Error analysis for empirical risk minimization over clipped ReLU networks in solving linear Kolmogorov partial differential equations (Q6662424)

scientific article; zbMATH DE number 7966454

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English	Error analysis for empirical risk minimization over clipped ReLU networks in solving linear Kolmogorov partial differential equations	scientific article; zbMATH DE number 7966454

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instance of

scholarly article

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title

Error analysis for empirical risk minimization over clipped ReLU networks in solving linear Kolmogorov partial differential equations (English)

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Numerical Mathematics: Theory, Methods and Applications

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publication date

14 January 2025

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zbMATH Keywords

linear Kolmogorov PDE

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curse of dimensionality

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empirical risk minimization

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generalization error

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MaRDI profile type

Publication

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cites work

Neural Network Learning

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On deep learning as a remedy for the curse of dimensionality in nonparametric regression

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Full error analysis for the training of deep neural networks

0 references

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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Finite Elements

0 references

Error bounds for approximation with neural networks

0 references

On the mathematical foundations of learning

0 references

Convergence Rate Analysis for Deep Ritz Method

0 references

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

0 references

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

0 references

Q5189317

0 references

A Proof that Artificial Neural Networks Overcome the Curse of Dimensionality in the Numerical Approximation of Black–Scholes Partial Differential Equations

0 references

A distribution-free theory of nonparametric regression

0 references

Loss of regularity for Kolmogorov equations

0 references

Solving high-dimensional partial differential equations using deep learning

0 references

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

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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 Rate of Convergence of Physics Informed Neural Networks for the Linear Second Order Elliptic PDEs

0 references

A Rate of Convergence of Weak Adversarial Neural Networks for the Second Order Parabolic PDEs

0 references

Deep nonparametric regression on approximate manifolds: nonasymptotic error bounds with polynomial prefactors

0 references

On the rate of convergence of fully connected deep neural network regression estimates

0 references

Oracle inequalities in empirical risk minimization and sparse recovery problems. École d'Été de Probabilités de Saint-Flour XXXVIII-2008.

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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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Nonparametric regression using deep neural networks with ReLU activation function

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Understanding Machine Learning

0 references

DGM: a deep learning algorithm for solving partial differential equations

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High-Dimensional Probability

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Convergence of Physics-Informed Neural Networks Applied to Linear Second-Order Elliptic Interface Problems

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Identifiers

DOI

10.4208/nmtma.oa-2024-0026

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Mathematics Subject Classification ID

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Sitelinks

Mathematics(1 entry)

mardi Publication:6662424