27 citations · 117 across the 15 of their papers we have counts for
17 papers
Large data global well-posedness for the modified Novikov-Veselov system
Adrian Nachman, Peter Perry, Daniel Tataru
The modified Novikov-Veselov system (mNV) is a cubic third order dispersive evolution in two space dimensions. It is also completely integrable, belonging to the same hierarchy as…
An optimal transport analogue of the Rudin Osher Fatemi model and its corresponding multiscale theory
Tristan Milne, Adrian Nachman
We develop a theory for image restoration with a learned regularizer that is analogous to that of Meyer's characterization of solutions of the classical variational method of Rudin…
A new method for determining Wasserstein 1 optimal transport maps from Kantorovich potentials, with deep learning applications
Tristan Milne, Étienne Bilocq, Adrian Nachman
Wasserstein 1 optimal transport maps provide a natural correspondence between points from two probability distributions, and , which is useful in many applications. Availabl…
Trust the Critics: Generatorless and Multipurpose WGANs with Initial Convergence Guarantees
Tristan Milne, Étienne Bilocq, Adrian Nachman
Inspired by ideas from optimal transport theory we present Trust the Critics (TTC), a new algorithm for generative modelling. This algorithm eliminates the trainable generator from…
Wasserstein GANs with Gradient Penalty Compute Congested Transport
Tristan Milne, Adrian Nachman
Wasserstein GANs with Gradient Penalty (WGAN-GP) are a very popular method for training generative models to produce high quality synthetic data. While WGAN-GP were initially devel…
A Multiscale Theory for Image Registration and Nonlinear Inverse Problems
Klas Modin, Adrian Nachman, Luca Rondi
In an influential paper, Tadmor, Nezzar and Vese (Multiscale Model. Simul. (2004)) introduced a hierarchical decomposition of an image as a sum of constituents of different scales.…