Related papers: A stochastic perturbation approach to nonlinear bi…
We consider the inference problem for parameters in stochastic differential equation models from discrete time observations (e.g. experimental or simulation data). Specifically, we study the case where one does not have access to…
This article is devoted to providing a review of mathematical formulations in which Polynomial Chaos Theory (PCT) has been incorporated into stochastic model predictive control (SMPC). In the past decade, PCT has been shown to provide a…
This paper discusses a method enabling optimal control of nonlinear systems that are subject to parametric uncertainty. A stochastic optimal tracking problem is formulated that can be expressed in function of the first two stochastic…
Uncertainty quantification seeks to provide a quantitative means to understand complex systems that are impacted by parametric uncertainty. The polynomial chaos method is a computational approach to solve stochastic partial differential…
A central challenge in physics is to describe non-equilibrium systems driven by randomness, such as a randomly growing interface, or fluids subject to random fluctuations that account e.g. for local stresses and heat fluxes not related to…
Differential equations with random parameters have gained significant prominence in recent years due to their importance in mathematical modelling and data assimilation. In many cases, random ordinary differential equations (RODEs) are…
Over the last few years there have been dramatic advances in our understanding of mathematical and computational models of complex systems in the presence of uncertainty. This has led to a growth in the area of uncertainty quantification as…
Polynomial Chaos Expansions represent a powerful tool to simulate stochastic models of dynamical systems. Yet, deriving the expansion's coefficients for complex systems might require a significant and non-trivial manipulation of the model,…
Model predictive control is an advanced control approach for multivariable systems with constraints, which is reliant on an accurate dynamic model. Most real dynamic models are however affected by uncertainties, which can lead to…
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…
Polynomial chaos expansions (PCE) have proven efficiency in a number of fields for propagating parametric uncertainties through computational models of complex systems, namely structural and fluid mechanics, chemical reactions and…
Polynomial chaos based methods enable the efficient computation of output variability in the presence of input uncertainty in complex models. Consequently, they have been used extensively for propagating uncertainty through a wide variety…
We present an approach to the simulation of quantum systems driven by classical stochastic processes that is based on the polynomial chaos expansion, a well-known technique in the field of uncertainty quantification. The polynomial chaos…
Polynomial chaos expansion (PCE) is a classical and widely used surrogate modeling technique in physical simulation and uncertainty quantification. By taking a linear combination of a set of basis polynomials - orthonormal with respect to…
In this paper, we combine deterministic splitting methods with a polynomial chaos expansion method for solving stochastic parabolic evolution problems. The stochastic differential equation is reduced to a system of deterministic equations…
Discrete numerical methods with finite time-steps represent a practical technique to solve initial-value problems involving nonlinear differential equations. These methods seem particularly useful to the study of chaos since no analytical…
Polynomial chaos expansions (PCE) allow us to propagate uncertainties in the coefficients of differential equations to the statistics of their solutions. Their main advantage is that they replace stochastic equations by systems of…
Building surrogate models with uncertainty quantification capabilities is essential for many engineering applications where randomness, such as variability in material properties, is unavoidable. Polynomial Chaos Expansion (PCE) is widely…
We present a Bayesian non-parametric way of inferring stochastic differential equations for both regression tasks and continuous-time dynamical modelling. The work has high emphasis on the stochastic part of the differential equation, also…
Nonlinear dynamical systems with continuous variables can be used for solving combinatorial optimization problems with discrete variables. Numerical simulations of them are also useful as heuristic algorithms with a desirable property,…