Fetching the paper…
Reading the bibliography…
Existing neural operator architectures face challenges when solving multiphysics problems with coupled partial differential equations (PDEs) due to complex geometries, interactions between physical variables, and the limited amounts of high-resolution training data.
Proposal for numerical benchmarking of fluid-structure interaction between an elastic object and laminar incompressible flow
Stefan Turek and Jaroslav Hron · 2006
Earlier work this paper cites.
Computational science and engineering
Gilbert Strang · 2007
Earlier work this paper cites.
Linear instability of asymmetric poiseuille flows
Dick Kachuma and Ian Sobey · 2007
Earlier work this paper cites.
Automated solution of differential equations by the finite element method: The FEniCS book
Anders Logg, Kent-Andre Mardal, and Garth Wells · 2012
Earlier work this paper cites.
Batch normalization: Accelerating deep network training by reducing internal covariate shift
Sergey Ioffe and Christian Szegedy · 2015
Earlier work this paper cites.
U-net: Convolutional networks for biomedical image segmentation
Olaf Ronneberger, Philipp Fischer, and Thomas Brox · 2015
Earlier work this paper cites.
Instance normalization: The missing ingredient for fast stylization
Dmitry Ulyanov, Andrea Vedaldi, and Victor Lempitsky · 2016
Earlier work this paper cites.
Jimmy Lei Ba, Jamie Ryan Kiros, and Geoffrey E Hinton · 2016
Earlier work this paper cites.
Interaction networks for learning about objects, relations and physics
Peter Battaglia, Razvan Pascanu, Matthew Lai, Danilo Jimenez Rezende, et al · 2016
Earlier work this paper cites.
Atmospheric and oceanic fluid dynamics
Geoffrey K Vallis · 2017
Earlier work this paper cites.
Relative effects of asymmetry and wall slip on the stability of plane channel flow
Sukhendu Ghosh · 2017
Earlier work this paper cites.
Improving language understanding by generative pre-training
Alec Radford, Karthik Narasimhan, Tim Salimans, Ilya Sutskever, et al · 2018
Earlier work this paper cites.
Group normalization
Yuxin Wu and Kaiming He · 2018
Earlier work this paper cites.
Lu Lu, Pengzhan Jin, and George Em Karniadakis · 2019
Earlier work this paper cites.
Fourier neural operator for parametric partial differential equations
Zongyi Li, Nikola Kovachki, Kamyar Azizzadenesheli, Burigede Liu, Kaushik Bhattacharya, Andrew Stuart, and Anima Anandkumar · 2020
Earlier work this paper cites.
A simple framework for contrastive learning of visual representations
Ting Chen, Simon Kornblith, Mohammad Norouzi, and Geoffrey Hinton · 2020
Cited alongside, same era.
turtlefsi: A robust and monolithic fenics-based fluid-structure interaction solver
Aslak W Bergersen, Andreas Slyngstad, Sebastian Gjertsen, Alban Souche, and Kristian Valen-Sendstad · 2020
Cited alongside, same era.
Neural operator: Graph kernel network for partial differential equations
Zongyi Li, Nikola Kovachki, Kamyar Azizzadenesheli, Burigede Liu, Kaushik Bhattacharya, Andrew Stuart, and Anima Anandkumar · 2020
Cited alongside, same era.
Emerging properties in self-supervised vision transformers
Mathilde Caron, Hugo Touvron, Ishan Misra, Hervé Jégou, Julien Mairal, Piotr Bojanowski, and Armand Joulin · 2021
Cited alongside, same era.
Learning transferable visual models from natural language supervision
Alec Radford, Jong Wook Kim, Chris Hallacy, Aditya Ramesh, Gabriel Goh, Sandhini Agarwal, Girish Sastry, Amanda Askell, Pamela Mishkin, Jack Clark, et al · 2021
Multiple physics pretraining for physical surrogate models
Michael McCabe, Bruno Régaldo-Saint Blancard, Liam Holden Parker, Ruben Ohana, Miles Cranmer, Alberto Bietti, Michael Eickenberg, Siavash Golkar, Geraud Krawezik, Francois Lanusse, et al · 2023
Later among the works it cites.
Neural operators for accelerating scientific simulations and design
Kamyar Azzizadenesheli, Nikola Kovachki, Zongyi Li, Miguel Liu-Schiaffini, Jean Kossaifi, and Anima Anandkumar · 2023
Later among the works it cites.
Multi-grid tensorized fourier neural operator for high resolution PDEs, 2023
Jean Kossaifi, Nikola Borislavov Kovachki, Kamyar Azizzadenesheli, and Anima Anandkumar · 2023
Later among the works it cites.
Spherical fourier neural operators: Learning stable dynamics on the sphere
Boris Bonev, Thorsten Kurth, Christian Hundt, Jaideep Pathak, Maximilian Baust, Karthik Kashinath, and Anima Anandkumar · 2023
Later among the works it cites.
alphaXiv searches the wider corpus for related work and actual follow-ups.
alphaXiv is searching for related work…
Cited alongside, same era.
An image is worth 16x16 words: Transformers for image recognition at scale
Alexey Dosovitskiy, Lucas Beyer, Alexander Kolesnikov, Dirk Weissenborn, Xiaohua Zhai, Thomas Unterthiner, Mostafa Dehghani, Matthias Minderer, Georg Heigold, Sylvain Gelly, et al · 2021
Cited alongside, same era.
Fourier neural operator for parametric partial differential equations
Zongyi Li, Nikola Borislavov Kovachki, Kamyar Azizzadenesheli, Kaushik Bhattacharya, Andrew Stuart, Anima Anandkumar, et al · 2021
Cited alongside, same era.
Swin transformer: Hierarchical vision transformer using shifted windows
Ze Liu, Yutong Lin, Yue Cao, Han Hu, Yixuan Wei, Zheng Zhang, Stephen Lin, and Baining Guo · 2021
Cited alongside, same era.
Neural operator: Learning maps between function spaces
Nikola Kovachki, Zongyi Li, Burigede Liu, Kamyar Azizzadenesheli, Kaushik Bhattacharya, Andrew Stuart, and Anima Anandkumar · 2021
Cited alongside, same era.
A learning-based multiscale method and its application to inelastic impact problems
Burigede Liu, Nikola Kovachki, Zongyi Li, Kamyar Azizzadenesheli, Anima Anandkumar, Andrew M Stuart, and Kaushik Bhattacharya · 2022
Cited alongside, same era.
Styleswin: Transformer-based gan for high-resolution image generation
Bowen Zhang, Shuyang Gu, Bo Zhang, Jianmin Bao, Dong Chen, Fang Wen, Yong Wang, and Baining Guo · 2022
Cited alongside, same era.
Masked autoencoders are scalable vision learners
Kaiming He, Xinlei Chen, Saining Xie, Yanghao Li, Piotr Dollár, and Ross Girshick · 2022
Cited alongside, same era.
Zongyi Li, Nikola Borislavov Kovachki, Chris Choy, Boyi Li, Jean Kossaifi, Shourya Prakash Otta, Mohammad Amin Nabian, Maximilian Stadler, Christian Hundt, Kamyar Azizzadenesheli, and Anima Anandkumar · 2023
Later among the works it cites.
PDEBENCH: An extensive benchmark for scientific machine learning, 2023
Makoto Takamoto, Timothy Praditia, Raphael Leiteritz, Dan MacKinlay, Francesco Alesiani, Dirk Pflüger, and Mathias Niepert · 2023
Later among the works it cites.
Learning neural pde solvers with parameter-guided channel attention
Makoto Takamoto, Francesco Alesiani, and Mathias Niepert · 2023
Later among the works it cites.
Scalable transformer for pde surrogate modeling
Zijie Li, Dule Shu, and Amir Barati Farimani · 2023
Later among the works it cites.
Palm: Scaling language modeling with pathways
Aakanksha Chowdhery, Sharan Narang, Jacob Devlin, Maarten Bosma, Gaurav Mishra, Adam Roberts, Paul Barham, Hyung Won Chung, Charles Sutton, Sebastian Gehrmann, et al · 2023
Later among the works it cites.
Self-supervised learning based on transformer for flow reconstruction and prediction
Bonan Xu, Yuanye Zhou, and Xin Bian · 2023
Later among the works it cites.
Self-supervised learning with lie symmetries for partial differential equations
Grégoire Mialon, Quentin Garrido, Hannah Lawrence, Danyal Rehman, Yann LeCun, and Bobak Kiani · 2023
Later among the works it cites.
Geometry-informed neural operator for large-scale 3d pdes
Zongyi Li, Nikola Borislavov Kovachki, Chris Choy, Boyi Li, Jean Kossaifi, Shourya Prakash Otta, Mohammad Amin Nabian, Maximilian Stadler, Christian Hundt, Kamyar Azizzadenesheli, et al · 2023
Later among the works it cites.
Dpot: Auto-regressive denoising operator transformer for large-scale pde pre-training
Zhongkai Hao, Chang Su, Songming Liu, Julius Berner, Chengyang Ying, Hang Su, Anima Anandkumar, Jian Song, and Jun Zhu · 2024
Closest in time.
Towards enforcing hard physics constraints in operator learning frameworks
Valentin Duruisseaux, Miguel Liu-Schiaffini, Julius Berner, and Anima Anandkumar · 2024
Closest in time.