On the spectral bias of coupled frequency predictor-corrector triangular DNN: the convergence analysis
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Publication:6179933
DOI10.1007/s13160-023-00617-3OpenAlexW4386963760MaRDI QIDQ6179933
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Publication date: 18 January 2024
Published in: Japan Journal of Industrial and Applied Mathematics (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1007/s13160-023-00617-3
Artificial neural networks and deep learning (68T07) Spectral, collocation and related methods for boundary value problems involving PDEs (65N35) Wave scattering in solid mechanics (74J20) Numerical solutions to stochastic differential and integral equations (65C30)
Cites Work
- Unnamed Item
- Unnamed Item
- Deep learning-based numerical methods for high-dimensional parabolic partial differential equations and backward stochastic differential equations
- Deep learning observables in computational fluid dynamics
- Hidden physics models: machine learning of nonlinear partial differential equations
- Iterative surrogate model optimization (ISMO): an active learning algorithm for PDE constrained optimization with deep neural networks
- A theoretical analysis of deep neural networks and parametric PDEs
- When and why PINNs fail to train: a neural tangent kernel perspective
- Physics-informed neural networks for high-speed flows
- Adaptive activation functions accelerate convergence in deep and physics-informed neural networks
- On the eigenvector bias of Fourier feature networks: from regression to solving multi-scale PDEs with physics-informed neural networks
- Physics-informed neural networks: a deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations
- Neural‐network‐based approximations for solving partial differential equations
- Deep learning in high dimension: Neural network expression rates for generalized polynomial chaos expansions in UQ
- Understanding and Mitigating Gradient Flow Pathologies in Physics-Informed Neural Networks
- A Phase Shift Deep Neural Network for High Frequency Approximation and Wave Problems
- Frequency Principle: Fourier Analysis Sheds Light on Deep Neural Networks
- Multi-Scale Deep Neural Network (MscaleDNN) for Solving Poisson-Boltzmann Equation in Complex Domains
- Extended Physics-Informed Neural Networks (XPINNs): A Generalized Space-Time Domain Decomposition Based Deep Learning Framework for Nonlinear Partial Differential Equations
- Deep Learning Architectures
- Wide neural networks of any depth evolve as linear models under gradient descent *
- Neural tangent kernel: convergence and generalization in neural networks (invited paper)
- Learning high frequency data via the coupled frequency predictor-corrector triangular DNN
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