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Entropic optimal transport problems are regularized versions of optimal transport problems. These models play an increasingly important role in machine learning and generative modelling. For finite spaces, these problems are commonly solved…
We introduce a novel adaptive Gaussian Process Regression (GPR) methodology for efficient construction of surrogate models for Bayesian inverse problems with expensive forward model evaluations. An adaptive design strategy focuses on…
Statistical significance testing of neural coherence is essential for distinguishing genuine cross-signal coupling from spurious correlations. A widely accepted approach uses surrogate-based inference, where null distributions are generated…
This paper studies the optimal rate of estimation in a finite Gaussian location mixture model in high dimensions without separation conditions. We assume that the number of components $k$ is bounded and that the centers lie in a ball of…
Flow matching (FM) is a family of training algorithms for fitting continuous normalizing flows (CNFs). Conditional flow matching (CFM) exploits the fact that the marginal vector field of a CNF can be learned by fitting least-squares…
Reliable tracking of moving boundaries is important for the simulation of compressible fluid flows and there are a lot of contributions in literature. We recognize from the classical piston problem, a typical moving boundary problem in gas…
Recently, optimization on the Riemannian manifold have provided valuable insights to the optimization community. In this regard, extending these methods to to the Wasserstein space is of particular interest, since optimization on…
The assignment problem, a cornerstone of operations research, seeks an optimal one-to-one mapping between agents and tasks to minimize total cost. This work traces its evolution from classical formulations and algorithms to modern optimal…
We develop structure preserving schemes for a class of nonlinear mobility continuity equation. When the mobility is a concave function, this equation admits a form of gradient flow with respect to a Wasserstein-like transport metric. Our…
Gaussian processes (GPs) are a Bayesian machine learning approach widely used to construct surrogate models for the uncertainty quantification of computer simulation codes in industrial applications. It provides both a mean predictor and an…
We introduce Wasserstein-like dynamical transport distances between vector-valued densities on the real line. The mobility function from the scalar theory is replaced by a mobility matrix, that is subject to positivity and concavity…
Diffusion models approximate the denoising distribution as a Gaussian and predict its mean, whereas flow matching models reparameterize the Gaussian mean as flow velocity. However, they underperform in few-step sampling due to…
This note gives a self-contained overview of some important properties of the Gromov-Wasserstein (GW) distance, compared with the standard linear optimal transport (OT) framework. More specifically, I explore the following questions: are GW…
Understanding the dynamics of phase boundaries in fluids requires quantitative knowledge about the microscale processes at the interface. We consider the sharp-interface motion of compressible two-component flow, and propose a heterogeneous…
The Gaussian-smoothed optimal transport (GOT) framework, pioneered in Goldfeld et al. (2020) and followed up by a series of subsequent papers, has quickly caught attention among researchers in statistics, machine learning, information…
Simulating the mechanical response of advanced materials can be done more accurately using concurrent multiscale models than with single-scale simulations. However, the computational costs stand in the way of the practical application of…
We present a finite dimensional variational model for multi-agent path-planning in which a group of agents traverses from initial positions to a target distribution in a moving medium. The model is derived using the agent-based formulation…
A functional for joint variational object segmentation and shape matching is developed. The formulation is based on optimal transport w.r.t. geometric distance and local feature similarity. Geometric invariance and modelling of…
This paper presents a new Gaussian process (GP) surrogate modeling for predicting the outcome of a physical experiment where some experimental inputs are controlled by other manipulating factors. Particularly, we are interested in the case…
Weak gravitational lensing maps compactly encode the evolution of cosmic large-scale structure and are a key tool for cosmological analyses. Performing inference directly at the map level allows flexible choices of statistics and can…