Deep neural networks with ReLU, leaky ReLU, and softplus activation provably overcome the curse of dimensionality for space-time solutions of semilinear partial differential equations.
Julia AckermannArnulf JentzenBenno KuckuckJoshua Lee PadgettPublished in: CoRR (2024)
Keyphrases
- space time
- partial differential equations
- neural network
- boundary value problem
- numerical algorithms
- spatial and temporal
- spatio temporal
- numerical solution
- anisotropic diffusion
- video sequences
- image denoising
- level set
- image processing
- nonlinear partial differential equations
- dynamic scenes
- differential equations
- image enhancement
- multiscale
- multiple view geometry
- energy functional
- numerical methods
- fourth order
- numerical scheme
- pattern recognition
- scan statistic
- interesting events
- motion estimation
- finite difference
- high quality
- computer vision