Fetching the paper…
Reading the bibliography…
Deep neural operators can learn nonlinear mappings between infinite-dimensional function spaces via deep neural networks.
Multilayer feedforward networks are universal approximators
Kurt Hornik, Maxwell Stinchcombe, and Halbert White · 1989
Earlier work this paper cites.
On a formula for the L2 Wasserstein metric between measures on Euclidean and Hilbert spaces
Matthias Gelbrich · 1990
Earlier work this paper cites.
Extrapolation and interpolation in neural network classifiers
E. Barnard and L.F.A. Wessels · 1992
Earlier work this paper cites.
Neural networks and the bias/variance dilemma
Stuart Geman, Elie Bienenstock, and René Doursat · 1992
Earlier work this paper cites.
Universal approximation to nonlinear operators by neural networks with arbitrary activation functions and its application to dynamical systems
Tianping Chen and Hong Chen · 1995
Earlier work this paper cites.
Predicting the output from a complex computer code when fast approximations are available
Marc C Kennedy and Anthony O’Hagan · 2000
Earlier work this paper cites.
Engineering design via surrogate modelling: a practical guide
András Sobester, Alexander Forrester, and Andy Keane · 2008
Earlier work this paper cites.
A survey on transfer learning
Sinno Jialin Pan and Qiang Yang · 2009
Earlier work this paper cites.
The elements of statistical learning: data mining, inference, and prediction
Trevor Hastie, Robert Tibshirani, Jerome H Friedman, and Jerome H Friedman · 2009
Earlier work this paper cites.
Rectified linear units improve restricted Boltzmann machines
Vinod Nair and Geoffrey E Hinton · 2010
Earlier work this paper cites.
An empirical investigation of catastrophic forgetting in gradient-based neural networks
Ian J Goodfellow, Mehdi Mirza, Da Xiao, Aaron Courville, and Yoshua Bengio · 2013
Earlier work this paper cites.
Gaussian error linear units (GeLUs)
Dan Hendrycks and Kevin Gimpel · 2016
Earlier work this paper cites.
Overcoming catastrophic forgetting in neural networks
James Kirkpatrick, Razvan Pascanu, Neil Rabinowitz, Joel Veness, Guillaume Desjardins, Andrei A Rusu, Kieran Milan, John Quan, Tiago Ramalho, Agnieszka Grabska-Barwinska, et al · 2017
Earlier work this paper cites.
Sigmoid-weighted linear units for neural network function approximation in reinforcement learning
Stefan Elfwing, Eiji Uchibe, and Kenji Doya · 2018
Earlier work this paper cites.
Workshop report on basic research needs for scientific machine learning: Core technologies for artificial intelligence
Nathan Baker, Frank Alexander, Timo Bremer, Aric Hagberg, Yannis Kevrekidis, Habib Najm, Manish Parashar, Abani Patra, James Sethian, Stefan Wild, et al · 2019
Earlier work this paper cites.
Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations
Maziar Raissi, Paris Perdikaris, and George Em Karniadakis · 2019
Earlier work this paper cites.
GMLS-Nets: A framework for learning from unstructured data
Nathaniel Trask, Ravi G Patel, Ben J Gross, and Paul J Atzberger · 2019
Earlier work this paper cites.
Reconciling modern machine-learning practice and the classical bias–variance trade-off
Mikhail Belkin, Daniel Hsu, Siyuan Ma, and Soumik Mandal · 2019
Earlier work this paper cites.
How neural networks extrapolate: From feedforward to graph neural networks
Keyulu Xu, Mozhi Zhang, Jingling Li, Simon S Du, Ken-ichi Kawarabayashi, and Stefanie Jegelka · 2020
Earlier work this paper cites.
A composite neural network that learns from multi-fidelity data: Application to function approximation and inverse PDE problems
Xuhui Meng and George Em Karniadakis · 2020
Earlier work this paper cites.
Extraction of mechanical properties of materials through deep learning from instrumented indentation
Lu Lu, Ming Dao, Punit Kumar, Upadrasta Ramamurty, George Em Karniadakis, and Subra Suresh · 2020
Earlier work this paper cites.
A comprehensive survey on transfer learning
Fuzhen Zhuang, Zhiyuan Qi, Keyu Duan, Dongbo Xi, Yongchun Zhu, Hengshu Zhu, Hui Xiong, and Qing He · 2020
Earlier work this paper cites.
Learning from very few samples: A survey
Jiang Lu, Pinghua Gong, Jieping Ye, and Changshui Zhang · 2020
Earlier work this paper cites.
Generalizing from a few examples: A survey on few-shot learning
Yaqing Wang, Quanming Yao, James T Kwok, and Lionel M Ni · 2020
Cited alongside, same era.
Fourier neural operator for parametric partial differential equations
Zongyi Li, Nikola Kovachki, Kamyar Azizzadenesheli, Burigede Liu, Kaushik Bhattacharya, Andrew Stuart, and Anima Anandkumar · 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.
Locally adaptive activation functions with slope recovery for deep and physics-informed neural networks
Ameya D Jagtap, Kenji Kawaguchi, and George Em Karniadakis · 2020
Cited alongside, same era.
Quantifying the generalization error in deep learning in terms of data distribution and neural network smoothness
Approximation rates of DeepONets for learning operators arising from advection–diffusion equations
Beichuan Deng, Yeonjong Shin, Lu Lu, Zhongqiang Zhang, and George Em Karniadakis · 2022
Closest in time.
A physics-informed variational DeepONet for predicting crack path in quasi-brittle materials
Somdatta Goswami, Minglang Yin, Yue Yu, and George Em Karniadakis · 2022
Closest in time.
Interfacing finite elements with deep neural operators for fast multiscale modeling of mechanics problems
Minglang Yin, Enrui Zhang, Yue Yu, and George Em Karniadakis · 2022
Closest in time.
MIONet: Learning multiple-input operators via tensor product
Pengzhan Jin, Shuai Meng, and Lu Lu · 2022
Closest in time.
A comprehensive and fair comparison of two neural operators (with practical extensions) based on FAIR data
Lu Lu, Xuhui Meng, Shengze Cai, Zhiping Mao, Somdatta Goswami, Zhongqiang Zhang, and George Em Karniadakis · 2022
alphaXiv searches the wider corpus for related work and actual follow-ups.
alphaXiv is searching for related work…
Pengzhan Jin, Lu Lu, Yifa Tang, and George Em Karniadakis · 2020
Cited alongside, same era.
Physics-informed machine learning
George Em Karniadakis, Ioannis G Kevrekidis, Lu Lu, Paris Perdikaris, Sifan Wang, and Liu Yang · 2021
Cited alongside, same era.
DeepXDE: A deep learning library for solving differential equations
Lu Lu, Xuhui Meng, Zhiping Mao, and George Em Karniadakis · 2021
Cited alongside, same era.
Learning nonlinear operators via DeepONet based on the universal approximation theorem of operators
Lu Lu, Pengzhan Jin, Guofei Pang, Handy Zang, and George Karniadakis · 2021
Cited alongside, same era.
Operator learning for predicting multiscale bubble growth dynamics
Chensen Lin, Zhen Li, Lu Lu, Shengze Cai, Martin Maxey, and George Em Karniadakis · 2021
Cited alongside, same era.
A seamless multiscale operator neural network for inferring bubble dynamics
Chensen Lin, Martin Maxey, Zhen Li, and George Em Karniadakis · 2021
Cited alongside, same era.
Deeponet prediction of linear instability waves in high-speed boundary layers
P Clark Di Leoni, Lu Lu, Charles Meneveau, George Karniadakis, and Tamer A Zaki · 2021
Cited alongside, same era.
Forecasting solar-thermal systems performance under transient operation using a data-driven machine learning approach based on the deep operator network architecture
Julian D. Osorio, Zhicheng Wang, George Karniadakis, Shengze Cai, Chrys Chryssostomidis, Mayank Panwar, and Rob Hovsapian · 2021
Cited alongside, same era.
Closest in time.
Lu Lu, Raphaël Pestourie, Steven G Johnson, and Giuseppe Romano · 2022
Closest in time.
Multifidelity deep operator networks
Amanda A Howard, Mauro Perego, George E Karniadakis, and Panos Stinis · 2022
Closest in time.
Bi-fidelity modeling of uncertain and partially unknown systems using DeepONets
Subhayan De, Malik Hassanaly, Matthew Reynolds, Ryan N King, and Alireza Doostan · 2022
Closest in time.
Uncertainty quantification in scientific machine learning: Methods, metrics, and comparisons
Apostolos F Psaros, Xuhui Meng, Zongren Zou, Ling Guo, and George Em Karniadakis · 2022
Closest in time.
Scalable uncertainty quantification for deep operator networks using randomized priors
Yibo Yang, Georgios Kissas, and Paris Perdikaris · 2022
Closest in time.
Christian Moya, Shiqi Zhang, Meng Yue, and Guang Lin · 2022
Closest in time.
Learning operators with coupled attention
Georgios Kissas, Jacob Seidman, Leonardo Ferreira Guilhoto, Victor M Preciado, George J Pappas, and Paris Perdikaris · 2022
Closest in time.
Xin-Yang Liu, Hao Sun, Min Zhu, Lu Lu, and Jian-Xun Wang · 2022
Closest in time.
Machine learning techniques for estimating mechanical properties of materials, June 30 2022
Lu Lu, Ming Dao, Subra Suresh, and George Karniadakis · 2022
Closest in time.
Deep transfer learning for partial differential equations under conditional shift with DeepONet
Somdatta Goswami, Katiana Kontolati, Michael D Shields, and George Em Karniadakis · 2022
Closest in time.
Nonlocal kernel network (NKN): a stable and resolution-independent deep neural network
Huaiqian You, Yue Yu, Marta D’Elia, Tian Gao, and Stewart Silling · 2022
Closest in time.
Deep kronecker neural networks: A general framework for neural networks with adaptive activation functions
Ameya D Jagtap, Yeonjong Shin, Kenji Kawaguchi, and George Em Karniadakis · 2022
Closest in time.
On the activation function dependence of the spectral bias of neural networks
Qingguo Hong, Qinyang Tan, Jonathan W Siegel, and Jinchao Xu · 2022
Closest in time.
Error estimates for DeepONets: A deep learning framework in infinite dimensions
Samuel Lanthaler, Siddhartha Mishra, and George E Karniadakis · 2022
Closest in time.
Generic bounds on the approximation error for physics-informed (and) operator learning
Tim De Ryck and Siddhartha Mishra · 2022
Closest in time.
Neural and gpc operator surrogates: construction and expression rate bounds
Lukas Herrmann, Christoph Schwab, and Jakob Zech · 2022
Closest in time.
Deep solution operators for variational inequalities via proximal neural networks
Christoph Schwab and Andreas Stein · 2022
Closest in time.