相关论文: Visualizing fluid flows via regularized optimal ma…

Cardiovascular diseases are a leading cause of death in the world, driving the development of patient-specific and benchmark models for blood flow analysis. This chapter provides a theoretical overview of the main categories of Reduced…

We present a novel reduced-order fluid simulation technique leveraging Dynamic Mode Decomposition (DMD) to achieve fast, memory-efficient, and user-controllable subspace simulation. We demonstrate that our approach combines the strengths of…

We propose a novel neural algorithm for the fundamental problem of computing the entropic optimal transport (EOT) plan between continuous probability distributions which are accessible by samples. Our algorithm is based on the saddle point…

The methodology to simulate transport phenomena in bulk systems is well-established. In contrast, there is no clear consensus about the choice of techniques to model cross-transport phenomena and phoretic transport, mainly because some of…

We study multi-marginal optimal transport (MOT) problems where the underlying cost has a graphical structure. These graphical multi-marginal optimal transport problems have found applications in several domains including traffic flow…

Many applications of computational fluid dynamics require multiple simulations of a flow under different input conditions. In this paper, a numerical algorithm is developed to efficiently determine a set of such simulations in which the…

Gaseous flows under an external force are intrinsically defined by their multi-scale nature due to the large variation of densities along the forcing direction. Devising a numerical method capable of accurately and efficiently solving…

A common recipe to improve diffusion models at test-time so that samples score highly against a user-specified reward is to introduce the gradient of the reward into the dynamics of the diffusion itself. This procedure is often ill posed,…

We introduce a finite-volume numerical scheme for solving stochastic gradient-flow equations. Such equations are of crucial importance within the framework of fluctuating hydrodynamics and dynamic density functional theory. Our proposed…

Sampling from diffusion probabilistic models (DPMs) can be viewed as a piecewise distribution transformation, which generally requires hundreds or thousands of steps of the inverse diffusion trajectory to get a high-quality image. Recent…

Finding a transformation between two unknown probability distributions from finite samples is crucial for modeling complex data distributions and performing tasks such as sample generation, domain adaptation and statistical inference. One…

Optical flow is a powerful tool for the study and analysis of motion in a sequence of images. In this article we study a Horn-Schunck type spatio-temporal regularization functional for image sequences that have a non-Euclidean, time varying…

We propose a volumetric formulation for computing the Optimal Transport problem defined on surfaces in $\mathbb{R}^3$, found in disciplines like optics, computer graphics, and computational methodologies. Instead of directly tackling the…

Optical flow is a fundamental technique for motion estimation, widely applied in video stabilization, interpolation, and object tracking. Traditional optical flow estimation methods rely on restrictive assumptions like brightness constancy…

We present a numerical methodology for construction of reduced order models, ROMs, of fluid flows through the combination of flow modal decomposition and regression analysis. Spectral proper orthogonal decomposition, SPOD, is applied to…

The time-fractional optimal transport (OT) and mean-field planning (MFP) models are developed to describe the anomalous transport of the agents in a heterogeneous environment such that their densities are transported from the initial…

In this work we propose, {analyze}, and validate a stabilized finite element method for a flow problem arising from the assessment of {4D Flow Magnetic Resonance Imaging quality}. Starting from the Navier-Stokes equation and splitting its…

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 study a model for traffic flow on networks based on a hyperbolic system of conservation laws with discontinuous flux. Each equation describes the density evolution of vehicles having a common path along the network. In this…

Flow matching casts sample generation as learning a continuous-time velocity field that transports noise to data. Existing flow matching networks typically predict each point's velocity independently, considering only its location and time…