A 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.
Arnulf JentzenDiyora SalimovaTimo WeltiPublished in: CoRR (2018)
Keyphrases
- partial differential equations
- solving partial differential equations
- anisotropic diffusion
- artificial neural networks
- diffusion equation
- nonlinear diffusion
- image denoising
- diffusion process
- perona malik
- level set
- image processing
- finite difference
- image enhancement
- heat equation
- multiscale
- reaction diffusion
- noise removal
- numerical solution
- wavelet coefficients
- numerical algorithms
- numerical scheme
- neural network
- fourth order
- finite difference method
- numerical methods
- ordinary differential equations
- curve evolution
- shock filter
- difference equations
- energy functional
- basis functions
- linear combination
- scalar valued
- high order
- denoising
- numerical integration
- boundary value problem
- conservation laws
- natural images
- taylor series expansion
- nonlinear partial differential equations