Improved Analysis of PINNs: Alleviate the CoD for Compositional Solutions

DOI10.4208/aam.oa-2023-0021MaRDI QIDQ6151354

Pingwen Zhang, Cheng Yuan, Yu Ling Jiao, Jerry Zhijian Yang, Xiliang Lu

Publication date: 11 March 2024

Published in: Annals of Applied Mathematics (Search for Journal in Brave)

zbMATH Keywords

approximationdeep neural networkcomposition function

Mathematics Subject Classification ID

Artificial neural networks and deep learning (68T07) Numerical methods for partial differential equations, boundary value problems (65N99)

Cites Work

• Unnamed Item
• Weak adversarial networks for high-dimensional partial differential equations
• Learning constitutive relations from indirect observations using deep neural networks
• The Deep Ritz Method: a deep learning-based numerical algorithm for solving variational problems
• Solving the Kolmogorov PDE by means of deep learning
• Approximation rates for neural networks with encodable weights in smoothness spaces
• The Barron space and the flow-induced function spaces for neural network models
• Learning constitutive relations using symmetric positive definite neural networks
• Nonparametric regression using deep neural networks with ReLU activation function
• Error bounds for approximations with deep ReLU networks
• Physics-informed neural networks: a deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations
• Universal approximation bounds for superpositions of a sigmoidal function
• A Multivariate Faa di Bruno Formula with Applications
• Feedforward Neural Networks and Compositional Functions with Applications to Dynamical Systems
• Convergence Rate Analysis for Deep Ritz Method
• A Rate of Convergence of Physics Informed Neural Networks for the Linear Second Order Elliptic PDEs
• Deep Network Approximation for Smooth Functions
• Machine Learning and Computational Mathematics
• The Mathematical Theory of Finite Element Methods
• A Regularity Theory for Static Schrödinger Equations on \(\boldsymbol{\mathbb{R}}\)^d in Spectral Barron Spaces

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