相关论文: Lagrangian Flow Matching: A Least-Action Framework…

As a powerful technique in generative modeling, Flow Matching (FM) aims to learn velocity fields from noise to data, which is often explained and implemented as solving Optimal Transport (OT) problems. In this study, we bridge FM and the…

Flow Matching has limited ability in achieving one-step generation due to its reliance on learned curved trajectories. Previous studies have attempted to address this limitation by either modifying the coupling distribution to prevent…

We propose a consistency model based on the optimal-transport flow. A physics-informed design of partially input-convex neural networks (PICNN) plays a central role in constructing the flow field that emulates the displacement…

In this work, a unified representation of all the time-varying dynamics is accomplished with a Lagrangian framework for analyzing Fisher-Rao regularized dynamical optimal mass transport (OMT) derived flows. While formally equivalent to the…

We study the Lagrangian dynamics of passive tracers in a simple model of a driven two-dimensional vortex resembling real-world geophysical flow patterns. Using a discrete approximation of the system's transfer operator, we construct a…

The use of guidance to steer sampling toward desired outcomes has been widely explored within diffusion models, especially in applications such as image and trajectory generation. However, incorporating guidance during training remains…

Solving optimal transport (OT) on random minibatches is a common surrogate for exact OT in large-scale learning. In flow matching (FM), this surrogate is used to obtain OT-like couplings that can straighten probability paths and reduce…

Time-varying vector fields produced by computational fluid dynamics simulations are often prohibitively large and pose challenges for accurate interactive analysis and exploration. To address these challenges, reduced Lagrangian…

Flow Matching is a powerful framework for learning transport maps between probability distributions. Yet its standard single-parameter formulation is not designed to capture multi-parameter variations where the resulting transport should be…

Simulation-free methods for training continuous-time generative models construct probability paths that go between noise distributions and individual data samples. Recent works, such as Flow Matching, derived paths that are optimal for each…

We propose dynamical optimal transport (OT) problems constrained in a parameterized probability subset. In application problems such as deep learning, the probability distribution is often generated by a parameterized mapping function. In…

Mainstream flow matching methods typically focus on learning the local velocity field, which inherently requires multiple integration steps during generation. In contrast, Mean Velocity Flow models establish a relationship between the local…

Optimal transport (OT) and Schr{\"o}dinger bridge (SB) problems have emerged as powerful frameworks for transferring probability distributions with minimal cost. However, existing approaches typically focus on endpoint matching while…

We propose a defiltering method of turbulent flow fields for Lagrangian particle tracking using machine learning techniques. Numerical simulation of Lagrangian particle tracking is commonly used in various fields. In general, practical…

We consider large-scale traffic assignment problems and develop a path-based compression framework. In particular, we partition paths into major and minor paths according to a set of nominal flows and a prescribed threshold, and retain the…

Coarse-grained (CG) molecular simulations have become a standard tool to study molecular processes on time- and length-scales inaccessible to all-atom simulations. Parameterizing CG force fields to match all-atom simulations has mainly…

We extend flow matching to ensembles of linear systems in both deterministic and stochastic settings. Averaging over system parameters induces memory leading to a non-Markovian interpolation problem for the stochastic case. In this setting,…

Expanding on neural operators, we propose a novel framework for stochastic process learning across arbitrary domains. In particular, we develop operator flow matching (OFM) for learning stochastic process priors on function spaces. OFM…

Despite the success of classical traffic flow (e.g., second-order macroscopic) models and data-driven (e.g., Machine Learning - ML) approaches in traffic state estimation, those approaches either require great efforts for parameter…

In this paper, we show how to study the evolution of a system, given imprecise knowledge about the state of the system and the dynamics laws. Our approach is based on Fuzzy Set Theory, and it will be shown that the \emph{Fuzzy Dynamics} of…