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2410.02113
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Mamba Neural Operator: Who Wins? Transformers vs. State-Space Models for PDEs
3 October 2024
Chun-Wun Cheng
Jiahao Huang
Yi Zhang
Guang Yang
Carola-Bibiane Schonlieb
Angelica I Aviles-Rivero
AI4CE
Mamba
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Papers citing
"Mamba Neural Operator: Who Wins? Transformers vs. State-Space Models for PDEs"
31 / 31 papers shown
A Mathematical Explanation of Transformers
X. Tai
Hao Liu
Lingfeng Li
Raymond H. F. Chan
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226
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PDE Solvers Should Be Local: Fast, Stable Rollouts with Learned Local Stencils
Chun-Wun Cheng
Bin Dong
Carola-Bibiane Schönlieb
Angelica I Aviles-Rivero
AI4CE
175
0
0
30 Sep 2025
Merging Memory and Space: A State Space Neural Operator
Nodens F. Koren
Samuel Lanthaler
361
0
0
31 Jul 2025
An Attention-based Spatio-Temporal Neural Operator for Evolving Physics
V. Karkaria
Doksoo Lee
Yi-Ping Chen
Yue Yu
Wei Chen
AI4CE
239
0
0
12 Jun 2025
Latent Mamba Operator for Partial Differential Equations
Karn Tiwari
Niladri Dutta
N. M. A. Krishnan
P. PrathoshA
Mamba
AI4CE
353
2
0
25 May 2025
GeoMaNO: Geometric Mamba Neural Operator for Partial Differential Equations
Xi Han
Jingwei Zhang
Dimitris Samaras
Fei Hou
Hong Qin
AI4CE
439
2
0
17 May 2025
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
555
29
0
28 Jan 2025
Automatic selection of the best neural architecture for time series forecasting
Qianying Cao
Shanqing Liu
Alan John Varghese
Jérome Darbon
M. Triantafyllou
George Karniadakis
AI4TS
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1.0K
5
0
21 Jan 2025
VMamba: Visual State Space Model
Neural Information Processing Systems (NeurIPS), 2024
Yue Liu
Yunjie Tian
Yuzhong Zhao
Hongtian Yu
Lingxi Xie
Yaowei Wang
Qixiang Ye
Jianbin Jiao
Yunfan Liu
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1,973
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31 Dec 2024
HAMLET: Graph Transformer Neural Operator for Partial Differential Equations
International Conference on Machine Learning (ICML), 2024
Andrey Bryutkin
Jiahao Huang
Zhongying Deng
Guang Yang
Carola-Bibiane Schönlieb
Angelica E. Avilés-Rivero
255
21
0
05 Feb 2024
Gated Linear Attention Transformers with Hardware-Efficient Training
Aaron Courville
Bailin Wang
Songlin Yang
Yikang Shen
Yoon Kim
617
365
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11 Dec 2023
Mamba: Linear-Time Sequence Modeling with Selective State Spaces
Albert Gu
Tri Dao
Mamba
809
6,333
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01 Dec 2023
GNOT: A General Neural Operator Transformer for Operator Learning
International Conference on Machine Learning (ICML), 2023
Zhongkai Hao
Zhengyi Wang
Hang Su
Chengyang Ying
Yinpeng Dong
Songming Liu
Ze Cheng
Jian Song
Jun Zhu
AI4CE
391
359
0
28 Feb 2023
PDEBENCH: An Extensive Benchmark for Scientific Machine Learning
Neural Information Processing Systems (NeurIPS), 2022
M. Takamoto
T. Praditia
Raphael Leiteritz
Dan MacKinlay
Francesco Alesiani
Dirk Pflüger
Mathias Niepert
AI4CE
762
380
0
13 Oct 2022
On the Parameterization and Initialization of Diagonal State Space Models
Neural Information Processing Systems (NeurIPS), 2022
Albert Gu
Ankit Gupta
Karan Goel
Christopher Ré
582
531
0
23 Jun 2022
Transformer for Partial Differential Equations' Operator Learning
Zijie Li
Kazem Meidani
A. Farimani
476
281
0
26 May 2022
Factorized Fourier Neural Operators
International Conference on Learning Representations (ICLR), 2021
Alasdair Tran
A. Mathews
Lexing Xie
Cheng Soon Ong
AI4CE
469
246
0
27 Nov 2021
Adaptive Fourier Neural Operators: Efficient Token Mixers for Transformers
John Guibas
Morteza Mardani
Zong-Yi Li
Andrew Tao
Anima Anandkumar
Bryan Catanzaro
389
354
0
24 Nov 2021
Combining Recurrent, Convolutional, and Continuous-time Models with Linear State-Space Layers
Albert Gu
Isys Johnson
Karan Goel
Khaled Kamal Saab
Tri Dao
Atri Rudra
Christopher Ré
519
1,061
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26 Oct 2021
Choose a Transformer: Fourier or Galerkin
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Shuhao Cao
555
381
0
31 May 2021
Machine learning accelerated computational fluid dynamics
Proceedings of the National Academy of Sciences of the United States of America (PNAS), 2021
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Jamie A. Smith
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Qing Wang
M. Brenner
Stephan Hoyer
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618
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28 Jan 2021
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Model Reduction and Neural Networks for Parametric PDEs
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Bamdad Hosseini
Nikola B. Kovachki
Andrew M. Stuart
653
433
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07 May 2020
Neural Operator: Graph Kernel Network for Partial Differential Equations
International Conference on Learning Representations (ICLR), 2020
Zong-Yi Li
Nikola B. Kovachki
Kamyar Azizzadenesheli
Burigede Liu
K. Bhattacharya
Andrew M. Stuart
Anima Anandkumar
630
986
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07 Mar 2020
AI Feynman: a Physics-Inspired Method for Symbolic Regression
Science Advances (Sci Adv), 2019
S. Udrescu
Max Tegmark
664
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27 May 2019
Latent-space Physics: Towards Learning the Temporal Evolution of Fluid Flow
S. Wiewel
M. Becher
N. Thürey
AI4CE
395
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27 Feb 2018
Deep learning for universal linear embeddings of nonlinear dynamics
Nature Communications (Nat. Commun.), 2017
Bethany Lusch
J. Nathan Kutz
Steven L. Brunton
524
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27 Dec 2017
Attention Is All You Need
Neural Information Processing Systems (NeurIPS), 2017
Ashish Vaswani
Noam M. Shazeer
Niki Parmar
Jakob Uszkoreit
Llion Jones
Aidan Gomez
Lukasz Kaiser
Illia Polosukhin
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