Rectified deep neural networks overcome the curse of dimensionality in the numerical approximation of gradient-dependent semilinear heat equations.
Ariel NeufeldTuan Anh NguyenPublished in: CoRR (2024)
Keyphrases
- neural network
- solving partial differential equations
- partial differential equations
- finite difference
- numerical methods
- curve evolution
- pattern recognition
- mathematical model
- piecewise constant
- neural network model
- fuzzy logic
- error bounds
- numerical analysis
- approximation error
- multilayer perceptron
- approximation methods
- numerical integration
- numerical calculation
- artificial neural networks
- genetic algorithm
- numerical algorithms
- chemical reaction
- numerical solution
- back propagation
- dynamical systems
- training algorithm
- fuzzy systems
- finite element
- differential equations
- alternating direction
- difference equations
- fault diagnosis
- edge detection
- linear systems
- gauss seidel method
- gauss seidel
- stochastic differential equations
- image denoising
- numerical scheme
- sensitivity analysis
- numerical simulations
- neural nets