Related papers: Quantum Schrodinger bridges: large deviations and …
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…
An alternative method is proposed for deriving the time dependent Schroedinger equation from the pictures of wave and matrix mechanics. The derivation is of a mixed classical quantum character, since time is treated as a classical variable,…
In this paper, the classical Schr\"odinger equation, which allows the study of classical dynamics in terms of wave functions, is analyzed theoretically and numerically. First, departing from classical (Newtonian) mechanics, and assuming an…
In this work, we revisit the discrete-time Schr\"{o}dinger Bridge (SB) and Density Steering (DS) problems for Gaussian mixture model (GMM) boundary distributions. Building on the existing literature, we construct a set of feasible Markovian…
Diffusion Schr\"odinger bridges (DSB) have recently emerged as a powerful framework for recovering stochastic dynamics via their marginal observations at different time points. Despite numerous successful applications, existing algorithms…
The Schr\"odinger bridge problem is concerned with finding a stochastic dynamical system bridging two marginal distributions that minimises a certain transportation cost. This problem, which represents a generalisation of optimal transport…
Score-based generative models have recently attracted significant attention for their ability to generate high-fidelity data by learning maps from simple Gaussian priors to complex data distributions. A natural generalization of this idea…
The stochastic dissipative Schrodinger equation is derived for an open quantum system consisting of a sub-system able to exchange energy with a thermal reservoir. The resultant evolution of the wave function also gives the evolution of the…
This paper introduces a novel deep-learning-based approach for numerical simulation of a time-evolving Schr\"odinger equation inspired by stochastic mechanics and generative diffusion models. Unlike existing approaches, which exhibit…
Stochastic flows of an advective-diffusive nature are ubiquitous in physical sciences. Of particular interest is the problem to reconcile observed marginal distributions with a given prior posed by E. Schrodinger in 1932/32 and known as the…
The stochastic Schr\"odinger equation, of classical or quantum type, allows to describe open quantum systems under measurement in continuous time. In this paper we review the link between these two descriptions and we study the properties…
Many natural dynamic processes -- such as in vivo cellular differentiation or disease progression -- can only be observed through the lens of static sample snapshots. While challenging, reconstructing their temporal evolution to decipher…
The bridge problem is to find an SDE (or sometimes an ODE) that bridges two given distributions. The application areas of the bridge problem are enormous, among which the recent generative modeling (e.g., conditional or unconditional image…
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…
This work studies the Schr\"odinger bridge problem for the kinematic equation on a compact connected Lie group. The objective is to steer a controlled diffusion between given initial and terminal densities supported over the Lie group while…
The master equation describing non-equilibrium one-dimensional problems like diffusion limited reactions or critical dynamics of classical spin systems can be written as a Schr\"odinger equation in which the wave function is the probability…
One of the greatest scientific achievements of physics in the 20th century is the discovery of quantum mechanics. The Schrodinger equation is the most fundamental equation in quantum mechanics describing the time-based evolution of the…
Time-dependent Schroedinger equation represents the basis of any quantum-theoretical approach. The question concerning its proper content in comparison to the classical physics has not been, however, fully answered until now. It will be…
The problem of reconciling a prior probability law on paths with data was introduced by E. Schr\"odinger in 1931/32. It represents an early formulation of a maximum likelihood problem. This specific formulation can also be seen as the…
We study a generalization of the Brownian bridge as a stochastic process that models the position and velocity of inertial particles between the two end-points of a time interval. The particles experience random acceleration and are assumed…