Computational optimal transport: With applications to data science
Optimal transport (OT) theory can be informally described using the words of the French
mathematician Gaspard Monge (1746–1818): A worker with a shovel in hand has to move a …
mathematician Gaspard Monge (1746–1818): A worker with a shovel in hand has to move a …
Non-commutative calculus, optimal transport and functional inequalities in dissipative quantum systems
We study dynamical optimal transport metrics between density matrices associated to
symmetric Dirichlet forms on finite-dimensional C^* C∗-algebras. Our setting covers …
symmetric Dirichlet forms on finite-dimensional C^* C∗-algebras. Our setting covers …
Jump processes as generalized gradient flows
We have created a functional framework for a class of non-metric gradient systems. The
state space is a space of nonnegative measures, and the class of systems includes the …
state space is a space of nonnegative measures, and the class of systems includes the …
Numerical analysis of a robust free energy diminishing finite volume scheme for parabolic equations with gradient structure
C Cancès, C Guichard - Foundations of Computational Mathematics, 2017 - Springer
We present a numerical method for approximating the solutions of degenerate parabolic
equations with a formal gradient flow structure. The numerical method we propose …
equations with a formal gradient flow structure. The numerical method we propose …
[HTML][HTML] Cosh gradient systems and tilting
MA Peletier, A Schlichting - Nonlinear Analysis, 2023 - Elsevier
We review a class of gradient systems with dissipation potentials of hyperbolic-cosine type.
We show how such dissipation potentials emerge in large deviations of jump processes …
We show how such dissipation potentials emerge in large deviations of jump processes …
Entropic Ricci curvature bounds for discrete interacting systems
M Fathi, J Maas - 2016 - projecteuclid.org
We develop a new and systematic method for proving entropic Ricci curvature lower bounds
for Markov chains on discrete sets. Using different methods, such bounds have recently …
for Markov chains on discrete sets. Using different methods, such bounds have recently …
On the difference between entropic cost and the optimal transport cost
S Pal - arXiv preprint arXiv:1905.12206, 2019 - arxiv.org
Consider the Monge-Kantorovich problem of transporting densities $\rho_0 $ to $\rho_1 $
on $\mathbb {R}^ d $ with a strictly convex cost function. A popular relaxation of the problem …
on $\mathbb {R}^ d $ with a strictly convex cost function. A popular relaxation of the problem …
Entropy dissipation of Fokker-Planck equations on graphs
We study the nonlinear Fokker-Planck equation on graphs, which is the gradient flow in the
space of probability measures supported on the nodes with respect to the discrete …
space of probability measures supported on the nodes with respect to the discrete …
Scaling limits of discrete optimal transport
P Gladbach, E Kopfer, J Maas - SIAM Journal on Mathematical Analysis, 2020 - SIAM
We consider dynamical transport metrics for probability measures on discretizations of a
bounded convex domain in \mathbbR^d. These metrics are natural discrete counterparts to …
bounded convex domain in \mathbbR^d. These metrics are natural discrete counterparts to …
Fisher-rao gradient flow: geodesic convexity and functional inequalities
The dynamics of probability density functions has been extensively studied in science and
engineering to understand physical phenomena and facilitate algorithmic design. Of …
engineering to understand physical phenomena and facilitate algorithmic design. Of …