Related papers: Finite-Time Analysis of Discrete-Time Stochastic I…
This paper investigates the theoretical behavior of generative models under finite training populations. Within the stochastic interpolation generative framework, we derive closed-form expressions for the optimal velocity field and score…
This paper studies the distributed optimization problem with possibly nonidentical local constraints, where its global objective function is composed of $N$ convex functions. The aim is to solve the considered optimization problem in a…
Diffusion-based generative models use stochastic differential equations (SDEs) and their equivalent ordinary differential equations (ODEs) to establish a smooth connection between a complex data distribution and a tractable prior…
This article presents a new mathematical framework to perform statistical analysis on time-indexed sequences of 2D or 3D shapes. At the core of this statistical analysis is the task of time interpolation of such data. Current models in use…
Generating graph-structured data requires learning the underlying distribution of graphs. Yet, this is a challenging problem, and the previous graph generative methods either fail to capture the permutation-invariance property of graphs or…
We consider the optimal control problem of a general nonlinear spatio-temporal system described by Partial Differential Equations (PDEs). Theory and algorithms for control of spatio-temporal systems are of rising interest among the…
We propose new continuous-time formulations for first-order stochastic optimization algorithms such as mini-batch gradient descent and variance-reduced methods. We exploit these continuous-time models, together with simple Lyapunov analysis…
Correlated with the trend of increasing degrees of freedom in robotic systems is a similar trend of rising interest in Spatio-Temporal systems described by Partial Differential Equations (PDEs) among the robotics and control communities.…
We consider the numerical approximation of general semilinear parabolic stochastic partial differential equations (SPDEs) driven by additive space-time noise. In contrast to the standard time stepping methods which uses basic increments of…
The present paper proposes new fully discrete schemes for long-time approximations of stochastic partial differential equations (SPDEs) with non-globally Lipschitz coefficients in a bounded domain $D \subset \R^d, d =1,2,3 $. A novel family…
We present a hybrid a-priori/a-posteriori goal oriented error estimator for a combination of dynamic iteration-based solution of ordinary differential equations discretized by finite elements. Our novel error estimator combines estimates…
We compare two approaches to the predictive modeling of dynamical systems from partial observations at discrete times. The first is continuous in time, where one uses data to infer a model in the form of stochastic differential equations,…
Stochastic differential equation mixed-effects models (SDEMEMs) are flexible hierarchical models that are able to account for random variability inherent in the underlying time-dynamics, as well as the variability between experimental units…
Score-based modeling through stochastic differential equations (SDEs) has provided a new perspective on diffusion models, and demonstrated superior performance on continuous data. However, the gradient of the log-likelihood function, i.e.,…
This paper addresses the quantitative verification of finite-time constrained occupation time for stochastic continuous-time systems governed by stochastic differential equations (SDEs). Unlike classical reachability analysis, which focuses…
This paper introduces a new framework for analyzing the stability of discrete-time model predictive controllers acting on continuous-time systems. The proposed framework introduces the distinction between discretization time (used to…
This paper presents a new stochastic finite element method for computing structural stochastic responses. The method provides a new expansion of stochastic response and decouples the stochastic response into a combination of a series of…
We introduce a framework for the control of discrete-time switched stochastic systems with uncertain distributions. In particular, we consider stochastic dynamics with additive noise whose distribution lies in an ambiguity set of…
The purpose of this paper is to establish asymptotic behaviors of time-inhomogeneous multi-scale stochastic differential equations (SDEs). To achieve them, we analyze the evolution system of measures for time-inhomogeneous Markov…
Retarded stochastic differential equations (SDEs) constitute a large collection of systems arising in various real-life applications. Most of the existing results make crucial use of dissipative conditions. Dealing with "pure delay" systems…