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Model Reduction and Neural Networks for Parametric PDEs

7 May 2020

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

28 / 28 papers shown

Title
Operator Learning for Schrödinger Equation: Unitarity, Error Bounds, and Time Generalization Yash Patel Unique Subedi Ambuj Tewari 46 0 0 23 May 2025
EquiNO: A Physics-Informed Neural Operator for Multiscale Simulations Hamidreza Eivazi Jendrik-Alexander Tröger Stefan H. A. Wittek Stefan Hartmann Andreas Rausch AI4CE 95 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 169 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 120 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 127 5 0 03 Oct 2024
A fast neural hybrid Newton solver adapted to implicit methods for nonlinear dynamics Tianyu Jin G. Maierhofer Katharina Schratz Yang Xiang 171 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 86 1 0 19 Jun 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 472 5 0 05 Jan 2024
Generating synthetic data for neural operators Erisa Hasani Rachel A. Ward AI4CE 128 8 0 04 Jan 2024
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 126 9 0 04 Mar 2023
Multipole Graph 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 216 395 0 16 Jun 2020
Numerical Solution of the Parametric Diffusion Equation by Deep Neural Networks Moritz Geist P. Petersen Mones Raslan R. Schneider Gitta Kutyniok 80 83 0 25 Apr 2020
On the convergence of physics informed neural networks for linear second-order elliptic and parabolic type PDEs Yeonjong Shin Jérome Darbon George Karniadakis PINN 67 79 0 03 Apr 2020
EikoNet: Solving the Eikonal equation with Deep Neural Networks Jonathan D. Smith Kamyar Azizzadenesheli Zachary E. Ross 42 132 0 25 Mar 2020
Neural Operator: Graph Kernel Network for Partial Differential Equations Zong-Yi Li Nikola B. Kovachki Kamyar Azizzadenesheli Burigede Liu K. Bhattacharya Andrew M. Stuart Anima Anandkumar 202 748 0 07 Mar 2020
A comprehensive deep learning-based approach to reduced order modeling of nonlinear time-dependent parametrized PDEs S. Fresca Luca Dede' Andrea Manzoni AI4CE 73 265 0 12 Jan 2020
Lift & Learn: Physics-informed machine learning for large-scale nonlinear dynamical systems E. Qian Boris Kramer Benjamin Peherstorfer Karen E. Willcox AI4CE 89 267 0 17 Dec 2019
DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operators Lu Lu Pengzhan Jin George Karniadakis 248 2,150 0 08 Oct 2019
Regression-clustering for Improved Accuracy and Training Cost with Molecular-Orbital-Based Machine Learning Lixue Cheng Nikola B. Kovachki Matthew Welborn Thomas F. Miller 51 45 0 04 Sep 2019
Learning Neural PDE Solvers with Convergence Guarantees Jun-Ting Hsieh Shengjia Zhao Stephan Eismann L. Mirabella Stefano Ermon AI4CE 61 145 0 04 Jun 2019
Nonlinear Approximation and (Deep) ReLU Networks Ingrid Daubechies Ronald A. DeVore S. Foucart Boris Hanin G. Petrova 100 142 0 05 May 2019
A Discussion on Solving Partial Differential Equations using Neural Networks Tim Dockhorn 44 62 0 15 Apr 2019
A Theoretical Analysis of Deep Neural Networks and Parametric PDEs Gitta Kutyniok P. Petersen Mones Raslan R. Schneider 87 198 0 31 Mar 2019
Deep Neural Networks Motivated by Partial Differential Equations Lars Ruthotto E. Haber AI4CE 124 491 0 12 Apr 2018
Bayesian Deep Convolutional Encoder-Decoder Networks for Surrogate Modeling and Uncertainty Quantification Yinhao Zhu N. Zabaras UQCV BDL 111 646 0 21 Jan 2018
The Deep Ritz method: A deep learning-based numerical algorithm for solving variational problems E. Weinan Ting Yu 123 1,389 0 30 Sep 2017
Self-Normalizing Neural Networks Günter Klambauer Thomas Unterthiner Andreas Mayr Sepp Hochreiter 466 2,518 0 08 Jun 2017
Besov priors for Bayesian inverse problems Masoumeh Dashti Stephen Harris Andrew M. Stuart 89 119 0 04 May 2011