Adaptive quadratures for nonlinear approximation of low-dimensional PDEs using smooth neural networks.
Alexandre MagueresseSantiago BadiaPublished in: CoRR (2023)
Keyphrases
- low dimensional
- neural network
- partial differential equations
- high dimensional
- adaptive neural
- solving partial differential equations
- nonlinear manifold learning
- difference equations
- dimensionality reduction
- linear dimensionality reduction
- nonlinear dynamic systems
- numerical integration
- diffusion equation
- euclidean space
- manifold learning
- data points
- neural network model
- high dimensional data
- pattern recognition
- low dimensional manifolds
- principal component analysis
- image processing
- taylor series
- feature space
- artificial neural networks
- auto associative
- anisotropic diffusion
- image denoising
- numerical solution
- nonlinear systems
- adaptive control
- active contours
- differential equations
- image segmentation
- feed forward
- feature selection