Fetching the paper…
Reading the bibliography…
Deep Operator Networks are an increasingly popular paradigm for solving regression in infinite dimensions and hence solve families of PDEs in one shot.
Neural-network-based approximations for solving partial differential equations
MWMG Dissanayake and Nhan Phan-Thien · 1994
Earlier work this paper cites.
An efficient numerical scheme for burgers’ equation
Yiu-Chung Hon and XZ Mao · 1998
Earlier work this paper cites.
Artificial neural networks for solving ordinary and partial differential equations
Isaac E Lagaris, Aristidis Likas, and Dimitrios I Fotiadis · 1998
Earlier work this paper cites.
Neural-network methods for boundary value problems with irregular boundaries
Isaac E Lagaris, Aristidis C Likas, and Dimitris G Papageorgiou · 2000
Earlier work this paper cites.
Finite Element Methods, nov 15 2004
Susanne C. Brenner and Carsten Carstensen · 2004
Earlier work this paper cites.
Understanding machine learning: From theory to algorithms
Shai Shalev-Shwartz and Shai Ben-David · 2014
Earlier work this paper cites.
Spectrally-normalized margin bounds for neural networks
Peter L Bartlett, Dylan J Foster, and Matus J Telgarsky · 2017
Earlier work this paper cites.
Size-independent sample complexity of neural networks
Noah Golowich, Alexander Rakhlin, and Ohad Shamir · 2018
Earlier work this paper cites.
Hidden physics models: Machine learning of nonlinear partial differential equations
Maziar Raissi and George Em Karniadakis · 2018
Earlier work this paper cites.
Maziar Raissi, Alireza Yazdani, and George Em Karniadakis · 2018
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.
Deeponet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operators
Lu Lu, Pengzhan Jin, and George Em Karniadakis · 2019
Earlier work this paper cites.
fpinns: Fractional physics-informed neural networks
Guofei Pang, Lu Lu, and George Em Karniadakis · 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 E Karniadakis · 2019
Earlier work this paper cites.
Conservative physics-informed neural networks on discrete domains for conservation laws: Applications to forward and inverse problems
Ameya D Jagtap, Ehsan Kharazmi, and George Em Karniadakis · 2020
Earlier work this paper cites.
Analytic study of double descent in binary classification: The impact of loss
Ganesh Ramachandra Kini and Christos Thrampoulidis · 2020
Earlier work this paper cites.
Physics-informed neural networks for high-speed flows
Zhiping Mao, Ameya D Jagtap, and George Em Karniadakis · 2020
Earlier work this paper cites.
Physics informed neural networks (pinns) for approximating nonlinear dispersive pdes
Genming Bai, Ujjwal Koley, Siddhartha Mishra, and Roberto Molinaro · 2021
Earlier work this paper cites.
Investigating the Role of Overparameterization While Solving the Pendulum with DeepONets
Pulkit Gopalani and Anirbit Mukherjee · 2021
Cited alongside, same era.
Extended physics-informed neural networks (xpinns): A generalized space-time domain decomposition based deep learning framework for nonlinear partial differential equations
Ameya D Jagtap and George E Karniadakis · 2021
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.
Multiscale deeponet for nonlinear operators in oscillatory function spaces for building seismic wave responses
Lizuo Liu and Wei Cai · 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.
Application of advection diffusion equation for determination of contaminants in aqueous solution: A mathematical analysis
Muhammad Masudur Rahaman, Humaira Takia, Md Kamrul Hasan, Md Bellal Hossain, Shamim Mia, and Khokon Hossen · 2022
Later among the works it cites.
Generic bounds on the approximation error for physics-informed (and) operator learning
Tim De Ryck and Siddhartha Mishra · 2022
Later among the works it cites.
Enhanced deeponet for modeling partial differential operators considering multiple input functions
Lesley Tan and Liang Chen · 2022
Later among the works it cites.
Wavelet neural operator: a neural operator for parametric partial differential equations
Tapas Tripura and S. Chakraborty · 2022
Later among the works it cites.
Transfer learning enhanced deeponet for long-time prediction of evolution equations
Wuzhe Xu, Yulong Lu, and Li Wang · 2022
Later among the works it cites.
alphaXiv searches the wider corpus for related work and actual follow-ups.
alphaXiv is searching for related work…
Deep double descent: Where bigger models and more data hurt
Preetum Nakkiran, Gal Kaplun, Yamini Bansal, Tristan Yang, Boaz Barak, and Ilya Sutskever · 2021
Cited alongside, same era.
B-pinns: Bayesian physics-informed neural networks for forward and inverse pde problems with noisy data
Liu Yang, Xuhui Meng, and George Em Karniadakis · 2021
Cited alongside, same era.
A coupled variational encoder-decoder-deeponet surrogate model for the rayleigh-benard convection problem
J. Almeida, P. R. B. Rocha, Allan Moreira De Carvalho, and A. C. Nogueira · 2022
Cited alongside, same era.
Scientific machine learning through physics–informed neural networks: Where we are and what’s next
Salvatore Cuomo, Vincenzo Schiano Di Cola, Fabio Giampaolo, Gianluigi Rozza, Maziar Raissi, and Francesco Piccialli · 2022
Cited alongside, same era.
A model of double descent for high-dimensional binary linear classification
Zeyu Deng, Abla Kammoun, and Christos Thrampoulidis · 2022
Cited alongside, same era.
Capacity Bounds for the DeepONet Method of Solving Differential Equations
Pulkit Gopalani, Sayar Karmakar, and Anirbit Mukherjee · 2022
Cited alongside, same era.
Deep transfer learning for partial differential equations under conditional shift with deeponet
S. Goswami, Katiana Kontolati, M. Shields, and G. Karniadakis · 2022
Cited alongside, same era.
Multiauto-deeponet: A multi-resolution autoencoder deeponet for nonlinear dimension reduction, uncertainty quantification and operator learning of forward and inverse stochastic problems
Jiahao Zhang, Shiqi Zhang, and Guang Lin · 2022
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
Closest in time.
A universal law of robustness via isoperimetry
Sébastien Bubeck and Mark Sellke · 2023
Closest in time.
Fourier neural operator for fluid flow in small-shape 2d simulated porous media dataset
A. Choubineh, Jie Chen, David A. Wood, Frans Coenen, and Fei Ma · 2023
Closest in time.
Fourier neural operator for plasma modelling
Vignesh Gopakumar, S. Pamela, L. Zanisi, Zong-Yi Li, Anima Anandkumar, and Mast Team · 2023
Closest in time.
Learning in latent spaces improves the predictive accuracy of deep neural operators
Katiana Kontolati, Somdatta Goswami, George Em Karniadakis, and Michael D Shields · 2023
Closest in time.
Fourier neural operator surrogate model to predict 3d seismic waves propagation
F. Lehmann, F. Gatti, M. Bertin, and D. Clouteau · 2023
Closest in time.
Sparsity-aware generalization theory for deep neural networks
Ramchandran Muthukumar and Jeremias Sulam · 2023
Closest in time.
Sequential deep learning operator network (s-deeponet) for time-dependent loads
Jaewan Park, Shashank Kushwaha, Junyan He, S. Koric, D. Abueidda, and I. Jasiuk · 2023
Closest in time.
Convolutional neural operators
Bogdan Raonic, Roberto Molinaro, Tobias Rohner, Siddhartha Mishra, and Emmanuel de Bezenac · 2023
Closest in time.
Deep learning and computational physics (lecture notes)
Deep Ray, Orazio Pinti, and Assad A Oberai · 2023
Closest in time.
On size-independent sample complexity of relu networks
Mark Sellke · 2023
Closest in time.
A wavelet neural operator based elastography for localization and quantification of tumors
Tapas Tripura, Abhilash Awasthi, Sitikantha Roy, and Souvik Chakraborty · 2023
Closest in time.