Solving High Dimensional Partial Differential Equations Using Tensor Neural Network and A Posteriori Error Estimators.
Yifan WangZhongshuo LinYangfei LiaoHaochen LiuHehu XiePublished in: CoRR (2023)
Keyphrases
- partial differential equations
- neural network
- high dimensional
- high order
- anisotropic diffusion
- numerical solution
- dimensionality reduction
- image denoising
- scalar valued
- level set
- image enhancement
- numerical algorithms
- image processing
- fourth order
- diffusion tensor
- differential equations
- energy functional
- pattern recognition
- finite difference
- problems in image processing
- higher order
- multiscale
- numerical scheme
- finite difference method
- structure tensor
- diffusion equation
- nonlinear partial differential equations
- feature extraction
- mathematical morphology
- feature space
- curve evolution
- low dimensional
- object recognition
- numerical methods
- estimation error