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Strong semantic representations improve the convergence and generation quality of diffusion and flow models. Existing approaches largely rely on external models, which require separate training, operate on misaligned objectives, and exhibit…

We exhibit conditions under which the flow of marginal distributions of a discontinuous semimartingale $\xi$ can be matched by a Markov process, whose infinitesimal generator is expressed in terms of the local characteristics of $\xi$. Our…

Many modern techniques employed in physics, such a computation of path integrals, rely on random walks on graphs that can be represented as Markov chains. Traditionally, estimates of running times of such sampling algorithms are computed…

We propose a simple discrete time semi-supervised graph embedding approach to link prediction in dynamic networks. The learned embedding reflects information from both the temporal and cross-sectional network structures, which is performed…

The study presents a novel approach for stochastic nonlinear model updating in structural dynamics, employing a Bayesian framework integrated with Markov Chain Monte Carlo (MCMC) sampling for parameter estimation by using an approximated…

This work introduces a self and mutually exciting point process that embeds flexible residuals and intensity with discretely Markovian dynamics. By allowing the integration of diverse residual distributions, this model serves as an…

This study introduces a novel approach for learning mixtures of Markov chains, a critical process applicable to various fields, including healthcare and the analysis of web users. Existing research has identified a clear divide in…

Predictability of behavior has emerged an an important characteristic in many fields including biology, medicine, and marketing. Behavior can be recorded as a sequence of actions performed by an individual over a given time period. This…

The study of many-body quantum dynamics in strongly-correlated systems is extremely challenging. To date few numerical methods exist which are capable of simulating the non-equilibrium dynamics of two-dimensional quantum systems, in part…

We consider different Markovian embedding schemes of non-Markovian stochastic processes that are described by generalized Langevin equations (GLE) and obey thermal detailed balance under equilibrium conditions. At thermal equilibrium…

This paper presents an application of statistical machine learning to the field of watermarking. We propose a new attack model on additive spread-spectrum watermarking systems. The proposed attack is based on Bayesian statistics. We…

Solving inverse problems -- recovering signals from incomplete or noisy measurements -- is fundamental in science and engineering. Score-based generative models (SGMs) have recently emerged as a powerful framework for this task. Two main…

We consider the inverse problem of reconstructing the posterior measure over the trajec- tories of a diffusion process from discrete time observations and continuous time constraints. We cast the problem in a Bayesian framework and derive…

This paper introduces time-continuous numerical schemes to simulate stochastic differential equations (SDEs) arising in mathematical finance, population dynamics, chemical kinetics, epidemiology, biophysics, and polymeric fluids. These…

Differential equations containing memory terms that depend nonlinearly on past states model a variety of non-Markovian processes. In this study, we present a Markovian embedding procedure for such equations with distributed delay by…

Direct simulation of biomolecular dynamics in thermal equilibrium is challenging due to the metastable nature of conformation dynamics and the computational cost of molecular dynamics. Biased or enhanced sampling methods may improve the…

In nonlinear dynamical systems, tipping refers to a critical transition from one steady state to another, typically catastrophic, steady state, often resulting from a saddle-node bifurcation. Recently, the machine-learning framework of…

Modelling random dynamical systems in continuous time, diffusion processes are a powerful tool in many areas of science. Model parameters can be estimated from time-discretely observed processes using Markov chain Monte Carlo (MCMC) methods…

Our goal was to develop a robust algorithm for numerical simulation of one-dimensional shallow-water flow in a complex multiply-connected channel network with arbitrary geometry and variable topography. We apply a central-upwind scheme with…

Streamflow is a dynamical process that integrates water movement in space and time within basin boundaries. The authors characterize the dynamics associated with streamflow time series data from about seventy-one U.S. Geological Survey…