Model Reduction and Neural Networks for Parametric PDEs

7 May 2020

Papers citing "Model Reduction and Neural Networks for Parametric PDEs"

50 / 51 papers shown

Title
PODNO: Proper Orthogonal Decomposition Neural Operators Zilan Cheng Zhongjian Wang Li-Lian Wang Mejdi Azaiez 34 0 0 25 Apr 2025
EquiNO: A Physics-Informed Neural Operator for Multiscale Simulations Hamidreza Eivazi Jendrik-Alexander Tröger Stefan H. A. Wittek Stefan Hartmann Andreas Rausch AI4CE 43 0 0 27 Mar 2025
Data-Efficient Kernel Methods for Learning Differential Equations and Their Solution Operators: Algorithms and Error Analysis Yasamin Jalalian Juan Felipe Osorio Ramirez Alexander W. Hsu Bamdad Hosseini H. Owhadi 43 0 0 02 Mar 2025
Verification and Validation for Trustworthy Scientific Machine Learning John D. Jakeman Lorena A. Barba J. Martins Thomas O'Leary-Roseberry AI4CE 58 0 0 21 Feb 2025
Mamba Neural Operator: Who Wins? Transformers vs. State-Space Models for PDEs Chun-Wun Cheng Jiahao Huang Yi Zhang Guang Yang Carola-Bibiane Schonlieb Angelica I Aviles-Rivero Mamba AI4CE 90 2 0 03 Oct 2024
Neural Operator-Based Proxy for Reservoir Simulations Considering Varying Well Settings, Locations, and Permeability Fields Daniel Badawi Eduardo Gildin OOD AI4CE 15 4 0 13 Jul 2024
A fast neural hybrid Newton solver adapted to implicit methods for nonlinear dynamics Tianyu Jin G. Maierhofer Katharina Schratz Yang Xiang 36 1 0 04 Jul 2024
Coupled Input-Output Dimension Reduction: Application to Goal-oriented Bayesian Experimental Design and Global Sensitivity Analysis Qiao Chen Elise Arnaud Ricardo Baptista O. Zahm 40 1 0 19 Jun 2024
Physics-Aware Neural Implicit Solvers for multiscale, parametric PDEs with applications in heterogeneous media Matthaios Chatzopoulos P. Koutsourelakis AI4CE 39 3 0 29 May 2024
Efficient Prior Calibration From Indirect Data O. Deniz Akyildiz M. Girolami Andrew M. Stuart A. Vadeboncoeur 38 1 0 28 May 2024
Discretization Error of Fourier Neural Operators S. Lanthaler Andrew M. Stuart Margaret Trautner 39 4 0 03 May 2024
Generalization Error Guaranteed Auto-Encoder-Based Nonlinear Model Reduction for Operator Learning Hao Liu Biraj Dahal Rongjie Lai Wenjing Liao AI4CE 28 5 0 19 Jan 2024
Nonlinear functional regression by functional deep neural network with kernel embedding Zhongjie Shi Jun Fan Linhao Song Ding-Xuan Zhou Johan A. K. Suykens 54 5 0 05 Jan 2024
Generating synthetic data for neural operators Erisa Hasani Rachel A. Ward AI4CE 47 8 0 04 Jan 2024
GIT-Net: Generalized Integral Transform for Operator Learning Chao Wang Alexandre H. Thiery AI4CE 31 0 0 05 Dec 2023
Inverse Problems with Learned Forward Operators Simon Arridge Andreas Hauptmann Yury Korolev 31 1 0 21 Nov 2023
Geometry-Informed Neural Operator for Large-Scale 3D PDEs Zong-Yi Li Nikola B. Kovachki Chris Choy Boyi Li Jean Kossaifi ... M. A. Nabian Maximilian Stadler Christian Hundt Kamyar Azizzadenesheli Anima Anandkumar AI4CE 34 131 0 01 Sep 2023
Capturing Local Temperature Evolution during Additive Manufacturing through Fourier Neural Operators Jiangce Chen Wenzhuo Xu Martha Baldwin Björn Nijhuis T. Boogaard Noelia Grande Gutiérrez S. Narra Christopher McComb AI4CE 20 2 0 04 Jul 2023
Error Bounds for Learning with Vector-Valued Random Features S. Lanthaler Nicholas H. Nelsen 27 12 0 26 May 2023
Nonlocality and Nonlinearity Implies Universality in Operator Learning S. Lanthaler Zong-Yi Li Andrew M. Stuart 20 16 0 26 Apr 2023
In-Context Operator Learning with Data Prompts for Differential Equation Problems Liu Yang Siting Liu Tingwei Meng Stanley J. Osher 38 57 0 17 Apr 2023
Coupled Multiwavelet Neural Operator Learning for Coupled Partial Differential Equations Xiongye Xiao De-An Cao Ruochen Yang Gaurav Gupta Gengshuo Liu Chenzhong Yin R. Balan P. Bogdan 66 9 0 04 Mar 2023
Variational Autoencoding Neural Operators Jacob H. Seidman Georgios Kissas George J. Pappas P. Perdikaris DRL AI4CE 27 7 0 20 Feb 2023
An Enhanced V-cycle MgNet Model for Operator Learning in Numerical Partial Differential Equations Jianqing Zhu Juncai He Qiumei Huang 30 4 0 02 Feb 2023
Learning Functional Transduction Mathieu Chalvidal Thomas Serre Rufin VanRullen AI4CE 35 2 0 01 Feb 2023
L-HYDRA: Multi-Head Physics-Informed Neural Networks Zongren Zou George Karniadakis AI4CE 18 26 0 05 Jan 2023
KoopmanLab: machine learning for solving complex physics equations Wei Xiong Muyuan Ma Xiaomeng Huang Ziyang Zhang Pei Sun Yang Tian AI4CE 26 13 0 03 Jan 2023
Exploring Physical Latent Spaces for High-Resolution Flow Restoration Chloé Paliard Nils Thuerey Kiwon Um AI4CE 15 0 0 21 Nov 2022
Physics-Guided, Physics-Informed, and Physics-Encoded Neural Networks in Scientific Computing Salah A. Faroughi N. Pawar C. Fernandes Maziar Raissi Subasish Das N. Kalantari S. K. Mahjour PINN AI4CE 27 48 0 14 Nov 2022
Neuro-symbolic partial differential equation solver Pouria A. Mistani Samira Pakravan Rajesh Ilango S. Choudhry Frédéric Gibou 31 1 0 25 Oct 2022
JAX-DIPS: Neural bootstrapping of finite discretization methods and application to elliptic problems with discontinuities Pouria A. Mistani Samira Pakravan Rajesh Ilango Frédéric Gibou 16 8 0 25 Oct 2022
Nonlinear Reconstruction for Operator Learning of PDEs with Discontinuities S. Lanthaler Roberto Molinaro Patrik Hadorn Siddhartha Mishra 48 24 0 03 Oct 2022
Limitations of neural network training due to numerical instability of backpropagation Clemens Karner V. Kazeev P. Petersen 32 3 0 03 Oct 2022
Minimax Optimal Kernel Operator Learning via Multilevel Training Jikai Jin Yiping Lu Jose H. Blanchet Lexing Ying 23 11 0 28 Sep 2022
Approximate Bayesian Neural Operators: Uncertainty Quantification for Parametric PDEs Emilia Magnani Nicholas Kramer Runa Eschenhagen Lorenzo Rosasco Philipp Hennig UQCV BDL 13 9 0 02 Aug 2022
Derivative-Informed Neural Operator: An Efficient Framework for High-Dimensional Parametric Derivative Learning Thomas O'Leary-Roseberry Peng Chen Umberto Villa Omar Ghattas AI4CE 32 39 0 21 Jun 2022
NOMAD: Nonlinear Manifold Decoders for Operator Learning Jacob H. Seidman Georgios Kissas P. Perdikaris George J. Pappas AI4CE 29 68 0 07 Jun 2022
Approximation of Functionals by Neural Network without Curse of Dimensionality Yahong Yang Yang Xiang 21 6 0 28 May 2022
Transformer for Partial Differential Equations' Operator Learning Zijie Li Kazem Meidani A. Farimani 42 140 0 26 May 2022
Neural Operator with Regularity Structure for Modeling Dynamics Driven by SPDEs Peiyan Hu Qi Meng Bin Chen Shiqi Gong Yue Wang Wei Chen Rongchan Zhu Zhirui Ma Tie-Yan Liu AI4CE 21 11 0 13 Apr 2022
MIONet: Learning multiple-input operators via tensor product Pengzhan Jin Shuai Meng Lu Lu 20 155 0 12 Feb 2022
Learning Operators with Coupled Attention Georgios Kissas Jacob H. Seidman Leonardo Ferreira Guilhoto V. Preciado George J. Pappas P. Perdikaris 24 109 0 04 Jan 2022
Factorized Fourier Neural Operators Alasdair Tran A. Mathews Lexing Xie Cheng Soon Ong AI4CE 26 141 0 27 Nov 2021
slimTrain -- A Stochastic Approximation Method for Training Separable Deep Neural Networks Elizabeth Newman Julianne Chung Matthias Chung Lars Ruthotto 39 6 0 28 Sep 2021
Choose a Transformer: Fourier or Galerkin Shuhao Cao 39 221 0 31 May 2021
Two-layer neural networks with values in a Banach space Yury Korolev 21 23 0 05 May 2021
Machine learning accelerated computational fluid dynamics Dmitrii Kochkov Jamie A. Smith Ayya Alieva Qing Wang M. Brenner Stephan Hoyer AI4CE 34 826 0 28 Jan 2021
POD-DL-ROM: enhancing deep learning-based reduced order models for nonlinear parametrized PDEs by proper orthogonal decomposition S. Fresca Andrea Manzoni AI4CE 18 212 0 28 Jan 2021
Calibration and Uncertainty Quantification of Convective Parameters in an Idealized GCM Oliver R. A. Dunbar A. Garbuno-Iñigo T. Schneider Andrew M. Stuart 17 58 0 24 Dec 2020
Fourier Neural Operator for Parametric Partial Differential Equations Zong-Yi Li Nikola B. Kovachki Kamyar Azizzadenesheli Burigede Liu K. Bhattacharya Andrew M. Stuart Anima Anandkumar AI4CE 205 2,287 0 18 Oct 2020