SelectNet: self-paced learning for high-dimensional partial differential equations (Q2131038)

scientific article; zbMATH DE number 7513823

Language	Label	Description	Also known as
English	SelectNet: self-paced learning for high-dimensional partial differential equations	scientific article; zbMATH DE number 7513823

Statements

instance of

scholarly article

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title

SelectNet: self-paced learning for high-dimensional partial differential equations (English)

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Journal of Computational Physics

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publication date

25 April 2022

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full work available at URL

https://arxiv.org/abs/2001.04860

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zbMATH Keywords

high-dimensional PDEs

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deep neural networks

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self-paced learning

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selected sampling

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least square method

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convergence

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describes a project that uses

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Universal approximation bounds for superpositions of a sigmoidal function

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Q4558169

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Approximation by superpositions of a sigmoidal function

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Neural‐network‐based approximations for solving partial differential equations

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Q5396673

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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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A priori estimates of the population risk for two-layer neural networks

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Exponential convergence of the deep neural network approximation for analytic functions

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The Deep Ritz Method: a deep learning-based numerical algorithm for solving variational problems

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A FAST, STABLE AND ACCURATE NUMERICAL METHOD FOR THE BLACK–SCHOLES EQUATION OF AMERICAN OPTIONS

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Symmetric positive linear differential equations

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On the approximation by single hidden layer feedforward neural networks with fixed weights

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Solving high-dimensional partial differential equations using deep learning

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Multilayer feedforward networks are universal approximators

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A proof that rectified deep neural networks overcome the curse of dimensionality in the numerical approximation of semilinear heat equations

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Overcoming the curse of dimensionality in the approximative pricing of financial derivatives with default risks

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Solving for high-dimensional committor functions using artificial neural networks

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Neural algorithm for solving differential equations

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Lower bounds for approximation by MLP neural networks

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Numerical solution for high order differential equations using a hybrid neural network-optimization method

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New Error Bounds for Deep ReLU Networks Using Sparse Grids

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Error bounds for deep ReLU networks using the Kolmogorov-Arnold superposition theorem

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Deep ReLU Networks Overcome the Curse of Dimensionality for Generalized Bandlimited Functions

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Adaptive Deep Learning for High-Dimensional Hamilton--Jacobi--Bellman Equations

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Optimal approximation of piecewise smooth functions using deep ReLU 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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Nonlinear approximation via compositions

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Deep Network With Approximation Error Being Reciprocal of Width to Power of Square Root of Depth

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DGM: a deep learning algorithm for solving partial differential equations

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Error bounds for approximations with deep ReLU networks

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Sparse grid spaces for the numerical solution of the electronic Schrödinger equation

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Weak adversarial networks for high-dimensional partial differential equations

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Identifiers

Mathematics Subject Classification ID

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10.1016/J.JCP.2021.110444

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Sitelinks

Mathematics(1 entry)

mardi Publication:2131038