Related papers: Unbalanced optimal transport for stochastic partic…
We present and study a Particle method for the stationary solutions of a class of transport equations. This method is inspired by non-stationary Particle methods, the time variable being replaced by one spatial variable. Particles…
3D Gaussian Splatting (3DGS) has demonstrated its potential in reconstructing scenes from unposed images. However, optimization-based 3DGS methods struggle with sparse views due to limited prior knowledge. Meanwhile, feed-forward Gaussian…
The superior performance of ensemble methods with infinite models are well known. Most of these methods are based on optimization problems in infinite-dimensional spaces with some regularization, for instance, boosting methods and convex…
We develop an Euler-type method to predict the evolution of a time-dependent probability measure without explicitly learning an operator that governs its evolution. We use linearized optimal transport theory to prove that the measure-valued…
Many numerical and learning algorithms rely on the solution of the Monge-Kantorovich problem and Wasserstein distances, which provide appropriate distributional metrics. While the natural approach is to treat the problem as an…
We develop a theory of optimal transport for stationary random measures with a focus on stationary point processes and construct a family of distances on the set of stationary random measures. These induce a natural notion of interpolation…
Most inverse problems from physical sciences are formulated as PDE-constrained optimization problems. This involves identifying unknown parameters in equations by optimizing the model to generate PDE solutions that closely match measured…
Current research on robust trajectory planning for autonomous agents aims to mitigate uncertainties arising from disturbances and modeling errors while ensuring guaranteed safety. Existing methods primarily utilize stochastic optimal…
Wasserstein barycenters provide a geometrically meaningful way to aggregate probability distributions, built on the theory of optimal transport. They are difficult to compute in practice, however, leading previous work to restrict their…
In this paper, we present a novel algorithm for quantifying uncertainty and information gained within 3D Gaussian Splatting (3D-GS) through P-Optimality. While 3D-GS has proven to be a useful world model with high-quality rasterizations, it…
Robust aiding of inertial navigation systems in GNSS-denied environments is critical for the removal of accumulated navigation error caused by the drift and bias inherent in inertial sensors. One way to perform such an aiding uses matching…
Motivated by variational inference methods, we propose a zeroth-order algorithm for solving optimization problems in the space of Gaussian probability measures. The algorithm is based on an interacting system of Gaussian particles that…
Recent research has emphasized the benefits of accurately reconstructing the initial Lagrangian positions of biased tracers from their positions at a later time, to gain cosmological information. A weighted semi-discrete optimal transport…
Learning-based techniques are increasingly effective at controlling complex systems using data-driven models. However, most work done so far has focused on learning individual tasks or control laws. Hence, it is still a largely unaddressed…
Optimal Transport has received much attention in Machine Learning as it allows to compare probability distributions by exploiting the geometry of the underlying space. However, in its original formulation, solving this problem suffers from…
The reconstruction of charged particle trajectories is a crucial challenge of particle physics experiments as it directly impacts particle reconstruction and physics performances. To reconstruct these trajectories, different reconstruction…
3D Gaussian Splatting (3DGS) has recently emerged in computer vision as a promising rendering technique. By adapting the principles of Elliptical Weighted Average (EWA) splatting to a modern differentiable pipeline, 3DGS enables real-time,…
We consider the problem of recovering an unknown matching between a set of $n$ randomly placed points in $\mathbb{R}^d$ and random perturbations of these points. This can be seen as a model for particle tracking and more generally, entity…
A method is presented to solve a stochastic, nonlinear optimal control problem representative of spacecraft trajectory design under uncertainty. The problem is reformulated as a chance constrained nonlinear program, or what is known as a…
State estimation in non-linear models is performed by tracking the posterior distribution recursively. A plethora of algorithms have been proposed for this task. Among them, the Gaussian particle filter uses a weighted set of particles to…