Consider the linear transport equation in 1D under an external confining potential
For
This paper introduces a novel generative encoder (GE) framework for generative imaging and image processing tasks like image reconstruction, compression, denoising, inpainting, deblurring, and super-resolution. GE unifies the generative capacity of GANs and the stability of AEs in an optimization framework instead of stacking GANs and AEs into a single network or combining their loss functions as in existing literature. GE provides a novel approach to visualizing relationships between latent spaces and the data space. The GE framework is made up of a pre-training phase and a solving phase. In the former, a GAN with generator
and the image
Consider the linear transport equation in 1D under an external confining potential
For
It is shown that for any positive integer
We consider the linear third order (in time) PDE known as the SMGTJ-equation, defined on a bounded domain, under the action of either Dirichlet or Neumann boundary control
Let
We study the convergence rate of a continuous-time simulated annealing process