Space-time error estimates for deep neural network approximations for differential equations (Q2683168)

scientific article; zbMATH DE number 7649348

Language	Label	Description	Also known as
English	Space-time error estimates for deep neural network approximations for differential equations	scientific article; zbMATH DE number 7649348

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instance of

scholarly article

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title

Space-time error estimates for deep neural network approximations for differential equations (English)

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Advances in Computational Mathematics

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publication date

3 February 2023

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full work available at URL

https://arxiv.org/abs/1908.03833

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zbMATH Keywords

ANNs

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PDEs

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space-time error

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describes a project that uses

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Deep Splitting Method for Parabolic PDEs

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Solving the Kolmogorov PDE by means of deep learning

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Machine learning approximation algorithms for high-dimensional fully nonlinear partial differential equations and second-order backward stochastic differential equations

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Deep optimal stopping

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Solving high-dimensional optimal stopping problems using deep learning

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Analysis of the Generalization Error: Empirical Risk Minimization over Deep Artificial Neural Networks Overcomes the Curse of Dimensionality in the Numerical Approximation of Black--Scholes Partial Differential Equations

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Machine learning for semi linear PDEs

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

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DNN expression rate analysis of high-dimensional PDEs: application to option pricing

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Asymptotic expansion as prior knowledge in deep learning method for high dimensional BSDEs

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Q5270493

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Solving Ordinary Differential Equations I

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Solving high-dimensional partial differential equations using deep learning

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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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Proof that deep artificial neural networks overcome the curse of dimensionality in the numerical approximation of Kolmogorov partial differential equations with constant diffusion and nonlinear drift coefficients

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A theoretical analysis of deep neural networks and parametric PDEs

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Topological properties of the set of functions generated by neural networks of fixed size

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Optimal approximation of piecewise smooth functions using deep ReLU neural networks

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Neural networks-based backward scheme for fully nonlinear PDEs

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Nonparametric regression using deep neural networks with ReLU activation function

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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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Identifiers

Mathematics Subject Classification ID

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10.1007/S10444-022-09970-2

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Sitelinks

Mathematics(1 entry)

mardi Publication:2683168