Deep neural network approximation for high-dimensional elliptic PDEs with boundary conditions.
Philipp GrohsLukas HerrmannPublished in: CoRR (2020)
Keyphrases
- boundary conditions
- boundary value problem
- neural network
- high dimensional
- partial differential equations
- diffusion equation
- poisson equation
- numerical scheme
- numerical solution
- reaction diffusion
- shape from shading
- low dimensional
- deformation field
- sufficient conditions
- level set
- anisotropic diffusion
- difference equations
- numerical methods
- finite element method
- dimensionality reduction
- artificial neural networks
- finite element model
- blood flow
- spline interpolation
- image processing
- differential equations
- image denoising
- back propagation
- high dimensional data
- feature space
- neural network model
- data points
- fixed point theorem
- energy functional
- approximation algorithms
- parameter space
- similarity search
- activation function
- variational inequalities
- knn