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Normalizing flows are prominent deep generative models that provide tractable probability distributions and efficient density estimation. However, they are well known to fail while detecting Out-of-Distribution (OOD) inputs as they directly…

This paper investigates the connections between rectified flows, flow matching, and optimal transport. Flow matching is a recent approach to learning generative models by estimating velocity fields that guide transformations from a source…

We address the initial source identification problem for the heat equation, a notably ill-posed inverse problem characterized by exponential instability. Departing from classical Tikhonov regularization, we propose a novel approach based on…

Optical flow estimation with occlusion or large displacement is a problematic challenge due to the lost of corresponding pixels between consecutive frames. In this paper, we discover that the lost information is related to a large quantity…

Due to the scarcity of annotated scene flow data, self-supervised scene flow learning in point clouds has attracted increasing attention. In the self-supervised manner, establishing correspondences between two point clouds to approximate…

Flow matching is a recent state-of-the-art framework for generative modeling based on ordinary differential equations (ODEs). While closely related to diffusion models, it provides a more general perspective on generative modeling. Although…

Modern large displacement optical flow algorithms usually use an initialization by either sparse descriptor matching techniques or dense approximate nearest neighbor fields. While the latter have the advantage of being dense, they have the…

Accurate and explainable out-of-distribution (OOD) detection is required to use machine learning systems safely. Previous work has shown that feature distance to decision boundaries can be used to identify OOD data effectively. In this…

In this paper we investigate the convergence of a recently popular class of first-order primal-dual algorithms for saddle point problems under the presence of errors occurring in the proximal maps and gradients. We study several types of…

In the era of end-to-end deep learning, many advances in computer vision are driven by large amounts of labeled data. In the optical flow setting, however, obtaining dense per-pixel ground truth for real scenes is difficult and thus such…

Bayesian inverse problems use observed data to update a prior probability distribution for an unknown state or parameter of a scientific system to a posterior distribution conditioned on the data. In many applications, the unknown parameter…

The estimation of optical flow is an ambiguous task due to the lack of correspondence at occlusions, shadows, reflections, lack of texture and changes in illumination over time. Thus, unsupervised methods face major challenges as they need…

Fluid approximation is a widely used approach for solving two-stage stochastic optimization problems, with broad applications in service system design such as call centers and healthcare operations. However, replacing the underlying random…

Physics-informed neural networks (PINNs) have emerged as a powerful tool for solving inverse problems, especially in cases where no complete information about the system is known and scatter measurements are available. This is especially…

The optimal power flow (OPF) problem, which plays a central role in operating electrical networks is considered. The problem is nonconvex and is in fact NP hard. Therefore, designing efficient algorithms of practical relevance is crucial,…

This paper studies the inverse problem of flow matching (FM) between distributions with finite exponential moment, a problem motivated by modern generative AI applications such as the distillation of flow matching models. Uniqueness of the…

This paper is concerned with an inverse moving point source problem in electromagnetics. The aim is to reconstruct the moving orbit from the tangential components of magnetic fields taken at a finite number of observation points. The…

A new model order reduction approach is proposed for parametric steady-state nonlinear fluid flows characterized by shocks and discontinuities whose spatial locations and orientations are strongly parameter dependent. In this method,…

Likelihood-free (a.k.a. simulation-based) inference problems are inverse problems with expensive, or intractable, forward models. ODE inverse problems are commonly treated as likelihood-free, as their forward map has to be numerically…

Optimal transport (OT) distances between probability distributions are parameterized by the ground metric they use between observations. Their relevance for real-life applications strongly hinges on whether that ground metric parameter is…