Related papers: Method of Distributions for Systems with Stochasti…
In this paper, a Convolution-Based Converter (CBC) is proposed to develop a methodology for removing the strong or fixed priors in estimating the probability distribution of targets based on observations in the stochastic process.…
Learning the cumulative distribution function (CDF) of an outcome variable conditional on a set of features remains challenging, especially in high-dimensional settings. Conditional transformation models provide a semi-parametric approach…
We present a stochastic and variational aspect of the Lax-Friedrichs scheme applied to hyperbolic scalar conservation laws. This is a finite difference version of Fleming's results ('69) that the vanishing viscosity method is characterized…
In this paper, we investigate finite-horizon optimal density steering problems for discrete-time stochastic linear dynamical systems whose state probability densities can be represented as Gaussian Mixture Models (GMMs). Our goal is to…
We present a computational framework to investigate steady state distributions and perform stability analysis for random ordinary differential equations driven by parameter uncertainty. Using the nonlinear Rosenzweig McArthur predator prey…
This paper establishes the averaging method to a coupled system consisting of two stochastic differential equations which has a slow component driven by fractional Brownian motion (FBM) with less regularity $1/3< H \leq 1/2$ and a fast…
Many problems arising in applications result in the need to probe a probability distribution for functions. Examples include Bayesian nonparametric statistics and conditioned diffusion processes. Standard MCMC algorithms typically become…
Integration of physics principles with data-driven methods has attracted great attention in recent few years. In this study, a physics-informed dynamic mode decomposition (piDMD) method, where the mass conservation law is integrated with a…
A data-driven MPC scheme is proposed to safely control constrained stochastic linear systems using distributionally robust optimization. Distributionally robust constraints based on the Wasserstein metric are imposed to bound the state…
We model chaotic diffusion, in a symplectic 4D map by using the result of a theorem that was developed for stochastically perturbed integrable Hamiltonian systems. We explicitly consider a map defined by a free rotator (FR) coupled to a…
Learning dynamical systems from incomplete or noisy data is inherently ill-posed, as a single observation may correspond to multiple plausible futures. While physics-based ensemble forecasting relies on perturbing initial states to capture…
Diffusion models (DMs) have become the dominant paradigm of generative modeling in a variety of domains by learning stochastic processes from noise to data. Recently, diffusion denoising bridge models (DDBMs), a new formulation of…
Stochastic mechanics is based on the hypothesis that all matter is subject to universal modified Brownian motion. In this report, we calculated probability density distributions using concepts of stochastic mechanics independent of…
Learning-based control approaches have shown great promise in performing complex tasks directly from high-dimensional perception data for real robotic systems. Nonetheless, the learned controllers can behave unexpectedly if the trajectories…
Statistical system models provide the basis for the examination of various sorts of distributions. Classification distributions are a very common and versatile form of statistics in e.g. real economic, social, and IT systems. The…
We develop a statistical method to learn a molecular Hamiltonian matrix from a time-series of electron density matrices. We extend our previous method to larger molecular systems by incorporating physical properties to reduce…
We consider a general method for the approximation of the distribution of a process conditioned to not hit a given set. Existing methods are based on particle system that are failable, in the sense that, in many situations , they are not…
Recent innovations in diffusion probabilistic models have paved the way for significant progress in image, text and audio generation, leading to their applications in generative time series forecasting. However, leveraging such abilities to…
Conservation laws in the form of elliptic and parabolic partial differential equations (PDEs) are fundamental to the modeling of many problems such as heat transfer and flow in porous media. Many of such PDEs are stochastic due to the…
We consider the problem of the Bayesian inference of drift and diffusion coefficient functions in a stochastic differential equation given discrete observations of a realisation of its solution. We give conditions for the well-posedness and…