and Engineering (CMAME), 2025
Sidharth S. Menon
Ameya D. Jagtap
PINN
893
6
0
06 May 2025
PeSANet: Physics-encoded Spectral Attention Network for Simulating PDE-Governed Complex Systems
PeSANet: Physics-encoded Spectral Attention Network for Simulating PDE-Governed Complex SystemsInternational Joint Conference on Artificial Intelligence (IJCAI), 2025
Han Wan
Rui Zhang
Qi Wang
Wenshu Fan
Hao Sun
PINN
245
4
0
03 May 2025
PODNO: Proper Orthogonal Decomposition Neural Operators
PODNO: Proper Orthogonal Decomposition Neural Operators
Zilan Cheng
Zhongjian Wang
Li-Lian Wang
Mejdi Azaiez
218
1
0
25 Apr 2025
Equilibrium Conserving Neural Operators for Super-Resolution Learning
Equilibrium Conserving Neural Operators for Super-Resolution Learning
Vivek Oommen
Andreas E. Robertson
Daniel Diaz
Coleman Alleman
Zhen Zhang
Anthony D. Rollett
George Karniadakis
Rémi Dingreville
268
3
0
18 Apr 2025
DeepOHeat-v1: Efficient Operator Learning for Fast and Trustworthy Thermal Simulation and Optimization in 3D-IC Design
DeepOHeat-v1: Efficient Operator Learning for Fast and Trustworthy Thermal Simulation and Optimization in 3D-IC DesignIEEE Transactions on Components, Packaging, and Manufacturing Technology (TCPMT), 2025
Xinling Yu
Ziyue Liu
Hai Li
Yixing Li
Xin Ai
Zhiyu Zeng
Ian Young
Zheng Zhang
AI4CE
479
1
0
04 Apr 2025
Implicit Neural Differential Model for Spatiotemporal Dynamics
Implicit Neural Differential Model for Spatiotemporal Dynamics
Deepak Akhare
P. Du
Tengfei Luo
Jian-Xun Wang
PINNAI4CE
204
1
0
03 Apr 2025
A discrete physics-informed training for projection-based reduced order models with neural networks
A discrete physics-informed training for projection-based reduced order models with neural networks
N. Sibuet
S. A. D. Parga
J. R. Bravo
R. Rossi
310
3
0
31 Mar 2025
New universal operator approximation theorem for encoder-decoder architectures (Preprint)
New universal operator approximation theorem for encoder-decoder architectures (Preprint)
Janek Gödeke
Pascal Fernsel
210
1
0
31 Mar 2025
Integral regularization PINNs for evolution equations
Integral regularization PINNs for evolution equations
Xiaodong Feng
Haojiong Shangguan
Tao Tang
Xiaoliang Wan
PINN
283
0
0
31 Mar 2025
Enhancing Physics-Informed Neural Networks with a Hybrid Parallel Kolmogorov-Arnold and MLP Architecture
Enhancing Physics-Informed Neural Networks with a Hybrid Parallel Kolmogorov-Arnold and MLP Architecture
Zuyu Xu
Bin Lv
196
4
0
30 Mar 2025
Generative Latent Neural PDE Solver using Flow Matching
Generative Latent Neural PDE Solver using Flow Matching
Zijie Li
Anthony Zhou
Amir Barati Farimani
DiffMAI4CE
316
12
0
28 Mar 2025
Uncertainty propagation in feed-forward neural network models
Uncertainty propagation in feed-forward neural network modelsNeural Networks (NN), 2025
Jeremy Diamzon
Daniele Venturi
392
1
0
27 Mar 2025
EquiNO: A Physics-Informed Neural Operator for Multiscale Simulations
EquiNO: A Physics-Informed Neural Operator for Multiscale Simulations
Hamidreza Eivazi
Jendrik-Alexander Tröger
Stefan H. A. Wittek
Stefan Hartmann
Andreas Rausch
AI4CE
434
2
0
27 Mar 2025
HyperNOs: Automated and Parallel Library for Neural Operators Research
HyperNOs: Automated and Parallel Library for Neural Operators Research
Massimiliano Ghiotto
302
1
0
23 Mar 2025
Scalable physics-informed deep generative model for solving forward and inverse stochastic differential equations
Scalable physics-informed deep generative model for solving forward and inverse stochastic differential equations
Shaoqian Zhou
Wen You
Ling Guo
Xuhui Meng
DiffMMedIm
320
1
0
23 Mar 2025
Enhancing Fourier Neural Operators with Local Spatial Features
Enhancing Fourier Neural Operators with Local Spatial Features
Chaoyu Liu
Davide Murari
Chris Budd
Lihao Liu
Carola-Bibiane Schönlieb
Carola-Bibiane Schönlieb
AI4CE
321
9
0
22 Mar 2025
Physics-Informed Deep B-Spline Networks
Physics-Informed Deep B-Spline Networks
Zhuoyuan Wang
Raffaele Romagnoli
Jasmine Ratchford
Yorie Nakahira
PINNAI4CE
261
1
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21 Mar 2025
Enhanced Vascular Flow Simulations in Aortic Aneurysm via Physics-Informed Neural Networks and Deep Operator Networks
Enhanced Vascular Flow Simulations in Aortic Aneurysm via Physics-Informed Neural Networks and Deep Operator Networks
Oscar L. Cruz-González
Valérie Deplano
Badih Ghattas
MedImAI4CE
221
1
0
19 Mar 2025
StFT: Spatio-temporal Fourier Transformer for Long-term Dynamics Prediction
StFT: Spatio-temporal Fourier Transformer for Long-term Dynamics Prediction
Da Long
Shandian Zhe
Samuel Williams
L. Oliker
Zhe Bai
AI4TSAI4CE
344
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0
14 Mar 2025
Identifying Trustworthiness Challenges in Deep Learning Models for Continental-Scale Water Quality Prediction
Identifying Trustworthiness Challenges in Deep Learning Models for Continental-Scale Water Quality Prediction
Xiaobo Xia
Xiaofeng Liu
Jiale Liu
K. Fang
Lu Lu
Samet Oymak
William S. Currie
Tongliang Liu
408
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Symbolic Neural Ordinary Differential EquationsAAAI Conference on Artificial Intelligence (AAAI), 2025
Xin Li
Chengli Zhao
Xue Zhang
Xiaojun Duan
284
3
0
11 Mar 2025
Parametric Value Approximation for General-sum Differential Games with State Constraints
Lei Zhang
Mukesh Ghimire
Wenlong Zhang
Z. Xu
Yi Ren
261
0
0
10 Mar 2025
Data-Driven Probabilistic Air-Sea Flux Parameterization
Data-Driven Probabilistic Air-Sea Flux Parameterization
Jiarong Wu
Pavel Perezhogin
D. Gagne
Brandon Reichl
Aneesh C. Subramanian
Elizabeth Thompson
Laure Zanna
360
0
0
06 Mar 2025
Cauchy Random Features for Operator Learning in Sobolev Space
Cauchy Random Features for Operator Learning in Sobolev Space
Chunyang Liao
Deanna Needell
Hayden Schaeffer
438
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DeepONet Augmented by Randomized Neural Networks for Efficient Operator Learning in PDEs
Zhaoxi Jiang
Fei Wang
247
0
0
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Finite Element Operator Network for Solving Elliptic-type parametric PDEs
Finite Element Operator Network for Solving Elliptic-type parametric PDEsSIAM Journal on Scientific Computing (SISC), 2023
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Seungchan Ko
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428
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Machine learning for modelling unstructured grid data in computational physics: a review
Machine learning for modelling unstructured grid data in computational physics: a reviewInformation Fusion (Inf. Fusion), 2025
Sibo Cheng
Marc Bocquet
Weiping Ding
Tobias S. Finn
Rui Fu
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Yong Zeng
Mingrui Zhang
Hao Zhou
Kewei Zhu
Rossella Arcucci
PINNAI4CE
553
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DGenNO: A Novel Physics-aware Neural Operator for Solving Forward and Inverse PDE Problems based on Deep, Generative Probabilistic Modeling
DGenNO: A Novel Physics-aware Neural Operator for Solving Forward and Inverse PDE Problems based on Deep, Generative Probabilistic ModelingJournal of Computational Physics (JCP), 2025
Yaohua Zang
P. Koutsourelakis
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533
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Pseudo-Physics-Informed Neural Operators: Enhancing Operator Learning from Limited Data
Pseudo-Physics-Informed Neural Operators: Enhancing Operator Learning from Limited Data
Keyan Chen
Yile Li
Da Long
Zhitong Xu
Wei W. Xing
Jacob Hochhalter
Shandian Zhe
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146
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Transfer Learning in Physics-Informed Neural Networks: Full Fine-Tuning, Lightweight Fine-Tuning, and Low-Rank Adaptation
Transfer Learning in Physics-Informed Neural Networks: Full Fine-Tuning, Lightweight Fine-Tuning, and Low-Rank AdaptationInternational Journal of Mechanical System Dynamics (IJMSD), 2025
Yizheng Wang
Jinshuai Bai
M. Eshaghi
C. Anitescu
X. Zhuang
Timon Rabczuk
Yinghua Liu
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359
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