Publications (63)
Convergence of the vertical Gradient flow for the Gaussian Monge problem
Erik Jansson, Klas Modin
We investigate a matrix dynamical system related to optimal mass transport in the linear category, namely, the problem of finding an optimal invertible matrix by which two covarian…
Diffeomorphic density registration
Martin Bauer, Sarang Joshi, Klas Modin
In this book chapter we study the Riemannian Geometry of the density registration problem: Given two densities (not necessarily probability densities) defined on a smooth finite di…
Symplectic Isospectral Runge--Kutta Methods as Lie group methods
Paolo Cifani, Klas Modin, Cecilia Pagliantini +1
We compare three approaches for structure preserving numerical integration of isospectral flows on quadratic Lie algebras. Such flows originate from Hamiltonian dynamics on the cot…
Simple unbalanced optimal transport
Boris Khesin, Klas Modin, Luke Volk
We introduce and study a simple model capturing the main features of unbalanced optimal transport. It is based on equipping the conical extension of the group of all diffeomorphism…
Casimir preserving spectrum of two-dimensional turbulence
Paolo Cifani, Milo Viviani, Erwin Luesink +2
We present predictions of the energy spectrum of forced two-dimensional turbulence obtained by employing a structure-preserving integrator. In particular, we construct a finite-mod…
Information geometry of diffeomorphism groups
Boris Khesin, Gerard MisioÅek, Klas Modin
The study of diffeomorphism groups and their applications to problems in analysis and geometry has a long history. In geometric hydrodynamics, pioneered by V.~Arnold in the 1960s,…