Related papers: Solving Schr\"{o}dinger bridge problem via continu…
We discuss a connection (and a proper place in this framework) of the unforced and deterministically forced Burgers equation for local velocity fields of certain flows, with probabilistic solutions of the so-called Schr\"{o}dinger…
We consider the problem to steer a linear dynamical system with full state observation from an initial gaussian distribution in state-space to a final one with minimum energy control. The system is stochastically driven through the control…
We consider the Schr\"odinger bridge problem which, given ensemble measurements of the initial and final configurations of a stochastic dynamical system and some prior knowledge on the dynamics, aims to reconstruct the "most likely"…
The Schr\"odinger bridge problem seeks the optimal stochastic process that connects two given probability distributions with minimal energy modification. While the Sinkhorn algorithm is widely used to solve the static optimal transport…
Since the early nineties, it has been observed that the Schroedinger bridge problem can be formulated as a stochastic control problem with atypical boundary constraints. This in turn has a fluid dynamic counterpart where the flow of…
Consider a reference Markov process with initial distribution $\pi_{0}$ and transition kernels $\{M_{t}\}_{t\in[1:T]}$, for some $T\in\mathbb{N}$. Assume that you are given distribution $\pi_{T}$, which is not equal to the marginal…
We study a martingale Schr\"odinger bridge problem: given two probability distributions, find their martingale coupling with minimal relative entropy. Our main result provides Schr\"odinger potentials for this coupling. Namely, under…
Transporting between arbitrary distributions is a fundamental goal in generative modeling. Recently proposed diffusion bridge models provide a potential solution, but they rely on a joint distribution that is difficult to obtain in…
Understanding the continuous evolution of populations from discrete temporal snapshots is a critical research challenge, particularly in fields like developmental biology and systems medicine where longitudinal tracking of individual…
The dynamic Schr\"odinger bridge problem seeks a stochastic process that defines a transport between two target probability measures, while optimally satisfying the criteria of being closest, in terms of Kullback-Leibler divergence, to a…
The Schrodinger Bridge and Bass (SBB) formulation, which jointly controls drift and volatility, is an established extension of the classical Schrodinger Bridge (SB). Building on this framework, we introduce LightSBB-M, an algorithm that…
Monge-Kantorovich optimal mass transport (OMT) provides a blueprint for geometries in the space of positive densities -- it quantifies the cost of transporting a mass distribution into another. In particular, it provides natural options for…
Optimal transportation provides a means of lifting distances between points on a geometric domain to distances between signals over the domain, expressed as probability distributions. On a graph, transportation problems can be used to…
This article introduces a new class of fast algorithms to approximate variational problems involving unbalanced optimal transport. While classical optimal transport considers only normalized probability distributions, it is important for…
Solving transport problems, i.e. finding a map transporting one given distribution to another, has numerous applications in machine learning. Novel mass transport methods motivated by generative modeling have recently been proposed, e.g.…
Diffusion models have become the go-to method for large-scale generative models in real-world applications. These applications often involve data distributions confined within bounded domains, typically requiring ad-hoc thresholding…
Reconstructing dynamics using samples from sparsely time-resolved snapshots is an important problem in both natural sciences and machine learning. Here, we introduce a new deep learning approach for solving regularized unbalanced optimal…
We propose the Entropic-regularized Robust Optimal Transport (E-ROBOT) framework, a novel method that combines the robustness of ROBOT with the computational and statistical benefits of entropic regularization. We show that, rooted in the…
We investigate distributed classical and quantum approaches for the survivable network design problem (SNDP), sometimes called the generalized Steiner problem. These problems generalize many complex graph problems of interest, such as the…
Accurate modeling of system dynamics holds intriguing potential in broad scientific fields including cytodynamics and fluid mechanics. This task often presents significant challenges when (i) observations are limited to cross-sectional…