相关论文: Triangular Flows for Generative Modeling: Statisti…

We use persistent homology to build a quantitative understanding of large complex systems that are driven far-from-equilibrium; in particular, we analyze image time series of flow field patterns from numerical simulations of two important…

We study the three-dimensional clustering of velocity stagnation points, of nulls of the vorticity and of the Lagrangian acceleration, and of inertial particles in turbulent flows at fixed Reynolds numbers, but under different large-scale…

This paper is devoted to establishing some results on the density and multiplicity of solutions to the fractional Nirenberg problem which is equivalent to studying the conformally invariant equation $P_\sigma(v)=K…

In this short note we apply the recently proposed data-driven RANS closure modelling framework of Schmelzer et al. (2020) to fully three-dimensional, high Reynolds number flows: namely wall-mounted cubes and cuboids at Re=40,000, and a…

Generating a Boltzmann distribution in high dimension has recently been achieved with Normalizing Flows, which enable fast and exact computation of the generated density, and thus unbiased estimation of expectations. However, current…

Let $(M,J,\Omega)$ be a closed polarized complex manifold of K\"ahler type. Let $G$ be the maximal compact subgroup of the automorphism group of $(M,J)$. On the space of K\"ahler metrics that are invariant under $G$ and represent the…

The accurate and efficient modeling of granular flows and their interactions with external bodies is an open research problem. Continuum methods can be used to capture complexities neglected by terramechanics models without the…

Using time-series of stereoscopic particle image velocimetry data, we study the response of a turbulent von K\'{a}rm\'{a}n swirling flow to a continuous breaking of its forcing symmetry. Experiments are carried over a wide Reynolds number…

Effective Hamiltonians arise in several problems, including homogenization of Hamilton--Jacobi equations, nonlinear control systems, Hamiltonian dynamics, and Aubry--Mather theory. In Aubry--Mather theory, related objects, Mather measures,…

Non-spherical particles transported by an anisotropic turbulent flow preferentially align with the mean shear and intermittently tumble when the local strain fluctuates. Such an intricate behaviour is here studied for inertialess,…

We introduce a highly expressive class of function approximators called Splat Regression Models. Model outputs are mixtures of heterogeneous and anisotropic bump functions, termed splats, each weighted by an output vector. The power of…

This paper introduces Tensor Gauge Flow Models, a new class of Generative Flow Models that generalize Gauge Flow Models and Higher Gauge Flow Models by incorporating higher-order Tensor Gauge Fields into the Flow Equation. This extension…

We model a 3D turbulent fluid, evolving toward a statistical equilibrium, by adding to the equations for the mean field $(v, p)$ a term like $-\alpha \nabla\cdot(\ell(x) D v_t)$. This is of the Kelvin-Voigt form, where the Prandtl mixing…

There have been many attempts to derive continuum models for dense granular flow, but a general theory is still lacking. Here, we start with Mohr-Coulomb plasticity for quasi-2D granular materials to calculate (average) stresses and slip…

A simple analytical model for a turbulent flow is proposed, which considers the flow as a collection of localized spatial structures that are composed of elementary "cells" in which the state of the particles (atoms or molecules) is…

Normalizing Flows are generative models that directly maximize the likelihood. Previously, the design of normalizing flows was largely constrained by the need for analytical invertibility. We overcome this constraint by a training procedure…

Flows are exact-likelihood generative neural networks that transform samples from a simple prior distribution to the samples of the probability distribution of interest. Boltzmann Generators (BG) combine flows and statistical mechanics to…

Normalizing flows are a class of flexible deep generative models that offer easy likelihood computation. Despite their empirical success, there is little theoretical understanding of their expressiveness. In this work, we study residual…

Rectified flow (Liu et al., 2022; Liu, 2022; Wu et al., 2023) is a method for defining a transport map between two distributions, and enjoys popularity in machine learning, although theoretical results supporting the validity of these…

In this paper, we prove estimates and quantitative regularity results for the harmonic map flow. First, we consider H^1_loc-maps u defined on a parabolic ball P\subset M\times R and with target manifold N, that have bounded Dirichlet-energy…