Related papers: A Closed-Form Framework for Schr\"odinger Bridges …
The dynamical formulation of the optimal transport can be extended through various choices of the underlying geometry (kinetic energy), and the regularization of density paths (potential energy). These combinations yield different…
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…
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 analyze the Schr\"odingerization method for quantum simulation of a general class of non-unitary dynamics with inhomogeneous source terms. The Schr\"odingerization technique, introduced in [31], transforms any linear ordinary and partial…
State space models (SSMs) have emerged as a powerful framework for modelling long-range dependencies in sequence data. Unlike traditional recurrent neural networks (RNNs) and convolutional neural networks (CNNs), SSMs offer a structured and…
Large-size populations consisting of a continuum of identical and non-cooperative agents with stochastic dynamics are useful in modeling various biological and engineered systems. This paper addresses the stochastic control problem of…
Skew-Gaussian processes (SkewGPs) extend the multivariate Unified Skew-Normal distributions over finite dimensional vectors to distribution over functions. SkewGPs are more general and flexible than Gaussian processes, as SkewGPs may also…
Score-based diffusion models have emerged as powerful techniques for generating samples from high-dimensional data distributions. These models involve a two-phase process: first, injecting noise to transform the data distribution into a…
Learning to sample from complex unnormalized distributions is a fundamental challenge in computational physics and machine learning. While score-based and variational methods have achieved success in continuous domains, extending them to…
How to steer a given joint state probability density function to another over finite horizon subject to a controlled stochastic dynamics with hard state (sample path) constraints? In applications, state constraints may encode safety…
Sampling from probability distributions is an important problem in statistics and machine learning, specially in Bayesian inference when integration with respect to posterior distribution is intractable and sampling from the posterior is…
Many solid mechanics problems on complex geometries are conventionally solved using discrete boundary methods. However, such an approach can be cumbersome for problems involving evolving domain boundaries due to the need to track boundaries…
This study investigates the dynamics of Score-based Generative Models (SGMs) by treating the score estimation error as a stochastic source driving the Fokker-Planck equation. Departing from particle-centric SDE analyses, we employ an SPDE…
Recently, there has been a growing interest in generative models based on diffusions driven by the empirical robustness of these methods in generating high-dimensional photorealistic images and the possibility of using the vast existing…
We characterize the Schr\"odinger bridge problems by a family of Mckean-Vlasov stochastic control problems with no terminal time distribution constraint. In doing so, we use the theory of Hilbert space embeddings of probability measures and…
Stochastic evolution underpins several approaches to the dynamics of open quantum systems, such as random modulation of Hamiltonian parameters, the stochastic Schrodinger equation (SSE), and the stochastic Liouville equation (SLE). These…
Recent advances in diffusion bridge models leverage Doob's $h$-transform to establish fixed endpoints between distributions, demonstrating promising results in image translation and restoration tasks. However, these approaches frequently…
For the first time, the general nonlinear Schr\"odinger equation is investigated, in which the chromatic dispersion and potential are specified by two arbitrary functions. The equation in question is a natural generalization of a wide class…
We present a novel framework for CBCT-to-MDCT translation, grounded in the Schrodinger Bridge (SB) formulation, which integrates GAN-derived priors with human-guided conditional diffusion. Unlike conventional GANs or diffusion models, our…
We propose a novel dispersive regularization framework for the numerical simulation of the one-dimensional shallow water equations (SWE). The classical hyperbolic system is regularized by a third-order dispersive term in the momentum…