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

Science Advances (Sci Adv), 2021

19 March 2021

ArXiv (abs)PDF HTML Github (342★)

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

50 / 379 papers shown

Title
Reference Neural Operators: Learning the Smooth Dependence of Solutions of PDEs on Geometric Deformations Ze Cheng Zhongkai Hao Xiaoqiang Wang Jianing Huang Youjia Wu Xudan Liu Yiru Zhao Songming Liu Hang Su AI4CE 138 5 0 27 May 2024
Spectral-Refiner: Accurate Fine-Tuning of Spatiotemporal Fourier Neural Operator for Turbulent Flows Shuhao Cao Francesco Brarda Ruipeng Li Yuanzhe Xi 362 0 0 27 May 2024
A finite element-based physics-informed operator learning framework for spatiotemporal partial differential equations on arbitrary domains Yusuke Yamazaki Ali Harandi Mayu Muramatsu A. Viardin Markus Apel T. Brepols Stefanie Reese Shahed Rezaei AI4CE 333 24 0 21 May 2024
PTPI-DL-ROMs: pre-trained physics-informed deep learning-based reduced order models for nonlinear parametrized PDEsComputer Methods in Applied Mechanics and Engineering (CMAME), 2024 Simone Brivio S. Fresca Andrea Manzoni AI4CE 270 11 0 14 May 2024
Generative flow induced neural architecture search: Towards discovering optimal architecture in wavelet neural operator Hartej Soin Tapas Tripura Souvik Chakraborty 201 3 0 11 May 2024
Introducing a microstructure-embedded autoencoder approach for reconstructing high-resolution solution field data from a reduced parametric spaceComputational Mechanics (CM), 2024 Rasoul Najafi Koopas Shahed Rezaei N. Rauter Richard Ostwald R. Lammering AI4CE 232 6 0 03 May 2024
Towards General Neural Surrogate Solvers with Specialized Neural AcceleratorsInternational Conference on Machine Learning (ICML), 2024 Chenkai Mao Robert Lupoiu Tianxiang Dai Mingkun Chen Jonathan A. Fan AI4CE 262 8 0 02 May 2024
Error analysis for finite element operator learning methods for solving parametric second-order elliptic PDEs Youngjoon Hong Seungchan Ko Jae Yong Lee 204 4 0 27 Apr 2024
BiLO: Bilevel Local Operator Learning for PDE Inverse Problems. Part I: PDE-Constrained Optimization Ray Zirui Zhang Christopher E. Miles Xiaohui Xie John S. Lowengrub 451 5 0 27 Apr 2024
Neural Operator induced Gaussian Process framework for probabilistic solution of parametric partial differential equations Sawan Kumar R. Nayek Souvik Chakraborty 214 7 0 24 Apr 2024
TENG: Time-Evolving Natural Gradient for Solving PDEs With Deep Neural Nets Toward Machine Precision Zhuo Chen Jacob McCarran Esteban Vizcaino Marin Soljacic Di Luo AI4CE 178 6 0 16 Apr 2024
Composite Bayesian Optimization In Function Spaces Using NEON -- Neural Epistemic Operator NetworksScientific Reports (Sci Rep), 2024 Leonardo Ferreira Guilhoto P. Perdikaris BDL 270 5 0 03 Apr 2024
MODNO: Multi Operator Learning With Distributed Neural OperatorsComputer Methods in Applied Mechanics and Engineering (CMAME), 2024 Zecheng Zhang 435 15 0 03 Apr 2024
A finite operator learning technique for mapping the elastic properties of microstructures to their mechanical deformations Shahed Rezaei Reza Najian Asl S. Faroughi Mahdi Asgharzadeh Ali Harandi Rasoul Najafi Koopas G. Laschet Stefanie Reese Markus Apel AI4CE 303 13 0 28 Mar 2024
SineNet: Learning Temporal Dynamics in Time-Dependent Partial Differential Equations Xuan Zhang Jacob Helwig Yu-Ching Lin Yaochen Xie Cong Fu Stephan Wojtowytsch Shuiwang Ji AI4CE 329 10 0 28 Mar 2024
Knowledge-guided Machine Learning: Current Trends and Future Prospects Anuj Karpatne X. Jia Vipin Kumar 282 22 0 24 Mar 2024
Neural Parameter Regression for Explicit Representations of PDE Solution Operators Konrad Mundinger Max Zimmer Sebastian Pokutta 242 1 0 19 Mar 2024
Adaptive Multilevel Neural Networks for Parametric PDEs with Error Estimation Janina Enrica Schutte Martin Eigel AI4CE 193 2 0 19 Mar 2024
Large-scale flood modeling and forecasting with FloodCastWater Research (Water Res.), 2024 Qingsong Xu Yilei Shi Jonathan Bamber Chaojun Ouyang Xiao Xiang Zhu AI4CE 193 37 0 18 Mar 2024
Approximation of RKHS Functionals by Neural Networks Tiancong Zhou Namjoon Suh Guang Cheng Xiaoming Huo 201 5 0 18 Mar 2024
A Pretraining-Finetuning Computational Framework for Material Homogenization Yizheng Wang Xiang Li Ziming Yan Yuqing Du Jinshuai Bai Bokai Liu Timon Rabczuk Yinghua Liu AI4CE 115 0 0 18 Mar 2024
A Framework for Strategic Discovery of Credible Neural Network Surrogate Models under UncertaintyComputer Methods in Applied Mechanics and Engineering (CMAME), 2024 Pratyush Kumar Singh Kathryn A. Farrell-Maupin D. Faghihi 292 12 0 13 Mar 2024
DPOT: Auto-Regressive Denoising Operator Transformer for Large-Scale PDE Pre-Training Zhongkai Hao Yan Yu Songming Liu Julius Berner Chengyang Ying Hang Su A. Anandkumar Jian Song Jun Zhu AI4TS AI4CE 345 76 0 06 Mar 2024
Macroscopic auxiliary asymptotic preserving neural networks for the linear radiative transfer equations Hongyan Li Song Jiang Wenjun Sun Liwei Xu Guanyu Zhou 182 5 0 04 Mar 2024
Hybrid data-driven and physics-informed regularized learning of cyclic plasticity with Neural Networks Stefan Hildebrand Sandra Klinge 156 4 0 04 Mar 2024
BP-DeepONet: A new method for cuffless blood pressure estimation using the physcis-informed DeepONet Lingfeng Li Xue-Cheng Tai Raymond H. F. Chan 188 3 0 29 Feb 2024
Latent Neural PDE Solver: a reduced-order modelling framework for partial differential equations Zijie Li Saurabh Patil Francis Ogoke Dule Shu Wilson Zhen Michael Schneier John R. Buchanan A. Farimani AI4CE 265 7 0 27 Feb 2024
A novel data generation scheme for surrogate modelling with deep operator networks Shivam Choubey Birupaksha Pal Manish Agrawal AI4CE 116 1 0 24 Feb 2024
Smooth and Sparse Latent Dynamics in Operator Learning with Jerk Regularization Xiaoyu Xie S. Mowlavi M. Benosman AI4CE 239 3 0 23 Feb 2024
Learning solution operators of PDEs defined on varying domains via MIONet Shanshan Xiao Pengzhan Jin Yifa Tang 268 6 0 23 Feb 2024
Deep adaptive sampling for surrogate modeling without labeled data Xili Wang Keju Tang Jiayu Zhai Xiaoliang Wan Chao Yang 150 7 0 17 Feb 2024
Kolmogorov n-Widths for Multitask Physics-Informed Machine Learning (PIML) Methods: Towards Robust Metrics Michael Penwarden H. Owhadi Robert M. Kirby AI4CE 160 3 0 16 Feb 2024
Neural Operators Meet Energy-based Theory: Operator Learning for Hamiltonian and Dissipative PDEs Yusuke Tanaka Takaharu Yaguchi Tomoharu Iwata N. Ueda AI4CE 360 0 0 14 Feb 2024
Approximating Families of Sharp Solutions to Fisher's Equation with Physics-Informed Neural Networks Franz M. Rohrhofer S. Posch C. Gößnitzer Bernhard C. Geiger 162 6 0 13 Feb 2024
Learning time-dependent PDE via graph neural networks and deep operator network for robust accuracy on irregular grids S. Cho Jae Yong Lee Hyung Ju Hwang GNN AI4CE 208 7 0 13 Feb 2024
A hybrid iterative method based on MIONet for PDEs: Theory and numerical examples Jun Hu Pengzhan Jin 197 15 0 11 Feb 2024
Reduced-order modeling of unsteady fluid flow using neural network ensembles Rakesh Halder Mohammadmehdi Ataei H. Salehipour Krzysztof J. Fidkowski Kevin J. Maki AI4CE 172 13 0 08 Feb 2024
HAMLET: Graph Transformer Neural Operator for Partial Differential EquationsInternational Conference on Machine Learning (ICML), 2024 Andrey Bryutkin Jiahao Huang Zhongying Deng Guang Yang Carola-Bibiane Schönlieb Angelica E. Avilés-Rivero 190 17 0 05 Feb 2024
Learning solutions of parametric Navier-Stokes with physics-informed neural networks M. Naderibeni Marcel J. T. Reinders L. Wu David Tax PINN 170 5 0 05 Feb 2024
Challenges in Training PINNs: A Loss Landscape Perspective Pratik Rathore Weimu Lei Zachary Frangella Lu Lu Madeleine Udell AI4CE PINN ODL 241 107 0 02 Feb 2024
Closure Discovery for Coarse-Grained Partial Differential Equations Using Grid-based Reinforcement Learning Jan-Philipp von Bassewitz Sebastian Kaltenbach Petros Koumoutsakos AI4CE 417 2 0 01 Feb 2024
Operator learning without the adjoint Nicolas Boullé Diana Halikias Samuel E. Otto Alex Townsend 145 9 0 31 Jan 2024
Ricci flow-guided autoencoders in learning time-dependent dynamics Andrew Gracyk AI4CE 488 2 0 26 Jan 2024
Approximation of Solution Operators for High-dimensional PDEs Nathan Gaby Xiaojing Ye 204 0 0 18 Jan 2024
RiemannONets: Interpretable Neural Operators for Riemann ProblemsComputer Methods in Applied Mechanics and Engineering (CMAME), 2024 Ahmad Peyvan Vivek Oommen Ameya Dilip Jagtap George Karniadakis AI4CE 236 39 0 16 Jan 2024
PDE Generalization of In-Context Operator Networks: A Study on 1D Scalar Nonlinear Conservation LawsJournal of Computational Physics (JCP), 2024 Liu Yang Stanley J. Osher AI4CE 327 27 0 14 Jan 2024
Peridynamic Neural Operators: A Data-Driven Nonlocal Constitutive Model for Complex Material ResponsesComputer Methods in Applied Mechanics and Engineering (CMAME), 2024 S. Jafarzadeh Stewart Silling Ning Liu Zhongqiang Zhang Yue Yu AI4CE 260 33 0 11 Jan 2024
Gain Scheduling with a Neural Operator for a Transport PDE with Nonlinear Recirculation Maxence Lamarque Luke Bhan R. Vázquez Miroslav Krstic 185 14 0 04 Jan 2024
Integration of physics-informed operator learning and finite element method for parametric learning of partial differential equations Shahed Rezaei Ahmad Moeineddin Michael Kaliske Markus Apel AI4CE 260 5 0 04 Jan 2024
Generating synthetic data for neural operatorsSMAI Journal of Computational Mathematics (SMAI-JCM), 2024 Erisa Hasani Rachel A. Ward AI4CE 517 11 0 04 Jan 2024