Fetching the paper…
Reading the bibliography…
Memory complexity and data scarcity have so far prohibited learning solution operators of partial differential equations (PDEs) at high resolutions.
Uber die partiellen differenzengleichungen der mathematischen physik
R. Courant, K. Friedrichs, and H. Lewy · 1928
Earlier work this paper cites.
Multigrid methods for variational problems: General theory for the v- cycle
S. F. McCormick · 1985
Earlier work this paper cites.
Infinite-dimensional dynamical systems in mechanics and physics
Roger Temam · 1988
Earlier work this paper cites.
Domain decomposition algorithms
Tony F. Chan and Tarek P. Mathew · 1994
Earlier work this paper cites.
Neural operator: Graph kernel network for partial differential equations
Zongyi Li, Nikola Kovachki, Kamyar Azizzadenesheli, Burigede Liu, Kaushik Bhattacharya, Andrew Stuart, and Anima Anandkumar · 2003
Earlier work this paper cites.
Ensemble forecasting
Martin Leutbecher and Tim N Palmer · 2008
Earlier work this paper cites.
Tensor decompositions and applications
Tamara G Kolda and Brett W Bader · 2009
Earlier work this paper cites.
Partial differential equations
Lawrence C. Evans · 2010
Earlier work this paper cites.
A spectral fc solver for the compressible navier–stokes equations in general domains i: Explicit time-stepping
Nathan Albin and Oscar P. Bruno · 2011
Earlier work this paper cites.
Tensor-train decomposition
I. V. Oseledets · 2011
Earlier work this paper cites.
Uncertainty in weather and climate prediction
Julia Slingo and Tim Palmer · 2011
Earlier work this paper cites.
Invariant recurrent solutions embedded in a turbulent two-dimensional kolmogorov flow
Gary J. Chandler and Rich R. Kerswell · 2013
Earlier work this paper cites.
An Introduction to Computational Stochastic PDEs
Catherine E. Powell, Gabriel Lord, and Tony Shardlow · 2014
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.
Speeding-up convolutional neural networks using fine-tuned CP-decomposition
Vadim Lebedev, Yaroslav Ganin, Maksim Rakhuba, Ivan V. Oseledets, and Victor S. Lempitsky · 2015
Earlier work this paper cites.
Tensorizing neural networks
Alexander Novikov, Dmitry Podoprikhin, Anton Osokin, and Dmitry Vetrov · 2015
Earlier work this paper cites.
Jimmy Lei Ba, Jamie Ryan Kiros, and Geoffrey E Hinton · 2016
Earlier work this paper cites.
Convolutional neural networks for steady flow approximation
Xiaoxiao Guo, Wei Li, and Francesco Iorio · 2016
Earlier work this paper cites.
Identity mappings in deep residual networks
Kaiming He, Xiangyu Zhang, Shaoqing Ren, and Jian Sun · 2016
Cited alongside, same era.
Compression of deep convolutional neural networks for fast and low power mobile applications
Yong-Deok Kim, Eunhyeok Park, Sungjoo Yoo, Taelim Choi, Lu Yang, and Dongjun Shin · 2016
Cited alongside, same era.
Tensors for data mining and data fusion: Models, applications, and scalable algorithms
Evangelos E Papalexakis, Christos Faloutsos, and Nicholas D Sidiropoulos · 2016
Cited alongside, same era.
Instance normalization: The missing ingredient for fast stylization
Dmitry Ulyanov, Andrea Vedaldi, and Victor Lempitsky · 2016
Cited alongside, same era.
Solving ill-posed inverse problems using iterative deep neural networks
Jonas Adler and Ozan Oktem · 2017
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 · 2020
Later among the works it cites.
Meshfreeflownet: A physics-constrained deep continuous space-time super-resolution framework
Soheil Esmaeilzadeh, Kamyar Azizzadenesheli, Karthik Kashinath, Mustafa Mustafa, Hamdi A Tchelepi, Philip Marcus, Mr Prabhat, Anima Anandkumar, et al · 2020
Later among the works it cites.
Factorized higher-order CNNs with an application to spatio-temporal emotion estimation
Jean Kossaifi, Antoine Toisoul, Adrian Bulat, Yannis Panagakis, Timothy M Hospedales, and Maja Pantic · 2020
Later among the works it cites.
Adaptive fourier neural operators: Efficient token mixers for transformers
John Guibas, Morteza Mardani, Zongyi Li, Andrew Tao, Anima Anandkumar, and Bryan Catanzaro · 2021
Later among the works it cites.
alphaXiv searches the wider corpus for related work and actual follow-ups.
alphaXiv is searching for related work…
Wojciech M Czarnecki, Simon Osindero, Max Jaderberg, Grzegorz Swirszcz, and Razvan Pascanu · 2017
Cited alongside, same era.
Automatic differentiation in PyTorch
Adam Paszke, Sam Gross, Soumith Chintala, Gregory Chanan, Edward Yang, Zachary DeVito, Zeming Lin, Alban Desmaison, Luca Antiga, and Adam Lerer · 2017
Cited alongside, same era.
Tensor decomposition for signal processing and machine learning
Nicholas D Sidiropoulos, Lieven De Lathauwer, Xiao Fu, Kejun Huang, Evangelos E Papalexakis, and Christos Faloutsos · 2017
Cited alongside, same era.
Bayesian deep convolutional encoder–decoder networks for surrogate modeling and uncertainty quantification
Yinhao Zhu and Nicholas Zabaras · 2018
Cited alongside, same era.
Prediction of aerodynamic flow fields using convolutional neural networks
Saakaar Bhatnagar, Yaser Afshar, Shaowu Pan, Karthik Duraisamy, and Shailendra Kaushik · 2019
Cited alongside, same era.
Automated multi-stage compression of neural networks
Julia Gusak, Maksym Kholiavchenko, Evgeny Ponomarev, Larisa Markeeva, Philip Blagoveschensky, Andrzej Cichocki, and Ivan Oseledets · 2019
Cited alongside, same era.
Spectral learning on matrices and tensors
Majid Janzamin, Rong Ge, Jean Kossaifi, Anima Anandkumar, et al · 2019
Cited alongside, same era.
Gaurav Gupta, Xiongye Xiao, and Paul Bogdan · 2021
Later among the works it cites.
Tensorly-torch
Jean Kossaifi · 2021
Later among the works it cites.
Tensor methods in computer vision and deep learning
Yannis Panagakis, Jean Kossaifi, Grigorios G. Chrysos, James Oldfield, Mihalis A. Nicolaou, Anima Anandkumar, and Stefanos Zafeiriou · 2021
Later among the works it cites.
Seismic wave propagation and inversion with neural operators
Yan Yang, Angela F Gao, Jorge C Castellanos, Zachary E Ross, Kamyar Azizzadenesheli, and Robert W Clayton · 2021
Later among the works it cites.
The role of internal variability in global climate projections of extreme events
Mackenzie L Blanusa, Carla J López-Zurita, and Stephan Rasp · 2022
Later among the works it cites.
Monarch: Expressive structured matrices for efficient and accurate training
Tri Dao, Beidi Chen, Nimit S Sohoni, Arjun Desai, Michael Poli, Jessica Grogan, Alexander Liu, Aniruddh Rao, Atri Rudra, and Christopher Ré · 2022
Later among the works it cites.
The cost-accuracy trade-off in operator learning with neural networks
Maarten De Hoop, Daniel Zhengyu Huang, Elizabeth Qian, and Andrew M Stuart · 2022
Later among the works it cites.
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
Later among the works it cites.
Efficient learning of multiple nlp tasks via collective weight factorization on bert
Christos Papadopoulos, Yannis Panagakis, Manolis Koubarakis, and Mihalis Nicolaou · 2022
Later among the works it cites.
Jaideep Pathak, Shashank Subramanian, Peter Harrington, Sanjeev Raja, Ashesh Chattopadhyay, Morteza Mardani, Thorsten Kurth, David Hall, Zongyi Li, Kamyar Azizzadenesheli, et al · 2022
Later among the works it cites.
U-fno—an enhanced fourier neural operator-based deep-learning model for multiphase flow
Gege Wen, Zongyi Li, Kamyar Azizzadenesheli, Anima Anandkumar, and Sally M Benson · 2022
Later among the works it cites.
Accelerated full seismic waveform modeling and inversion with u-shaped neural operators
Yan Yang, Angela F Gao, Jorge C Castellanos, Zachary E Ross, Kamyar Azizzadenesheli, and Robert W Clayton · 2022
Later among the works it cites.
Factorized fourier neural operators
Alasdair Tran, Alexander Mathews, Lexing Xie, and Cheng Soon Ong · 2023
Closest in time.