Numerical solution of Poisson partial differential equations in high dimension using deep neural networks.
Mathias DusVirginie EhrlacherPublished in: CoRR (2023)
Keyphrases
- numerical solution
- high dimension
- partial differential equations
- neural network
- real valued
- feature selection
- image processing
- level set
- high dimensional
- anisotropic diffusion
- small sample
- image denoising
- pattern recognition
- input space
- differential equations
- high dimensional data
- multiscale
- image enhancement
- energy functional
- feature space
- finite difference
- diffusion equation
- numerical methods
- boundary value problem
- difference equations
- curve evolution
- high order
- support vector machine
- finite element
- numerical scheme
- exact solution
- radial basis function
- computational complexity
- model selection
- finite element method
- dimensionality reduction