Deep neural networks overcome the curse of dimensionality in the numerical approximation of semilinear partial differential equations.
Petru A. Cioica-LichtMartin HutzenthalerP. Tobias WernerPublished in: CoRR (2022)
Keyphrases
- partial differential equations
- solving partial differential equations
- neural network
- image denoising
- numerical methods
- level set
- anisotropic diffusion
- image processing
- numerical algorithms
- finite difference
- image enhancement
- numerical solution
- finite difference method
- numerical scheme
- multiscale
- curve evolution
- differential equations
- problems in image processing
- energy functional
- diffusion equation
- difference equations
- pattern recognition
- fourth order
- mathematical morphology
- lattice boltzmann
- image segmentation
- boundary value problem
- denoising
- high order
- markov random field
- mumford shah model
- conservation laws
- dynamical systems