Active learning based sampling for high-dimensional nonlinear partial differential equations
From MaRDI portal
Publication:2683063
DOI10.1016/j.jcp.2022.111848OpenAlexW4312053961MaRDI QIDQ2683063
Publication date: 3 February 2023
Published in: Journal of Computational Physics (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/2112.13988
Artificial intelligence (68Txx) Numerical methods for partial differential equations, initial value and time-dependent initial-boundary value problems (65Mxx) Numerical methods for partial differential equations, boundary value problems (65Nxx)
Related Items (1)
Uses Software
Cites Work
- Unnamed Item
- Unnamed Item
- Deep learning-based numerical methods for high-dimensional parabolic partial differential equations and backward stochastic differential equations
- Weak adversarial networks for high-dimensional partial differential equations
- Numerical solution for high order differential equations using a hybrid neural network-optimization method
- An introduction to MCMC for machine learning
- Inferring solutions of differential equations using noisy multi-fidelity data
- Machine learning of linear differential equations using Gaussian processes
- The Deep Ritz Method: a deep learning-based numerical algorithm for solving variational problems
- Approximation rates for neural networks with general activation functions
- DGM: a deep learning algorithm for solving partial differential equations
- 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
- Optimal approximation rate of ReLU networks in terms of width and depth
- The Barron space and the flow-induced function spaces for neural network models
- DPM: a deep learning PDE augmentation method with application to large-eddy simulation
- Conditional Karhunen-Loève expansion for uncertainty quantification and active learning in partial differential equation models
- Int-Deep: a deep learning initialized iterative method for nonlinear problems
- SelectNet: self-paced learning for high-dimensional partial differential equations
- Overcoming the curse of dimensionality in the numerical approximation of parabolic partial differential equations with gradient-dependent nonlinearities
- Solving for high-dimensional committor functions using artificial neural networks
- Neural algorithm for solving differential equations
- Active Learning
- Optimal Control Problems of Fully Coupled FBSDEs and Viscosity Solutions of Hamilton--Jacobi--Bellman Equations
- Universal approximation bounds for superpositions of a sigmoidal function
- Solving the quantum many-body problem with artificial neural networks
- Solving high-dimensional partial differential equations using deep learning
- Deep Network With Approximation Error Being Reciprocal of Width to Power of Square Root of Depth
- 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
- Deep ReLU Networks Overcome the Curse of Dimensionality for Generalized Bandlimited Functions
- DeepXDE: A Deep Learning Library for Solving Differential Equations
- Deep Network Approximation for Smooth Functions
- Overcoming the curse of dimensionality in the numerical approximation of semilinear parabolic partial differential equations
- Deep Network Approximation Characterized by Number of Neurons
- Solving Allen-Cahn and Cahn-Hilliard Equations using the Adaptive Physics Informed Neural Networks
- SwitchNet: A Neural Network Model for Forward and Inverse Scattering Problems
- Variance Components and Generalized Sobol' Indices
- Efficient Hierarchical Approximation of High‐Dimensional Option Pricing Problems
- Neural network approximation: three hidden layers are enough
This page was built for publication: Active learning based sampling for high-dimensional nonlinear partial differential equations