Transformer for Partial Differential Equations' Operator Learning

26 May 2022

Papers citing "Transformer for Partial Differential Equations' Operator Learning"

50 / 79 papers shown

Title
State-space models are accurate and efficient neural operators for dynamical systems Zheyuan Hu Nazanin Ahmadi Daryakenari Qianli Shen Kenji Kawaguchi George Karniadakis Mamba AI4CE 113 15 0 28 Jan 2025
Harnessing Scale and Physics: A Multi-Graph Neural Operator Framework for PDEs on Arbitrary Geometries Zhihao Li Haoze Song Di Xiao Zhilu Lai Wei Wang AI4CE 152 3 0 18 Nov 2024
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 106 4 0 03 Oct 2024
PhyMPGN: Physics-encoded Message Passing Graph Network for spatiotemporal PDE systems Bocheng Zeng Qi Wang Ming Yan Yang Liu Ruizhi Chengze Yi Zhang Hongsheng Liu Zidong Wang Hao Sun AI4CE 100 3 0 02 Oct 2024
Integrating Neural Operators with Diffusion Models Improves Spectral Representation in Turbulence Modeling Vivek Oommen Aniruddha Bora Zhen Zhang George Karniadakis DiffM 74 15 0 13 Sep 2024
Stochastic Optimal Control for Diffusion Bridges in Function Spaces Byoungwoo Park Jungwon Choi Sungbin Lim Juho Lee 61 3 0 31 May 2024
Leveraging Interpolation Models and Error Bounds for Verifiable Scientific Machine Learning Tyler Chang Andrew Gillette R. Maulik 111 2 0 04 Apr 2024
Universal Physics Transformers: A Framework For Efficiently Scaling Neural Operators Benedikt Alkin Andreas Fürst Simon Schmid Lukas Gruber Markus Holzleitner Johannes Brandstetter PINN AI4CE 108 11 0 19 Feb 2024
Invertible Fourier Neural Operators for Tackling Both Forward and Inverse Problems Da Long Zhitong Xu Qiwei Yuan Yin Yang Shandian Zhe AI4CE 119 5 0 18 Feb 2024
Monte Carlo Neural PDE Solver for Learning PDEs via Probabilistic Representation Rui Zhang Qi Meng Rongchan Zhu Yue Wang Wenlei Shi Shihua Zhang Zhi-Ming Ma Tie-Yan Liu DiffM AI4CE 80 5 0 10 Feb 2023
Learning the Solution Operator of Boundary Value Problems using Graph Neural Networks Winfried Lotzsch Simon Ohler Johannes Otterbach AI4CE 36 18 0 28 Jun 2022
Wavelet neural operator: a neural operator for parametric partial differential equations Tapas Tripura S. Chakraborty 40 63 0 04 May 2022
U-NO: U-shaped Neural Operators Md Ashiqur Rahman Zachary E. Ross Kamyar Azizzadenesheli AI4CE 83 140 0 23 Apr 2022
FourCastNet: A Global Data-driven High-resolution Weather Model using Adaptive Fourier Neural Operators Jaideep Pathak Shashank Subramanian P. Harrington S. Raja Ashesh Chattopadhyay ... Zong-Yi Li Kamyar Azizzadenesheli Pedram Hassanzadeh K. Kashinath Anima Anandkumar AI4Cl 129 674 0 22 Feb 2022
Message Passing Neural PDE Solvers Johannes Brandstetter Daniel E. Worrall Max Welling AI4CE 43 270 0 07 Feb 2022
Predicting Physics in Mesh-reduced Space with Temporal Attention Xu Han Han Gao Tobias Pfaff Jian-Xun Wang Liping Liu AI4CE 37 74 0 22 Jan 2022
Learning Operators with Coupled Attention Georgios Kissas Jacob H. Seidman Leonardo Ferreira Guilhoto V. Preciado George J. Pappas P. Perdikaris 54 112 0 04 Jan 2022
Graph Neural Networks Accelerated Molecular Dynamics Zijie Li Kazem Meidani Prakarsh Yadav A. Farimani GNN AI4CE 51 56 0 06 Dec 2021
Factorized Fourier Neural Operators Alasdair Tran A. Mathews Lexing Xie Cheng Soon Ong AI4CE 38 149 0 27 Nov 2021
Masked Autoencoders Are Scalable Vision Learners Kaiming He Xinlei Chen Saining Xie Yanghao Li Piotr Dollár Ross B. Girshick ViT TPM 352 7,600 0 11 Nov 2021
Physics-Informed Neural Operator for Learning Partial Differential Equations Zong-Yi Li Hongkai Zheng Nikola B. Kovachki David Jin Haoxuan Chen Burigede Liu Kamyar Azizzadenesheli Anima Anandkumar AI4CE 74 399 0 06 Nov 2021
Improved architectures and training algorithms for deep operator networks Sizhuang He Hanwen Wang P. Perdikaris AI4CE 66 105 0 04 Oct 2021
Multiwavelet-based Operator Learning for Differential Equations Gaurav Gupta Xiongye Xiao P. Bogdan 144 206 0 28 Sep 2021
U-FNO -- An enhanced Fourier neural operator-based deep-learning model for multiphase flow Gege Wen Zong-Yi Li Kamyar Azizzadenesheli Anima Anandkumar S. Benson AI4CE 45 374 0 03 Sep 2021
Characterizing possible failure modes in physics-informed neural networks Aditi S. Krishnapriyan A. Gholami Shandian Zhe Robert M. Kirby Michael W. Mahoney PINN AI4CE 78 626 0 02 Sep 2021
Neural Operator: Learning Maps Between Function Spaces Nikola B. Kovachki Zong-Yi Li Burigede Liu Kamyar Azizzadenesheli K. Bhattacharya Andrew M. Stuart Anima Anandkumar AI4CE 75 444 0 19 Aug 2021
Deep Learning for Reduced Order Modelling and Efficient Temporal Evolution of Fluid Simulations Pranshu Pant Ruchi Doshi Pranav Bahl A. Farimani AI4CE 23 80 0 09 Jul 2021
Choose a Transformer: Fourier or Galerkin Shuhao Cao 55 234 0 31 May 2021
RoFormer: Enhanced Transformer with Rotary Position Embedding Jianlin Su Yu Lu Shengfeng Pan Ahmed Murtadha Bo Wen Yunfeng Liu 108 2,307 0 20 Apr 2021
Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets Sizhuang He Hanwen Wang P. Perdikaris AI4CE 65 685 0 19 Mar 2021
Perceiver: General Perception with Iterative Attention Andrew Jaegle Felix Gimeno Andrew Brock Andrew Zisserman Oriol Vinyals João Carreira VLM ViT MDE 117 999 0 04 Mar 2021
On the eigenvector bias of Fourier feature networks: From regression to solving multi-scale PDEs with physics-informed neural networks Sizhuang He Hanwen Wang P. Perdikaris 156 452 0 18 Dec 2020
Graph Convolutional Neural Networks for Body Force Prediction Francis Ogoke Kazem Meidani Amirreza Hashemi A. Farimani GNN AI4CE 22 61 0 03 Dec 2020
A Deep Learning Approach for Predicting Spatiotemporal Dynamics From Sparsely Observed Data Priyabrata Saha Saibal Mukhopadhyay AI4CE 60 4 0 30 Nov 2020
An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale Alexey Dosovitskiy Lucas Beyer Alexander Kolesnikov Dirk Weissenborn Xiaohua Zhai ... Matthias Minderer G. Heigold Sylvain Gelly Jakob Uszkoreit N. Houlsby ViT 185 40,217 0 22 Oct 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 390 2,355 0 18 Oct 2020
Learning Mesh-Based Simulation with Graph Networks Tobias Pfaff Meire Fortunato Alvaro Sanchez-Gonzalez Peter W. Battaglia AI4CE 41 761 0 07 Oct 2020
Transformers for Modeling Physical Systems N. Geneva N. Zabaras AI4CE 33 139 0 04 Oct 2020
Rethinking Attention with Performers K. Choromanski Valerii Likhosherstov David Dohan Xingyou Song Andreea Gane ... Afroz Mohiuddin Lukasz Kaiser David Belanger Lucy J. Colwell Adrian Weller 113 1,548 0 30 Sep 2020
Combining Differentiable PDE Solvers and Graph Neural Networks for Fluid Flow Prediction Filipe de Avila Belbute-Peres T. Economon J. Zico Kolter AI4CE 69 229 0 08 Jul 2020
Fourier Features Let Networks Learn High Frequency Functions in Low Dimensional Domains Matthew Tancik Pratul P. Srinivasan B. Mildenhall Sara Fridovich-Keil N. Raghavan Utkarsh Singhal R. Ramamoorthi Jonathan T. Barron Ren Ng 80 2,384 0 18 Jun 2020
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 119 384 0 16 Jun 2020
Learning continuous-time PDEs from sparse data with graph neural networks V. Iakovlev Markus Heinonen Harri Lähdesmäki AI4CE 43 68 0 16 Jun 2020
The Random Feature Model for Input-Output Maps between Banach Spaces Nicholas H. Nelsen Andrew M. Stuart 46 142 0 20 May 2020
Model Reduction and Neural Networks for Parametric PDEs K. Bhattacharya Bamdad Hosseini Nikola B. Kovachki Andrew M. Stuart 127 323 0 07 May 2020
NeRF: Representing Scenes as Neural Radiance Fields for View Synthesis B. Mildenhall Pratul P. Srinivasan Matthew Tancik Jonathan T. Barron R. Ramamoorthi Ren Ng 82 2,601 0 19 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 92 718 0 07 Mar 2020
Learning to Simulate Complex Physics with Graph Networks Alvaro Sanchez-Gonzalez Jonathan Godwin Tobias Pfaff Rex Ying J. Leskovec Peter W. Battaglia PINN AI4CE 96 1,065 0 21 Feb 2020
PyTorch: An Imperative Style, High-Performance Deep Learning Library Adam Paszke Sam Gross Francisco Massa Adam Lerer James Bradbury ... Sasank Chilamkurthy Benoit Steiner Lu Fang Junjie Bai Soumith Chintala ODL 126 42,038 0 03 Dec 2019
Towards Physics-informed Deep Learning for Turbulent Flow Prediction Rui Wang K. Kashinath M. Mustafa A. Albert Rose Yu PINN AI4CE 21 361 0 20 Nov 2019