Adaptive quadratures for nonlinear approximation of low-dimensional PDEs using smooth neural networks.
Alexandre MagueresseSantiago BadiaPublished in: Comput. Math. Appl. (2024)
Keyphrases
- low dimensional
- neural network
- nonlinear manifold learning
- high dimensional
- adaptive neural
- difference equations
- partial differential equations
- artificial neural networks
- pattern recognition
- numerical integration
- diffusion equation
- dimensionality reduction
- linear dimensionality reduction
- data points
- high dimensional data
- principal component analysis
- manifold learning
- image processing
- auto associative
- solving partial differential equations
- low dimensional manifolds
- feed forward
- piecewise constant
- pattern classification
- lyapunov theory
- nonlinear diffusion
- numerical solution
- adaptive control
- differential equations
- approximation algorithms
- input space
- neural network model
- image denoising
- back propagation
- scale space
- fuzzy logic
- genetic algorithm