Related papers: Stochastic Formal Methods for Hybrid Systems
We consider parabolic PDEs with randomly switching boundary conditions. In order to analyze these random PDEs, we consider more general stochastic hybrid systems and prove convergence to, and properties of, a stationary distribution.…
We present a general framework for applying learning algorithms and heuristical guidance to the verification of Markov decision processes (MDPs). The primary goal of our techniques is to improve performance by avoiding an exhaustive…
The structured singular value (SSV), or mu, is used to assess the robust stability and performance of an uncertain linear time-invariant system. Existing algorithms compute upper and lower bounds on the SSV for structured uncertainties that…
In this paper we investigate the applicability of standard model checking approaches to verifying properties in probabilistic programming. As the operational model for a standard probabilistic program is a potentially infinite parametric…
Achieving safe control under uncertainty is a key problem that needs to be tackled for enabling real-world autonomous robots and cyber-physical systems. This paper introduces Probabilistic Safety Programs (PSP) that embed both the…
Many biological systems exhibit multiscale dynamics, where some species occur in high copy numbers while others remain rare. This heterogeneity necessitates hybrid modelling approaches: deterministic models are computationally efficient but…
Markov automata combine non-determinism, probabilistic branching, and exponentially distributed delays. This compositional variant of continuous-time Markov decision processes is used in reliability engineering, performance evaluation and…
This paper introduces a new parsimonious structure for mixture of autoregressive models. the weighting coefficients are determined through latent random variables, following a hidden Markov model. We propose a dynamic programming algorithm…
Probabilistic models based on continuous latent spaces, such as variational autoencoders, can be understood as uncountable mixture models where components depend continuously on the latent code. They have proven to be expressive tools for…
The general applicability and ease of use of the pseudo-marginal Metropolis--Hastings (PMMH) algorithm, and particle Metropolis--Hastings in particular, makes it a popular method for inference on discretely observed Markovian stochastic…
In this paper, we study the probabilistic stability analysis of a subclass of stochastic hybrid systems, called the Planar Probabilistic Piecewise Constant Derivative Systems (Planar PPCD), where the continuous dynamics is deterministic,…
We study the polyhedral structure of the static probabilistic lot-sizing problem and propose valid inequalities that integrate information from the chance constraint and the binary setup variables. We prove that the proposed inequalities…
We consider the safety evaluation of discrete time, stochastic systems over a finite horizon. Therefore, we discuss and link probabilistic invariance with reachability as well as reach-avoid problems. We show how to efficiently compute…
A method to quantify robust performance for situations where structured parameter variations and initial state errors rather than extraneous disturbances are the main performance limiting factors is presented. The approach is based on the…
The estimation of the probability of rare events is an important task in reliability and risk assessment. We consider failure events that are expressed in terms of a limit-state function, which depends on the solution of a partial…
A probabilistic framework is proposed for the optimization of efficient switched control strategies for physical systems dominated by stochastic excitation. In this framework, the equation for the state trajectory is replaced with an…
A dual hybrid Virtual Element scheme for plane linear elastic problems is presented and analysed. In particular, stability and convergence results have been established. The method, which is first order convergent, has been numerically…
Impulse methods are generalized to a family of integrators for Langevin systems with quadratic stiff potentials and arbitrary soft potentials. Uniform error bounds (independent from stiff parameters) are obtained on integrated positions…
We prove a convergence result for a large class of random models that encompasses the case of the BPHZ models used in the study of singular stochastic PDEs. We introduce for that purpose a useful variation on the notion of regularity…
Parametric statistical methods play a central role in analyzing risk through its underlying frequency and severity components. Given the wide availability of numerical algorithms and high-speed computers, researchers and practitioners often…