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Towards Size-Independent Generalization Bounds for Deep Operator Nets

23 May 2022

Papers citing "Towards Size-Independent Generalization Bounds for Deep Operator Nets"

31 / 31 papers shown

Title
Investigating the Ability of PINNs To Solve Burgers' PDE Near Finite-Time BlowUp Dibyakanti Kumar Anirbit Mukherjee 66 2 0 08 Oct 2023
Size Lowerbounds for Deep Operator Networks Anirbit Mukherjee Amartya Roy AI4CE 66 3 0 11 Aug 2023
Spherical Fourier Neural Operators: Learning Stable Dynamics on the Sphere Boris Bonev Thorsten Kurth Christian Hundt Jaideep Pathak Maximilian Baust K. Kashinath Anima Anandkumar AI4Cl AI4CE 74 147 0 06 Jun 2023
On Size-Independent Sample Complexity of ReLU Networks Mark Sellke 67 6 0 03 Jun 2023
Fourier Neural Operator Surrogate Model to Predict 3D Seismic Waves Propagation F. Lehmann F. Gatti M. Bertin Didier Clouteau AI4CE 64 27 0 20 Apr 2023
Learning in latent spaces improves the predictive accuracy of deep neural operators Katiana Kontolati S. Goswami George Karniadakis Michael D. Shields AI4CE 88 22 0 15 Apr 2023
Transfer Learning Enhanced DeepONet for Long-Time Prediction of Evolution Equations Wuzhe Xu Yulong Lu Li Wang 60 38 0 09 Dec 2022
FourCastNet: Accelerating Global High-Resolution Weather Forecasting using Adaptive Fourier Neural Operators Thorsten Kurth Shashank Subramanian P. Harrington Jaideep Pathak Morteza Mardani D. Hall Andrea Miele K. Kashinath Anima Anandkumar AI4Cl 86 193 0 08 Aug 2022
Deep transfer operator learning for partial differential equations under conditional shift S. Goswami Katiana Kontolati Michael D. Shields George Karniadakis 74 109 0 20 Apr 2022
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 Guang Lin 87 15 0 07 Apr 2022
Enhanced DeepONet for Modeling Partial Differential Operators Considering Multiple Input Functions Lesley Tan Liang Chen 49 14 0 17 Feb 2022
Neural Stochastic PDEs: Resolution-Invariant Learning of Continuous Spatiotemporal Dynamics C. Salvi M. Lemercier A. Gerasimovičs AI4CE 67 45 0 19 Oct 2021
A Farewell to the Bias-Variance Tradeoff? An Overview of the Theory of Overparameterized Machine Learning Yehuda Dar Vidya Muthukumar Richard G. Baraniuk 92 72 0 06 Sep 2021
Learning Dissipative Dynamics in Chaotic Systems Zong-Yi Li Miguel Liu-Schiaffini Nikola B. Kovachki Burigede Liu Kamyar Azizzadenesheli K. Bhattacharya Andrew M. Stuart Anima Anandkumar AI4CE 81 31 0 13 Jun 2021
A Study of the Mathematics of Deep Learning Anirbit Mukherjee 33 4 0 28 Apr 2021
Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets Sizhuang He Hanwen Wang P. Perdikaris AI4CE 97 707 0 19 Mar 2021
Teaching the Incompressible Navier-Stokes Equations to Fast Neural Surrogate Models in 3D Nils Wandel Michael Weinmann Reinhard Klein AI4CE 75 51 0 22 Dec 2020
Fourier Neural Operator for Parametric Partial Differential Equations Zong-Yi Li Nikola B. Kovachki Kamyar Azizzadenesheli Burigede Liu K. Bhattacharya Andrew M. Stuart Anima Anandkumar AI4CE 504 2,453 0 18 Oct 2020
Estimates on the generalization error of Physics Informed Neural Networks (PINNs) for approximating PDEs Siddhartha Mishra Roberto Molinaro PINN 77 175 0 29 Jun 2020
Dropout: Explicit Forms and Capacity Control R. Arora Peter L. Bartlett Poorya Mianjy Nathan Srebro 104 38 0 06 Mar 2020
Rethinking Bias-Variance Trade-off for Generalization of Neural Networks Zitong Yang Yaodong Yu Chong You Jacob Steinhardt Yi-An Ma 69 185 0 26 Feb 2020
DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operators Lu Lu Pengzhan Jin George Karniadakis 248 2,158 0 08 Oct 2019
Physics-informed Autoencoders for Lyapunov-stable Fluid Flow Prediction N. Benjamin Erichson Michael Muehlebach Michael W. Mahoney AI4CE PINN 71 141 0 26 May 2019
Stronger generalization bounds for deep nets via a compression approach Sanjeev Arora Rong Ge Behnam Neyshabur Yi Zhang MLT AI4CE 89 643 0 14 Feb 2018
Size-Independent Sample Complexity of Neural Networks Noah Golowich Alexander Rakhlin Ohad Shamir 154 551 0 18 Dec 2017
The Deep Ritz method: A deep learning-based numerical algorithm for solving variational problems E. Weinan Ting Yu 125 1,390 0 30 Sep 2017
DGM: A deep learning algorithm for solving partial differential equations Justin A. Sirignano K. Spiliopoulos AI4CE 93 2,067 0 24 Aug 2017
A PAC-Bayesian Approach to Spectrally-Normalized Margin Bounds for Neural Networks Behnam Neyshabur Srinadh Bhojanapalli Nathan Srebro 88 610 0 29 Jul 2017
Spectrally-normalized margin bounds for neural networks Peter L. Bartlett Dylan J. Foster Matus Telgarsky ODL 212 1,225 0 26 Jun 2017
Computing Nonvacuous Generalization Bounds for Deep (Stochastic) Neural Networks with Many More Parameters than Training Data Gintare Karolina Dziugaite Daniel M. Roy 117 820 0 31 Mar 2017
Norm-Based Capacity Control in Neural Networks Behnam Neyshabur Ryota Tomioka Nathan Srebro 292 591 0 27 Feb 2015