Empirical Risk Minimization over Artificial Neural Networks Overcomes the Curse of Dimensionality in the Numerical Approximation of Linear Kolmogorov Partial Differential Equations with Unbounded Initial Functions.
Jichang XiaoXiaoqun WangPublished in: CoRR (2023)
Keyphrases
- partial differential equations
- finite difference
- empirical risk minimization
- artificial neural networks
- numerical methods
- numerical algorithms
- numerical solution
- level set
- image processing
- image denoising
- anisotropic diffusion
- image enhancement
- multiscale
- energy functional
- statistical learning theory
- computationally tractable
- diffusion equation
- closed form
- finite element
- vc dimension
- differential equations
- uniform convergence
- rates of convergence
- linear systems
- phase transition
- empirical risk
- high order