Deep learning based on randomized quasi-Monte Carlo method for solving linear Kolmogorov partial differential equation (Q6582041)

scientific article; zbMATH DE number 7890919

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English	Deep learning based on randomized quasi-Monte Carlo method for solving linear Kolmogorov partial differential equation	scientific article; zbMATH DE number 7890919

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instance of

scholarly article

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title

Deep learning based on randomized quasi-Monte Carlo method for solving linear Kolmogorov partial differential equation (English)

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Journal of Computational and Applied Mathematics

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publication date

1 August 2024

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zbMATH Keywords

deep learning

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linear Kolmogorov equations

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randomized quasi-Monte Carlo

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generalization error

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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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DGM: a deep learning algorithm for solving partial differential equations

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

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Solving the Kolmogorov PDE by means of 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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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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Q4003879

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Quasi-Monte Carlo methods with applications in finance

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Q4549488

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A quasi-Monte Carlo data compression algorithm for machine learning

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Q5053263

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Higher-Order Quasi-Monte Carlo Training of Deep Neural Networks

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Enhancing Accuracy of Deep Learning Algorithms by Training with Low-Discrepancy Sequences

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Neural Network Learning

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Learning Theory

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Understanding Machine Learning

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Q4856469

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Low-discrepancy point sets obtained by digital constructions over finite fields

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Randomization of Number Theoretic Methods for Multiple Integration

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Q3160669

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On the mathematical foundations of learning

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

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Full error analysis for the training of deep neural networks

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Error bounds for approximation with neural networks

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Approximation rates for neural networks with encodable weights in smoothness spaces

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On the Error Rate of Importance Sampling with Randomized Quasi-Monte Carlo

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Halton Sequences Avoid the Origin

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Multidimensional Variation for Quasi-Monte Carlo

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

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Nonparametric regression using deep neural networks with ReLU activation function

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

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

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Identifiers

DOI

10.1016/j.cam.2024.116088

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Mathematics Subject Classification ID

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Sitelinks

Mathematics(1 entry)

mardi Publication:6582041