Quantifying the generalization error in deep learning in terms of data
distribution and neural network smoothness

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Quantifying the generalization error in deep learning in terms of data distribution and neural network smoothness

27 May 2019

George Karniadakis

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Papers citing "Quantifying the generalization error in deep learning in terms of data distribution and neural network smoothness"

16 / 16 papers shown

Title
Reliable extrapolation of deep neural operators informed by physics or sparse observations Min Zhu Handi Zhang Anran Jiao George Karniadakis Lu Lu 106 100 0 13 Dec 2022
Compute-Efficient Deep Learning: Algorithmic Trends and Opportunities Brian Bartoldson B. Kailkhura Davis W. Blalock 109 51 0 13 Oct 2022
Certified machine learning: Rigorous a posteriori error bounds for PDE defined PINNs Birgit Hillebrecht B. Unger PINN 84 5 0 07 Oct 2022
Overview frequency principle/spectral bias in deep learning Z. Xu Yaoyu Zhang Yaoyu Zhang FaML 92 74 0 19 Jan 2022
Embedding Principle: a hierarchical structure of loss landscape of deep neural networks Yaoyu Zhang Yuqing Li Zhongwang Zhang Yaoyu Zhang Z. Xu 86 23 0 30 Nov 2021
Approximation capabilities of measure-preserving neural networks Aiqing Zhu Pengzhan Jin Yifa Tang 84 8 0 21 Jun 2021
Embedding Principle of Loss Landscape of Deep Neural Networks Yaoyu Zhang Zhongwang Zhang Yaoyu Zhang Z. Xu 69 38 0 30 May 2021
Mosaic Flows: A Transferable Deep Learning Framework for Solving PDEs on Unseen Domains Hengjie Wang R. Planas Aparna Chandramowlishwaran Ramin Bostanabad AI4CE 149 64 0 22 Apr 2021
On Theory-training Neural Networks to Infer the Solution of Highly Coupled Differential Equations M. T. Rad A. Viardin M. Apel AI4CE 42 3 0 09 Feb 2021
Physics-informed neural networks with hard constraints for inverse design Lu Lu R. Pestourie Wenjie Yao Zhicheng Wang F. Verdugo Steven G. Johnson PINN 102 522 0 09 Feb 2021
Adaptive Checkpoint Adjoint Method for Gradient Estimation in Neural ODE Juntang Zhuang Nicha Dvornek Xiaoxiao Li S. Tatikonda X. Papademetris James Duncan BDL 127 112 0 03 Jun 2020
SympNets: Intrinsic structure-preserving symplectic networks for identifying Hamiltonian systems Pengzhan Jin Zhen Zhang Aiqing Zhu Yifa Tang George Karniadakis 105 21 0 11 Jan 2020
Deep learning architectures for nonlinear operator functions and nonlinear inverse problems Maarten V. de Hoop Matti Lassas C. Wong 78 26 0 23 Dec 2019
Variational Physics-Informed Neural Networks For Solving Partial Differential Equations E. Kharazmi Z. Zhang George Karniadakis 108 246 0 27 Nov 2019
DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operators Lu Lu Pengzhan Jin George Karniadakis 254 2,179 0 08 Oct 2019
DeepXDE: A deep learning library for solving differential equations Lu Lu Xuhui Meng Zhiping Mao George Karniadakis PINN AI4CE 101 1,555 0 10 Jul 2019