Related papers: WFR-FM: Simulation-Free Dynamic Unbalanced Optimal…
Wasserstein distributionally robust optimization (WDRO) optimizes against worst-case distributional shifts within a specified uncertainty set, leading to enhanced generalization on unseen adversarial examples, compared to standard…
Guidance of generative models is typically achieved by modifying the probability flow vector field through the addition of a guidance field. In this paper, we instead propose the Source-Guided Flow Matching (SGFM) framework, which modifies…
Reliable displacement measurement is fundamental for structural health monitoring and digital engineering workflows, as it provides direct structural response information. Vision-based measurement has emerged as a promising approach for…
Addressing challenges in urban water infrastructure systems including aging infrastructure, supply uncertainty, extreme events, and security threats, depend highly on water distribution networks modeling emphasizing the importance of…
Numerical stabilization techniques are often employed in under-resolved simulations of convection-dominated flows to improve accuracy and mitigate spurious oscillations. Specifically, the evolve--filter--relax (EFR) algorithm is a framework…
A new Wasserstein multi-element polynomial chaos expansion (WPCE) is proposed, which is inspired by recent advances in computational optimal transport for estimating Wasserstein distances. The developed method combines unsupervised learning…
Offline reinforcement learning (RL) aims to learn an optimal policy from a static dataset, making it particularly valuable in scenarios where data collection is costly, such as robotics. A major challenge in offline RL is distributional…
We propose a unified data-driven framework based on inverse optimal transport that can learn adaptive, nonlinear interaction cost function from noisy and incomplete empirical matching matrix and predict new matching in various matching…
Modern image formation algorithms in radio interferometry rely on repeated applications of the operator {\Phi} modelling the measurement process and its adjoint {Phi^\dagger} to enforce consistency with the acquired data, specifically via…
In this paper, we propose a data-based methodology to solve a multi-period stochastic optimal water flow (OWF) problem for water distribution networks (WDNs). The framework explicitly considers the pump schedule and water network head level…
Federated learning (FL) is a subfield of machine learning that avoids sharing local data with a central server, which can enhance privacy and scalability. The inability to consolidate data leads to a unique problem called dataset imbalance,…
We address the following problem: given two smooth densities on a manifold, find an optimal diffeomorphism that transforms one density into the other. Our framework builds on connections between the Fisher-Rao information metric on the…
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…
Optimal transport has gained much attention in image processing field, such as computer vision, image interpolation and medical image registration. Recently, Bredies et al. (ESAIM:M2AN 54:2351-2382, 2020) and Schmitzer et al. (IEEE T MED…
Reconstructing high-quality images from substantially undersampled k-space data for accelerated MRI presents a challenging ill-posed inverse problem. While supervised deep learning has revolutionized this field, it relies heavily on large…
Optimal transport (OT) provides powerful tools for comparing probability measures in various types. The Wasserstein distance which arises naturally from the idea of OT is widely used in many machine learning applications. Unfortunately,…
Flow models have rapidly become the go-to method for training and deploying large-scale generators, owing their success to inference-time flexibility via adjustable integration steps. A crucial ingredient in flow training is the choice of…
The space of probability densities is an infinite-dimensional Riemannian manifold, with Riemannian metrics in two flavors: Wasserstein and Fisher--Rao. The former is pivotal in optimal mass transport (OMT), whereas the latter occurs in…
Monocular scene flow estimation aims to recover dense 3D motion from image sequences, yet most existing methods are limited to two-frame inputs, restricting temporal modeling and robustness to occlusions. We propose RAFT-MSF++, a…
Enhancing the efficiency of high-quality image generation using Diffusion Models (DMs) is a significant challenge due to the iterative nature of the process. Flow Matching (FM) is emerging as a powerful generative modeling paradigm based on…