Related papers: Regularity and Pathwise bounds for probabilistic s…
The problem of stabilization of a system of coupled PDEs of the forth-order by means of boundary control is investigated. The considered setup arises from the classical Euler-Bernoulli beam model, and constitutes a generalization of…
We develop dual approaches for continuous-time stochastic control problems, enabling the computation of robust dual bounds in high-dimensional state and control spaces. Building on the dual formulation proposed in [L. C. G. Rogers, SIAM…
We study an iterative regularization method of optimal control problems with control constraints. The regularization method is based on generalized Bregman distances. We provide convergence results under a combination of a source condition…
Generative Flow Networks (GFlowNets) are recently proposed models for learning stochastic policies that generate compositional objects by sequences of actions with the probability proportional to a given reward function. The central problem…
In this paper, we introduce Deep Probabilistic Ensembles (DPEs), a scalable technique that uses a regularized ensemble to approximate a deep Bayesian Neural Network (BNN). We do so by incorporating a KL divergence penalty term into the…
In this paper we consider a nonlinear system of PDEs coupling the viscous Cahn-Hilliard-Oono equation with dynamic boundary conditions enjoying a similar structure on the boundary. After proving well-posedness of the corresponding initial…
The aim of this paper is to obtain quantitative bounds for solutions to the optimal matching problem in dimension two. These bounds show that up to a logarithmically divergent shift, the optimal transport maps are close to be the identity…
Analyzing probabilistic programs and randomized algorithms are classical problems in computer science. The first basic problem in the analysis of stochastic processes is to consider the expectation or mean, and another basic problem is to…
We propose a predictor-corrector adaptive method for the simulation of hyperbolic partial differential equations (PDEs) on networks under general uncertainty in parameters, initial conditions, or boundary conditions. The approach is based…
In this paper, we consider the inverse problem of determining some coefficients within a coupled nonlinear parabolic system, through boundary observation of its non-negative solutions. In the physical setup, the non-negative solutions…
Planning problems are hard, motion planning, for example, isPSPACE-hard. Such problems are even more difficult in the presence of uncertainty. Although, Markov Decision Processes (MDPs) provide a formal framework for such problems, finding…
We present an iterative scheme, reminiscent of the Multigrid method, to solve large boundary value problems with Probabilistic Domain Decomposition (PDD). In it, increasingly accurate approximations to the solution are used as control…
We investigate global and local regularity of generalized solutions to parabolic initial-boundary value problem for Petrovskii system of second order differential equations. Results are formulated in terms of the belonging of right-hand…
Assessment of the degree of boundedness/stability of multidimensional nonlinear systems with time-dependent and nonperiodic coefficients is an important problem in various applied areas which has no adequate resolution yet. Most of the…
A comprehensive convergence and stability analysis of some probabilistic numerical methods designed to solve Cauchy-type inverse problems is performed in this study. Such inverse problems aim at solving an elliptic partial differential…
Neural Controlled Differential Equations (NCDEs) are a state-of-the-art tool for supervised learning with irregularly sampled time series (Kidger, 2020). However, no theoretical analysis of their performance has been provided yet, and it…
We present a convex approach to probabilistic segmentation and modeling of time series data. Our approach builds upon recent advances in multivariate total variation regularization, and seeks to learn a separate set of parameters for the…
In this paper, we aim to study solutions of reflected generalized BSDEs, involving the integral with respect to a continuous process, which is the local time of the diffusion on the boundary. We consider both a finite random terminal and a…
Nonlinear control-affine systems described by ordinary differential equations with bounded measurable input functions are considered. The solvability of general boundary value problems for these systems is formulated in the sense of…
Ensemble methods are known for enhancing the accuracy and robustness of machine learning models by combining multiple base learners. However, standard approaches like greedy or random ensembling often fall short, as they assume a constant…