Related papers: Evolution variational inequalities with general co…
We start by reviewing recent probabilistic results on ergodic sums in a large class of (non-uniformly) hyperbolic dynamical systems. Namely, we describe the central limit theorem, the almost-sure convergence to the gaussian and other stable…
Reconstructing the evolutionary history relating a collection of molecular sequences is the main subject of modern Bayesian phylogenetic inference. However, the commonly used Markov chain Monte Carlo methods can be inefficient due to the…
Generative flows are promising tractable models for density modeling that define probabilistic distributions with invertible transformations. However, tractability imposes architectural constraints on generative flows, making them less…
In this paper, we address variational inequalities (VI) with a finite-sum structure. We introduce a novel single-loop stochastic variance-reduced algorithm, incorporating the Bregman distance function, and establish an optimal convergence…
Our ability to generalize beyond training data to novel, out-of-distribution, image degradations is a hallmark of primate vision. The predictive brain, exemplified by predictive coding networks (PCNs), has become a prominent neuroscience…
The classical theorems of inviscid stability have been extended for compressible flows past compliant surfaces. We consider normal modes imposed on a plane parallel compressible flow past compliant walls modelled as spring-backed plates and…
Flow matching has become a leading framework for generative modeling, but quantifying the uncertainty of its samples remains an open problem. Existing approaches retrain the model with auxiliary variance heads, maintain costly ensembles, or…
We consider Monge-Kantorovich optimal transport problems on $\mathbb{R}^d$, $d\ge 1$, with a convex cost function given by the cumulant generating function of a probability measure. Examples include the Wasserstein-2 transport whose cost…
The paper introduces scaled Bregman distances of probability distributions which admit non-uniform contributions of observed events. They are introduced in a general form covering not only the distances of discrete and continuous stochastic…
Sampling a target probability distribution with an unknown normalization constant is a fundamental challenge in computational science and engineering. Recent work shows that algorithms derived by considering gradient flows in the space of…
We use the framework of the first-order differential structure in metric measure spaces introduced by Gigli to define a notion of weak solutions to gradient flows of convex, lower semicontinuous and coercive functionals. We prove their…
The evolution of several physical and biological systems, ranging from neutron transport in multiplying media to epidemics or population dynamics, can be described in terms of branching exponential flights, a stochastic process which…
The study of passive scalar transport in a turbulent velocity field leads naturally to the notion of generalized flows which are families of probability distributions on the space of solutions to the associated ODEs, which no longer satisfy…
Energy-based models (EBMs) are powerful probabilistic models, but suffer from intractable sampling and density evaluation due to the partition function. As a result, inference in EBMs relies on approximate sampling algorithms, leading to a…
We develop an approach to the theory of relativistic geometric flows and emergent gravity defined by entropy functionals and related statistical thermodynamics models. Nonholonomic deformations of G. Perelman's functionals and related…
The problem of deriving a gradient flow structure for the porous medium equation which is {\em thermodynamic}, in that it arises from the large deviations of some microscopic particle system, is studied. To this end, a rescaled zero-range…
Through the asymptotic expansion, the large-time behavior of the incompressible Navier-Stokes flow in $n$-dimensional whole space is drawn. In particular, the logarithmic evolution included in the flow velocity is the focus of attention.…
Stochastic differential equations of Langevin-diffusion form have received significant attention, thanks to their foundational role in both Bayesian sampling algorithms and optimization in machine learning. In the latter, they serve as a…
A new concept of {\em an evolution system of measures for stochastic flows} is considered. It corresponds to the notion of an invariant measure for random dynamical systems (or cocycles). The existence of evolution systems of measures for…
We describe recent attempts to extract the shear viscosity of the dilute Fermi gas at unitarity from experiments involving scaling flows. A scaling flow is a solution of the hydrodynamic equations that preserves the shape of the density…