Related papers: Flows on convex polytopes
In this paper, we define a class of new geometric flows on a complete Riemannian manifold. The new flow is related to the generalized (third order) Landau-Lifishitz equation. On the other hand it could be thought of a special case of the…
We introduce a novel generative model for the representation of joint probability distributions of a possibly large number of discrete random variables. The approach uses measure transport by randomized assignment flows on the statistical…
Many components of data analysis in high energy physics and beyond require morphing one dataset into another. This is commonly solved via reweighting, but there are many advantages of preserving weights and shifting the data points instead.…
We present a set of polynomial equations that provides models of the lattice Boltzmann theory for any required level of accuracy and for any dimensional space in a general form. We explicitly derive two- and three-dimensional models…
For the model of a compressible barotropic fluid on a two dimensional rotating Riemmanian manifold we discuss a special class of smooth solutions having a form of a steady non-singular vortex moving with a bearing field. The model can be…
Normalizing flows have emerged as an important family of deep neural networks for modelling complex probability distributions. In this note, we revisit their coupling and autoregressive transformation layers as probabilistic graphical…
A central issue of the science of complex systems is the quantitative characterization of complexity. In the present work we address this issue by resorting to information geometry. Actually we propose a constructive way to associate to a -…
A new well model for one-phase flow in anisotropic porous media is introduced, where the mass exchange between well and a porous medium is modeled by spatially distributed source terms over a small neighborhood region. To this end, we first…
Assignment flows denote a class of dynamical models for contextual data labeling (classification) on graphs. We derive a novel parametrization of assignment flows that reveals how the underlying information geometry induces two processes…
Physical systems with complex unsteady dynamics, such as fluid flows, are often poorly represented by a single mean solution. For many practical applications, it is crucial to access the full distribution of possible states, from which…
Recently, studies on machine learning have focused on methods that use symmetry implicit in a specific manifold as an inductive bias. Grassmann manifolds provide the ability to handle fundamental shapes represented as shape spaces, enabling…
In this paper we construct multiparametric families of two dimensional metrics with polynomial first integral. Such integrable geodesic flows are described by solutions of some semi-Hamiltonian hydrodynamic type system. We find infinitely…
We study the mean curvature flow of smooth $n$-dimensional compact submanifolds with quadratic pinching in a Riemannian manifold $\mathcal{N}^{n+m}$. Our main focus is on the case of high codimension, $m\geq 2$. We establish a codimension…
Structurally stable (rough) flows on surfaces have only finitely many singularities and finitely many closed orbits, all of which are hyperbolic, and they have no trajectories joining saddle points. The violation of the last property leads…
In this article we write the equations of barotropic compressible fluid mechanics as a geodesic equation on an infinite-dimensional manifold. The equations are given by \begin{align} u_t + \nabla_uu = -\frac{1}{\rho} \grad p \\ \rho_t +…
We provide a general framework for constructing probability distributions on Riemannian manifolds, taking advantage of area-preserving maps and isometries. Control over distributions' properties, such as parameters, symmetry and modality…
We develop a novel policy synthesis algorithm, RMPflow, based on geometrically consistent transformations of Riemannian Motion Policies (RMPs). RMPs are a class of reactive motion policies designed to parameterize non-Euclidean behaviors as…
Hamiltonian flows on compact surfaces are characterized, and the topological invariants of such flows with finitely many singular points are constructed from the viewpoints of integrable systems, fluid mechanics, and dynamical systems.…
New elementary, self-contained proofs are presented for the topological and the smooth classification theorems of linear flows on finite-dimensional normed spaces. The arguments, and the examples that accompany them, highlight the…
We propose a novel entropy flow on weighted graphs, which provides a principled framework that characterizes the evolution of probability distributions over graph structures while sharing geometric intuition with discrete Ricci flow. We…