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On the spectral bias of coupled frequency predictor-corrector triangular DNN: the convergence analysis - MaRDI portal

On the spectral bias of coupled frequency predictor-corrector triangular DNN: the convergence analysis (Q6179933)

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scientific article; zbMATH DE number 7791041

Language	Label	Description	Also known as
English	On the spectral bias of coupled frequency predictor-corrector triangular DNN: the convergence analysis	scientific article; zbMATH DE number 7791041

Statements

scholarly article

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On the spectral bias of coupled frequency predictor-corrector triangular DNN: the convergence analysis (English)

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Japan Journal of Industrial and Applied Mathematics

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publication date

18 January 2024

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zbMATH Keywords

deep neural networks

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spectral bias

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neural tangent kernel

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MaRDI profile type

MaRDI publication profile

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full work available at URL

https://doi.org/10.1007/s13160-023-00617-3

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Deep learning in high dimension: Neural network expression rates for generalized polynomial chaos expansions in UQ

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Deep learning-based numerical methods for high-dimensional parabolic partial differential equations and backward stochastic differential equations

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Deep learning observables in computational fluid dynamics

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Iterative surrogate model optimization (ISMO): an active learning algorithm for PDE constrained optimization with deep neural networks

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Neural‐network‐based approximations for solving partial differential equations

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A theoretical analysis of deep neural networks and parametric PDEs

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Physics-informed neural networks for high-speed flows

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Hidden physics models: machine learning of nonlinear partial differential equations

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Adaptive activation functions accelerate convergence in deep and physics-informed neural networks

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Physics-informed neural networks: a deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations

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Frequency Principle: Fourier Analysis Sheds Light on Deep Neural Networks

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When and why PINNs fail to train: a neural tangent kernel perspective

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Understanding and Mitigating Gradient Flow Pathologies in Physics-Informed Neural Networks

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Extended Physics-Informed Neural Networks (XPINNs): A Generalized Space-Time Domain Decomposition Based Deep Learning Framework for Nonlinear Partial Differential Equations

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A Phase Shift Deep Neural Network for High Frequency Approximation and Wave Problems

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Multi-Scale Deep Neural Network (MscaleDNN) for Solving Poisson-Boltzmann Equation in Complex Domains

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Learning high frequency data via the coupled frequency predictor-corrector triangular DNN

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Deep Learning Architectures

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On the eigenvector bias of Fourier feature networks: from regression to solving multi-scale PDEs with physics-informed neural networks

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Neural tangent kernel: convergence and generalization in neural networks (invited paper)

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Wide neural networks of any depth evolve as linear models under gradient descent <sup>*</sup>

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Identifiers

10.1007/s13160-023-00617-3

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Mathematics Subject Classification ID

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zbMATH DE Number

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Sitelinks

Mathematics(1 entry)

mardi Publication:6179933

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