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We propose and analyse a novel, fully discrete numerical algorithm for the approximation of the generalised Stokes system forced by transport noise -- a prototype model for non-Newtonian fluids including turbulence. Utilising the Gradient…
In the context of uncertainty quantification, computational models are required to be repeatedly evaluated. This task is intractable for costly numerical models. Such a problem turns out to be even more severe for stochastic simulators, the…
Nonlinear non-Gaussian state-space models are ubiquitous in statistics, econometrics, information engineering and signal processing. Particle methods, also known as Sequential Monte Carlo (SMC) methods, provide reliable numerical…
There has been an increasing demand for formal methods in the design process of safety-critical synthetic genetic circuits. Probabilistic model checking techniques have demonstrated significant potential in analyzing the intrinsic…
A novel probabilistic numerical method for quantifying the uncertainty induced by the time integration of ordinary differential equations (ODEs) is introduced. Departing from the classical strategy to randomize ODE solvers by adding a…
We consider the continuous-time setting of linear time-invariant (LTI) systems in feedback with multiplicative stochastic uncertainties. The objective of the paper is to characterize the conditions of Mean-Square Stability (MSS) using a…
We study the problem of system identification for stochastic continuous-time dynamics, based on a single finite-length state trajectory. We present a method for estimating the possibly unstable open-loop matrix by employing properly…
We develop a stochastic Galerkin finite element method for nonlinear elasticity and apply it to reinforced concrete members with random material properties. The strategy is based on the modified Newton-Raphson method, which consists of an…
In this paper, we study randomized methods for feedback design of uncertain systems. The first contribution is to derive the sample complexity of various constrained control problems. In particular, we show the key role played by the…
We first investigate the structure of the systems derived from the gPC based stochastic Galerkin method for the nonlinear hyperbolic systems with random inputs. This method adopts a generalized Polynomial Chaos (gPC) approximations in the…
Nested integration problems arise in various scientific and engineering applications, including Bayesian experimental design, financial risk assessment, and uncertainty quantification. These nested integrals take the form $\int f\left(\int…
Recent years have seen unprecedented advance in the design and control of quantum computers. Nonetheless, their applicability is still restricted and access remains expensive. Therefore, a substantial amount of quantum algorithms research…
The increasing penetration of renewable energy resources in power systems, represented as random processes, converts the traditional deterministic economic dispatch problem into a stochastic one. To solve this stochastic economic dispatch,…
We consider split-step Milstein methods for the solution of stiff stochastic differential equations with an emphasis on systems driven by multi-channel noise. We show their strong order of convergence and investigate mean-square stability…
Sequential Monte Carlo (SMC) methods offer a principled approach to Bayesian uncertainty quantification but are traditionally limited by the need for full-batch gradient evaluations. We introduce a scalable variant by incorporating…
Stochastic simulation models are generative models that mimic complex systems to help with decision-making. The reliability of these models heavily depends on well-calibrated input model parameters. However, in many practical scenarios,…
The intrusive (sample-free) spectral stochastic finite element method (SSFEM) is a powerful numerical tool for solving stochastic partial differential equations (PDEs). However, it is not widely adopted in academic and industrial…
Tau-leaping is a family of algorithms for the approximate simulation of the discrete state continuous time Markov chains. Motivation for the development of such methods can be found, for instance, in the fields of chemical kinetics and…
In the Monte Carlo (MC) method statistical noise is usually present. Statistical noise may become dominant in the calculation of a distribution, usually by iteration, but is less Important in calculating integrals. The subject of the…
We develop a general polynomial chaos (gPC) based stochastic Galerkin (SG) for hyperbolic equations with random and singular coefficients. Due to the singu- lar nature of the solution, the standard gPC-SG methods may suffer from a poor or…