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We continue our investigation to the use of the variational method to derive flow relations for generalized Newtonian fluids in confined geometries. While in the previous investigations we used the straight circular tube geometry with eight…
We continue our analysis of the thresholding scheme from the variational viewpoint and prove a conditional convergence result towards Brakke's notion of mean curvature flow. Our proof is based on a localized version of the minimizing…
The continuous variable quantum computing platform constitutes a promising candidate for realizing quantum advantage, as exemplified in Gaussian Boson Sampling. While noise in the experiments makes the computation attainable for classical…
We perform (2+1)-D simulations of viscous anisotropic hydrodynamics (VAH) under boost-invariant and conformal conditions. Comparing both VAH and traditional viscous hydrodynamics with kinetic theory in the relaxation-time approximation as…
The well-known hydrodynamical representation of the Schr\"{o}dinger equation is reformulated by extending the idea of Nelson-Yasue's stochastic variational method. The fluid flow is composed by the two stochastic processes from the past and…
Flow matching has recently emerged as a promising alternative to diffusion-based generative models, offering faster sampling and simpler training by learning continuous flows governed by ordinary differential equations. Despite growing…
We consider the motion of incompressible viscous fluid in a rectangle, imposing the periodicity condition in one direction and the no-slip boundary condition in the other. Assuming that the flow is subject to an external random force, white…
Optical flow estimation remains challenging due to untextured areas, motion boundaries, occlusions, and more. Thus, the estimated flow is not equally reliable across the image. To that end, post-hoc confidence measures have been introduced…
We propose a unified framework that employs variational inference (VI) with (conditional) normalizing flows (NFs) to train both between-model and within-model proposals for reversible jump Markov chain Monte Carlo, enabling efficient…
We consider the statistical inverse problem of estimating a background flow field (e.g., of air or water) from the partial and noisy observation of a passive scalar (e.g., the concentration of a solute), a common experimental approach to…
The field of general-purpose robotics has recently embraced powerful probabilistic diffusion-based models to learn the complex embodiment behaviours. However, existing models often come with significant trade-offs, namely high computational…
Many physical systems of interest involve the close interaction of a flow in a domain with complex, time-varying boundaries. Treatment of boundaries of this nature is cumbersome due to the difficulty in explicitly tracking boundaries that…
In the past few years, deep generative models, such as generative adversarial networks \autocite{GAN}, variational autoencoders \autocite{vaepaper}, and their variants, have seen wide adoption for the task of modelling complex data…
We introduce an analogue to Kato's Criterion regarding the inviscid convergence of stochastic Navier-Stokes flows to the strong solution of the deterministic Euler equation. Our assumptions cover additive, multiplicative and transport type…
We introduce an ordinary differential equation (ODE) based deep generative method for learning conditional distributions, named Conditional F\"ollmer Flow. Starting from a standard Gaussian distribution, the proposed flow could approximate…
We introduce stochastic normalizing flows, an extension of continuous normalizing flows for maximum likelihood estimation and variational inference (VI) using stochastic differential equations (SDEs). Using the theory of rough paths, the…
Traditional approaches to variational inference rely on parametric families of variational distributions, with the choice of family playing a critical role in determining the accuracy of the resulting posterior approximation. Simple…
We investigate parameteric Navier-Stokes equations for a viscous, incompressible flow in bounded domains. The coefficients of the equations are perturbed by high-dimensional random parameters, this fits in particular for modelling flows in…
Recent work has established a path-gradient estimator for simple variational Gaussian distributions and has argued that the path-gradient is particularly beneficial in the regime in which the variational distribution approaches the exact…
We formulate the flow of thick fluids as evolution variational and quasi-variational inequalities, with a variable threshold on the absolute value of the deformation rate tensor. In the variational case, we show the existence and uniqueness…