Related papers: Tractable Optimal Experimental Design using Transp…
We formulate and solve a class of finite-time transport and mixing problems in the set-oriented framework. The aim is to obtain optimal discrete-time perturbations in nonlinear dynamical systems to transport a specified initial measure on…
Automated chemical synthesis, materials fabrication, and spectroscopic physical measurements often bring forth the challenge of process trajectory optimization, i.e., discovering the time dependence of temperature, electric field, or…
We develop a framework for goal-oriented optimal design of experiments (GOODE) for large-scale Bayesian linear inverse problems governed by PDEs. This framework differs from classical Bayesian optimal design of experiments (ODE) in the…
The power and flexibility of Optimal Transport (OT) have pervaded a wide spectrum of problems, including recent Machine Learning challenges such as unsupervised domain adaptation. Its essence of quantitatively relating two probability…
This paper introduces a graph-based, potential-guided method for path planning problems in unknown environments, where obstacles are unknown until the robots are in close proximity to the obstacle locations. Inspired by optimal transport…
Characterising intractable high-dimensional random variables is one of the fundamental challenges in stochastic computation. The recent surge of transport maps offers a mathematical foundation and new insights for tackling this challenge by…
Accurate estimation of parameters is paramount in developing high-fidelity models for complex dynamical systems. Model-based optimal experiment design (OED) approaches enable systematic design of dynamic experiments to generate input-output…
Transport-based density estimation methods are receiving growing interest because of their ability to efficiently generate samples from the approximated density. We further invertigate the sequential transport maps framework proposed from…
This paper presents a multiscale approach to efficiently compute approximate optimal transport plans between point sets. It is particularly well-suited for point sets that are in high-dimensions, but are close to being intrinsically…
Optimal Transport is a theory that allows to define geometrical notions of distance between probability distributions and to find correspondences, relationships, between sets of points. Many machine learning applications are derived from…
In this paper we wish to tackle stochastic programs affected by ambiguity about the probability law that governs their uncertain parameters. Using optimal transport theory, we construct an ambiguity set that exploits the knowledge about the…
Persistence diagrams (PDs) are now routinely used to summarize the underlying topology of complex data. Despite several appealing properties, incorporating PDs in learning pipelines can be challenging because their natural geometry is not…
In this work, we aim at efficiently solving a parametrized family of optimal transport problems by using model order reduction methods. We propose a reduced-order model by adding to the primal (respectively dual) version of the…
An adaptive, adversarial methodology is developed for the optimal transport problem between two distributions $\mu$ and $\nu$, known only through a finite set of independent samples $(x_i)_{i=1..N}$ and $(y_j)_{j=1..M}$. The methodology…
Bayesian experimental design (BED) is a framework that uses statistical models and decision making under uncertainty to optimise the cost and performance of a scientific experiment. Sequential BED, as opposed to static BED, considers the…
In many applications of optimal transport (OT), the object of primary interest is the optimal transport map. This map rearranges mass from one probability distribution to another in the most efficient way possible by minimizing a specified…
Many real-world experimental design problems (a) evaluate multiple experimental conditions in parallel and (b) replicate each condition multiple times due to large and heteroscedastic observation noise. Given a fixed total budget, this…
We consider optimal sensor placement for a family of linear Bayesian inverse problems characterized by a deterministic hyper-parameter. The hyper-parameter describes distinct configurations in which measurements can be taken of the observed…
Mobility service route design requires demand information to operate in a service region. Transit planners and operators can access various data sources including household travel survey data and mobile device location logs. However, when…
We introduce an alternative approach for the analysis and numerical approximation of the optimal feedback control mapping. It consists in looking at a typical optimal control problem in such a way that feasible controls are mappings…