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Motivated by a wide variety of applications, this paper introduces a general class of networks of stochastic loss systems in which congestion renders lost revenue due to customers or jobs being permanently removed from the system. We seek…
In this paper, we consider coordinated control of feeder vehicles for first and last mode transportation. The model is macroscopic with volumes of demands and supplies along with flows of vehicles. We propose a one-shot problem for…
The transport approach is a useful tool to study dynamics of non-equilibrium systems. For heavy-ion collisions at intermediate energies, where both the smooth nucleon potential and the hard-core nucleon-nucleon collision are important, the…
This work presents a model reduction approach for problems with coherent structures that propagate over time such as convection-dominated flows and wave-type phenomena. Traditional model reduction methods have difficulties with these…
Bayesian neural network posterior distributions have a great number of modes that correspond to the same network function. The abundance of such modes can make it difficult for approximate inference methods to do their job. Recent work has…
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…
In its most general form, the optimal transport problem is an infinite-dimensional optimization problem, yet certain notable instances admit closed-form solutions. We identify the common source of this tractability as \textit{symmetry} and…
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…
Optimal transport (OT) is a widely used technique for distribution alignment, with applications throughout the machine learning, graphics, and vision communities. Without any additional structural assumptions on trans-port, however, OT can…
Optimal transport problems pose many challenges when considering their numerical treatment. We investigate the solution of a PDE-constrained optimisation problem subject to a particular transport equation arising from the modelling of image…
We show how to use a variational approximation to the logistic function to perform approximate inference in Bayesian networks containing discrete nodes with continuous parents. Essentially, we convert the logistic function to a Gaussian,…
We present a numerical method to solve the optimal transport problem with a quadratic cost when the source and target measures are periodic probability densities. This method is based on a numerical resolution of the corresponding…
Multi-robot mapping with neural implicit representations enables the compact reconstruction of complex environments. However, it demands robustness against communication challenges like packet loss and limited bandwidth. While prior works…
Single-cell technologies generate high-dimensional point clouds of cells, enabling detailed characterization of complex patient states and treatment responses. Yet each patient is represented by an irregular point cloud rather than a simple…
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…
Quantum computing and machine learning have potential for symbiosis. However, in addition to the hardware limitations from current devices, there are still basic issues that must be addressed before quantum circuits can usefully incorporate…
We propose a communication-efficient optimally structured gradient coding scheme to jointly address straggler resilience and communication efficiency in heterogeneous distributed learning. By establishing a unified framework that…
The trajectory optimization of the atmospheric entry of a reusable launch vehicle is studied. The objective is to maximize the crossrange of the vehicle subject to two control-inequality path constraints, two state-inequality path…
Inspired by the matching of supply to demand in logistical problems, the optimal transport (or Monge--Kantorovich) problem involves the matching of probability distributions defined over a geometric domain such as a surface or manifold. In…
We present LazyDINO, a transport map variational inference method for fast, scalable, and efficiently amortized solutions of high-dimensional nonlinear Bayesian inverse problems with expensive parameter-to-observable (PtO) maps. Our method…