相关论文: Moment-based Invariants for Probabilistic Loops wi…

While convergence of polynomial chaos approximation for linear equations is relatively well understood, a lot less is known for non-linear equations. The paper investigates this convergence for a particular equation with quadratic…

We give a new framework for proving the existence of low-degree, polynomial approximators for Boolean functions with respect to broad classes of non-product distributions. Our proofs use techniques related to the classical moment problem…

A method of calculating probability values from a system of marginal constraints is presented. Previous systems for finding the probability of a single attribute have either made an independence assumption concerning the evidence or have…

We present a method to construct high-order polynomial approximate invariants (AI) for non-integrable Hamiltonian dynamical systems, and apply it to modern ring-based particle accelerators. Taking advantage of a special property of one-turn…

Probabilistic modeling provides the capability to represent and manipulate uncertainty in data, models, predictions and decisions. We are concerned with the problem of learning probabilistic models of dynamical systems from measured data.…

We present a numerical algorithm for finding real non-negative solutions to polynomial equations. Our methods are based on the expectation maximization and iterative proportional fitting algorithms, which are used in statistics to find…

We demonstrate a data-driven method to solve for the invariant probability density function of a randomly perturbed dynamical system. The key idea is to replace the boundary condition of numerical schemes by a least squares problem…

This paper presents a program analysis method that generates program summaries involving polynomial arithmetic. Our approach builds on prior techniques that use solvable polynomial maps for summarizing loops. These techniques are able to…

Probabilistic and set-based methods are two approaches for model invalidation, parameter and state estimation. Both classes of methods use different types of data, i.e. deterministic or probabilistic data, which allow different statements…

We study the incremental knapsack problem, where one wishes to sequentially pack items into a knapsack whose capacity expands over a finite planning horizon, with the objective of maximizing time-averaged profits. While various…

Fractional statistical moments are utilized for various tasks of uncertainty quantification, including the estimation of probability distributions. However, an estimation of fractional statistical moments of costly mathematical models by…

In this paper, we investigate discrete-time decision-making problems in uncertain systems with partially observed states. We consider a non-stochastic model, where uncontrolled disturbances acting on the system take values in bounded sets…

Non-commutative polynomial optimization is a powerful technique with numerous applications in quantum nonlocality, quantum key distribution, causal inference, many-body physics, amongst others. The standard approach is to reduce such…

Because of the complexity of fluid flow solvers, non-intrusive uncertainty quantification techniques have been developed in aerodynamic simulations in order to compute the quantities of interest required in an optimization process, for…

We present an algorithm for finding the probabilities of rare events in nonequilibrium processes. The algorithm consists of evolving the system with a modified dynamics for which the required event occurs more frequently. By keeping track…

This paper presents a method to approximately solve stochastic optimal control problems in which the cost function and the system dynamics are polynomial. For stochastic systems with polynomial dynamics, the moments of the state can be…

A hybrid dynamical system switches between dynamic regimes at time- or state-triggered events. We propose an offline algorithm that simultaneously estimates discrete and continuous components of a hybrid system's state. We formulate state…

In this paper non-asymptotic moment estimates are derived for tail of distribution for discrete time polynomial martingale by means of martingale differences as a rule in the terms of unconditional and unconditional relative moments and…

A probabilistic performance-oriented controller design approach based on polynomial chaos expansion and optimization is proposed for flight dynamic systems. Unlike robust control techniques where uncertainties are conservatively handled,…

We compute probabilistic controlled invariant sets for nonlinear systems using Gaussian process state space models, which are data-driven models that account for unmodeled and unknown nonlinear dynamics. We propose a semidefinite…