Related papers: An Explicit Surrogate for Gaussian Mixture Flow Ma…

Variational inference with natural-gradient descent often shows fast convergence in practice, but its theoretical convergence guarantees have been challenging to establish. This is true even for the simplest cases that involve concave…

Gromov--Wasserstein optimal transport (GWOT) aligns metric measure spaces by matching their within-domain relational structures, but large-scale GWOT remains challenging because its objective is nonconvex and projection onto the transport…

Contextual optimization enhances decision quality by leveraging side information to improve predictions of uncertain parameters. However, existing approaches face significant challenges when dealing with multimodal or mixtures of…

We propose a framework, named Aggregated Wasserstein, for computing a dissimilarity measure or distance between two Hidden Markov Models with state conditional distributions being Gaussian. For such HMMs, the marginal distribution at any…

The adapted Wasserstein distance is a metric for quantifying distributional uncertainty and assessing the sensitivity of stochastic optimization problems on time series data. A computationally efficient alternative to it, is provided by the…

Building local surrogates to accelerate stationary point searches on potential energy surfaces spans decades of effort. Done correctly, surrogates can reduce the number of expensive electronic structure evaluations by roughly an order of…

We propose a fully discrete variational scheme for nonlinear evolution equations with gradient flow structure on the space of finite Radon measures on an interval with respect to a generalized version of the Wasserstein distance with…

Flow Matching has become a cornerstone of modern generative models like Stable Diffusion 3, largely due to the efficiency of its Rectified Flow (RF) variant. The success of RF hinges on iteratively learning straight trajectories, pushing…

Quantifying uncertainty in future climate projections is hindered by the prohibitive computational cost of running physical climate models, which severely limits the availability of training data. We propose a data-efficient framework for…

The Poisson-Nernst-Planck system of equations used to model ionic transport is interpreted as a gradient flow for the Wasserstein distance and a free energy in the space of probability measures with finite second moment. A variational…

Gromov--Wasserstein (GW) distances compare graphs, shapes, and point clouds through internal distances, without requiring a common coordinate system. This invariance is powerful, but discrete GW is a nonconvex quadratic optimal transport…

Machine learning systems operate under the assumption that training and test data are sampled from a fixed probability distribution. However, this assumptions is rarely verified in practice, as the conditions upon which data was acquired…

We introduce a new generative modeling framework, \textbf{Flow Matching with Arbitrary Auxiliary Paths (AuxPath-FM)}, which generalizes conditional flow matching by incorporating an auxiliary variable drawn from an arbitrary distribution…

This paper uses sample data to study the problem of comparing populations on finite-dimensional parallelizable Riemannian manifolds and more general trivial vector bundles. Utilizing triviality, our framework represents populations as…

We propose a new uncertainty estimator for gradient-free optimisation of black-box simulators using deep generative surrogate models. Optimisation of these simulators is especially challenging for stochastic simulators and higher…

We propose a new algorithm that uses an auxiliary neural network to express the potential of the optimal transport map between two data distributions. In the sequel, we use the aforementioned map to train generative networks. Unlike WGANs,…

We define a novel class of distances between statistical multivariate distributions by modeling an optimal transport problem on their marginals with respect to a ground distance defined on their conditionals. These new distances are metrics…

We present Riemannian Gaussian Variational Flow Matching (RG-VFM), a geometric extension of Variational Flow Matching (VFM) for generative modeling on manifolds. Motivated by the benefits of VFM, we derive a variational flow matching…

Machine learning surrogates are increasingly employed to replace expensive computational models for physics-based reliability analysis. However, their use introduces epistemic uncertainty from model approximation errors, which couples with…

Wasserstein gradient flow (WGF) is a common method to perform optimization over the space of probability measures. While WGF is guaranteed to converge to a first-order stationary point, for nonconvex functionals the converged solution does…