Active learning based sampling for high-dimensional nonlinear partial differential equations (Q2683063)

scientific article; zbMATH DE number 7649269

Language	Label	Description	Also known as
English	Active learning based sampling for high-dimensional nonlinear partial differential equations	scientific article; zbMATH DE number 7649269

Statements

instance of

scholarly article

0 references

title

Active learning based sampling for high-dimensional nonlinear partial differential equations (English)

0 references

0 references

0 references

Journal of Computational Physics

0 references

publication date

3 February 2023

0 references

full work available at URL

https://arxiv.org/abs/2112.13988

0 references

zbMATH Keywords

deep learning

0 references

active learning

0 references

adaptive sampling

0 references

nonlinear PDEs

0 references

high-dimensional

0 references

describes a project that uses

0 references

0 references

0 references

0 references

An introduction to MCMC for machine learning

0 references

Universal approximation bounds for superpositions of a sigmoidal function

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

0 references

Solving the quantum many-body problem with artificial neural networks

0 references

Q4386945

0 references

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

0 references

Deep learning-based numerical methods for high-dimensional parabolic partial differential equations and backward stochastic differential equations

0 references

The Barron space and the flow-induced function spaces for neural network models

0 references

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

0 references

Solving high-dimensional partial differential equations using deep learning

0 references

Int-Deep: a deep learning initialized iterative method for nonlinear problems

0 references

Overcoming the curse of dimensionality in the numerical approximation of semilinear parabolic partial differential equations

0 references

Overcoming the curse of dimensionality in the numerical approximation of parabolic partial differential equations with gradient-dependent nonlinearities

0 references

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

0 references

SwitchNet: A Neural Network Model for Forward and Inverse Scattering Problems

0 references

Solving for high-dimensional committor functions using artificial neural networks

0 references

Solving Allen-Cahn and Cahn-Hilliard Equations using the Adaptive Physics Informed Neural Networks

0 references

Neural algorithm for solving differential equations

0 references

Optimal Control Problems of Fully Coupled FBSDEs and Viscosity Solutions of Hamilton--Jacobi--Bellman Equations

0 references

Deep Network Approximation for Smooth Functions

0 references

DeepXDE: A Deep Learning Library for Solving Differential Equations

0 references

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

0 references

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

0 references

Variance Components and Generalized Sobol' Indices

0 references

Q3208026

0 references

Inferring solutions of differential equations using noisy multi-fidelity data

0 references

Machine learning of linear differential equations using Gaussian processes

0 references

Efficient Hierarchical Approximation of High‐Dimensional Option Pricing Problems

0 references

Active Learning

0 references

Deep Network Approximation Characterized by Number of Neurons

0 references

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

0 references

Neural network approximation: three hidden layers are enough

0 references

Optimal approximation rate of ReLU networks in terms of width and depth

0 references

Approximation rates for neural networks with general activation functions

0 references

DGM: a deep learning algorithm for solving partial differential equations

0 references

DPM: a deep learning PDE augmentation method with application to large-eddy simulation

0 references

Conditional Karhunen-Loève expansion for uncertainty quantification and active learning in partial differential equation models

0 references

Weak adversarial networks for high-dimensional partial differential equations

0 references

Identifiers

Mathematics Subject Classification ID

0 references

0 references

0 references

0 references

0 references

10.1016/J.JCP.2022.111848

0 references

Sitelinks

Mathematics(1 entry)

mardi Publication:2683063