Related papers: Normalizing Flows on Tori and Spheres
Normalizing flows have proven their efficacy for density estimation in Euclidean space, but their application to rotational representations, crucial in various domains such as robotics or human pose modeling, remains underexplored.…
In this paper we examine the flow generated by coupled surface and internal small-amplitude water waves in a two-fluid layer model, where we take the upper layer to be rotational (constant vorticity) and the lower layer to be irrotational.…
We present rectified flow, a surprisingly simple approach to learning (neural) ordinary differential equation (ODE) models to transport between two empirically observed distributions \pi_0 and \pi_1, hence providing a unified solution to…
In this paper, we provide a classification of steady solutions to two-dimensional incompressible Euler equations in terms of the set of flow angles. The first main result asserts that the set of flow angles of any bounded steady flow in the…
We approach the problem of learning continuous normalizing flows from a dual perspective motivated by entropy-regularized optimal transport, in which continuous normalizing flows are cast as gradients of scalar potential functions. This…
In this work, we investigate the use of normalizing flows to model conditional distributions. In particular, we use our proposed method to analyze inverse problems with invertible neural networks by maximizing the posterior likelihood. Our…
We revisit the well-known Curve Shortening Flow for immersed curves in the $d$-dimensional Euclidean space. We exploit a fundamental structure of the problem to derive a new global construction of a solution, that is, a construction that is…
A recently proposed renormalization group technique, based on the hierarchical structures present in theories with fluctuating geometry, is implemented in the model of branched polymers. The renormalization group equations can be solved…
Assuming a-priori a smooth generating vector field, we introduce a generally covariant measure of the flow geometry called the referential gradient of the flow. The main result is the explicit relation between the referential gradient and…
A new important relation between fluid mechanics and differential geometry is established. We study smooth steady solutions to the Euler equations with the additional property: the velocity vector is orthogonal to the gradient of the…
Fluid flows are omnipresent in nature and engineering disciplines. The reliable computation of fluids has been a long-lasting challenge due to nonlinear interactions over multiple spatio-temporal scales. The compressible Navier-Stokes…
We introduce the notion of Fermi flow for hypersurfaces in Riemannian manifolds. It turns out that this is a powerful tool to study the geometry of distance surfaces about a given initial hypersurface. Some of the results in this paper are…
Normalizing flows model a complex target distribution in terms of a bijective transform operating on a simple base distribution. As such, they enable tractable computation of a number of important statistical quantities, particularly…
Applications of normalizing flows to the sampling of field configurations in lattice gauge theory have so far been explored almost exclusively in two space-time dimensions. We report new algorithmic developments of gauge-equivariant flow…
Solutions of long, flexible polymer molecules are complex fluids that simultaneously exhibit fluid-like and solid-like behaviour. When subjected to external flows, dilute polymer solutions develop elastic turbulence - a unique chaotic flow…
Flows in networks (or graphs) play a significant role in numerous computer vision tasks. The scalar-valued edges in these graphs often lead to a loss of information and thereby to limitations in terms of expressiveness. For example,…
In this paper, we consider the mean curvature flow of convex hypersurfaces in Euclidean spaces with a general forcing term. We show that the flow may shrink to a point in finite time if the forcing term is small, or exist for all times and…
In this work, we study and solve the normalized Ricci flow equation for circle bundles over surfaces. Moreover, we study the asymptotic behavior of the solutions and their connections to some model geometries.
Consider a fluid flowing through a junction between two pipes with different sections. Its evolution is described by the 2D or 3D Euler equations, whose analytical theory is far from complete and whose numerical treatment may be rather…
Estimating the causal structure of observational data is a challenging combinatorial search problem that scales super-exponentially with graph size. Existing methods use continuous relaxations to make this problem computationally tractable…