Related papers: Statistical Properties of Rectified Flow
An adaptive, adversarial methodology is developed for the optimal transport problem between two distributions $\mu$ and $\nu$, known only through a finite set of independent samples $(x_i)_{i=1..N}$ and $(y_j)_{j=1..M}$. The methodology…
A simple algorithm for constructing an effective traffic model is presented. The algorithm uses statistically well-defined quantities extracted from the flow-density plot, and the resulting effective model naturally captures and predicts…
Traffic flow prediction is an important part of smart transportation. The goal is to predict future traffic conditions based on historical data recorded by sensors and the traffic network. As the city continues to build, parts of the…
Optimal transport is a powerful framework for computing distances between probability distributions. We unify the two main approaches to optimal transport, namely Monge-Kantorovitch and Sinkhorn-Cuturi, into what we define as Tsallis…
Flow matching has recently emerged as a flexible and efficient framework for generative modelling by learning deterministic transport dynamics between probability measures. In this work, we extend flow matching to the space of probability…
This thesis employs statistical learning technique to analyze, predict and solve the fixed charge network flow (FCNF) problem, which is common encountered in many real-world network problems. The cost structure for flows in the FCNF…
The optical flow of natural scenes is a combination of the motion of the observer and the independent motion of objects. Existing algorithms typically focus on either recovering motion and structure under the assumption of a purely static…
Alongside optimization-based planners, sampling-based approaches are often used in trajectory planning for autonomous driving due to their simplicity. Model predictive path integral control is a framework that builds upon optimization…
We study traffic flow on roads with a localized periodic inhomogeneity such as traffic signals, using a stochastic car-following model. We find that in cases of congestion, traffic flow can be optimized by controlling the inhomogeneity's…
We present a general (i.e., independent of the underlying model) interpolation technique based on optimal transportation of Gaussian models for parametric advection-dominated problems. The approach relies on a scalar testing function to…
Semantic segmentation and semantic image synthesis are two representative tasks in visual perception and generation. While existing methods consider them as two distinct tasks, we propose a unified framework (SemFlow) and model them as a…
The simultaneous presence of liquid and gas in porous media increases flow heterogeneity compared to saturated flows. However, so far the impact of saturation on flow statistics and transport dynamics remained unclear. Here, we develop a…
Inverse problems in physical or biological sciences often involve recovering an unknown parameter that is random. The sought-after quantity is a probability distribution of the unknown parameter, that produces data that aligns with…
Optimal Transport is a foundational mathematical theory that connects optimization, partial differential equations, and probability. It offers a powerful framework for comparing probability distributions and has recently become an important…
The optimal transport (OT) problem has gained significant traction in modern machine learning for its ability to: (1) provide versatile metrics, such as Wasserstein distances and their variants, and (2) determine optimal couplings between…
Cartograms are maps that rescale geographic regions (e.g., countries, districts) such that their areas are proportional to quantitative demographic data (e.g., population size, gross domestic product). Unlike conventional bar or pie charts,…
The coflow scheduling problem has emerged as a popular abstraction in the last few years to study data communication problems within a data center. In this basic framework, each coflow has a set of communication demands and the goal is to…
In this work, we introduce Modulated Flows (ModFlows), a novel approach for color transfer between images based on rectified flows. The primary goal of the color transfer is to adjust the colors of a target image to match the color…
Optimal transport (OT) theory provides powerful tools to compare probability measures. However, OT is limited to nonnegative measures having the same mass, and suffers serious drawbacks about its computation and statistics. This leads to…
We present an application of the recently developed ergodic theoretic machinery on scenery flows to a classical geometric measure theoretic problem in Euclidean spaces. We also review the enhancements to the theory required in our work. Our…