Related papers: Multi-marginal Schrodinger bridges
In this paper, we explore quantitative stability of multi-marginal Schr\"odinger bridges with respect to the marginal constraints. We focus on the case where the number of marginal constraints is large (i.e. ``many-marginals"). When this…
For a symmetric bridge coupled to infinite leads, in the presence of a dipole-coupled external ac-field with harmonic mixing, we solve the Schr\"odinger equation in the time-domain using open boundary conditions as well as in the…
Recent investigations have established the physical relevance of spatially-localized instability mechanisms in fluid dynamics and their potential for technological innovations in flow control. In this letter, we show that the mathematical…
This paper is about the construction of displacement interpolations on a discrete metric graph. Our approach is based on the approximation of any optimal transport problem whose cost function is a distance on a discrete graph by a sequence…
We consider the problem of steering a linear stochastic system between two end-point degenerate Gaussian distributions in finite time. This accounts for those situations in which some but not all of the state entries are uncertain at the…
Stochastic Spatio-Temporal processes are prevalent across domains ranging from modeling of plasma to the turbulence in fluids to the wave function of quantum systems. This letter studies a measure-theoretic description of such systems by…
We study the optimal control formulation for stochastic nonlinear Schrodinger equation (SNLSE) on a finite graph. By viewing the SNLSE as a stochastic Wasserstein Hamiltonian flow on density manifold, we show the global existence of a…
We propose a variational scheme for computing Wasserstein gradient flows. The scheme builds upon the Jordan--Kinderlehrer--Otto framework with the Benamou-Brenier's dynamic formulation of the quadratic Wasserstein metric and adds a…
We present a new hydrodynamic analogy of nonrelativistic quantum particles in potential wells. Similarities between a real variant of the Schr\"odinger equation and gravity-capillary shallow water waves are reported and analyzed. We show…
This paper considers the problem of minimizing the time average of a controlled stochastic process subject to multiple time average constraints on other related processes. The probability distribution of the random events in the system is…
Given an initial (resp., terminal) probability measure $\mu$ (resp., $\nu$) on $\mathbb{R}^d$, we characterize those optimal stopping times $\tau$ that maximize or minimize the functional $\mathbb{E} |B_0 - B_\tau|^{\alpha}$, $\alpha > 0$,…
In this work we explore a new framework for approximate Bayesian inference in large datasets based on stochastic control (i.e. Schr\"odinger bridges). We advocate stochastic control as a finite time and low variance alternative to popular…
In this paper, we consider a class of stochastic optimal control problems with risk constraints that are expressed as bounded probabilities of failure for particular initial states. We present here a martingale approach that diffuses a risk…
In this paper, we study Brinkman's equations with microscale properties that are highly heterogeneous in space and time. The time variations are controlled by a stochastic particle dynamics described by an SDE. The particle dynamics can be…
We study in this paper optimal mass transport over a strongly connected, directed graph on a given discrete time interval. Differently from previous literature, we do not assume full knowledge of the initial and final goods distribution…
In many practically important problems which rely on particles' transport in realistic corrugated channels, one is interested to know the probability that either of the extremities, (e.g., the one containing a chemically active site, or…
The motion of weakly inertial Brownian particles, transported by steady two-dimensional fluid flows, is investigated by means of asymptotic methods. We focus on the phenomenon of noise-induced separatrix crossing, which can force particles…
The Stokes-Brinkman equations model fluid flow in highly heterogeneous porous media. In this paper, we consider the numerical solution of the Stokes-Brinkman equations with stochastic permeabilities, where the permeabilities in subdomains…
We study the large-time behaviour of Brownian particles moving through a viscous medium in a confined potential, and which are further subjected to position-dependent driving forces that are periodic in time. We focus on the case where…
We formulate a class of velocity-free finite-particle methods for mass transport problems based on a time-discrete incremental variational principle that combines entropy and the cost of particle transport, as measured by the Wasserstein…