Related papers: A stochastic Galerkin method for optimal Dirichlet…
Mixed optimal stopping and stochastic control problems define variational inequalities with non-linear Hamilton-Jacobi-Bellman (HJB) operators, whose numerical solution is notoriously difficult and lack of reliable benchmarks. We first use…
We consider a hybridizable discontinuous Galerkin (HDG) method for an elliptic distributed optimal control problem and we propose a balancing domain decomposition by constraints (BDDC) preconditioner to solve the discretized system. We…
In this paper we study the mixed virtual element approximation to an elliptic optimal control problem with boundary observations. The objective functional of this type of optimal control problem contains the outward normal derivatives of…
We propose a new hybridizable discontinuous Galerkin (HDG) method to approximate the solution of a Dirichlet boundary control problem governed by an elliptic convection diffusion PDE. Even without a convection term, Dirichlet boundary…
We consider time discretization methods for abstract parabolic problems with inhomogeneous linear constraints. Prototype examples that fit into the general framework are the heat equation with inhomogeneous (time dependent) Dirichlet…
This paper studies an optimal control problem for continuous-time stochastic systems subject to reachability objectives specified in a subclass of metric interval temporal logic specifications, a temporal logic with real-time constraints.…
In uncertainty quantification, a stochastic modelling is often applied, where parameters are substituted by random variables. We investigate linear dynamical systems of ordinary differential equations with a quantity of interest as output.…
A linear PDE problem for randomly perturbed domains is considered in an adaptive Galerkin framework. The perturbation of the domain's boundary is described by a vector valued random field depending on a countable number of random variables…
The study of optimal control problems under uncertainty plays an important role in scientific numerical simulations. This class of optimization problems is strongly utilized in engineering, biology and finance. In this paper, a stochastic…
We investigate numerical behaviour of a convection diffusion equation with random coefficients by approximating statistical moments of the solution. Stochastic Galerkin approach, turning the original stochastic problem to a system of…
In this paper we investigate a priori error estimates for the space-time Galerkin finite element discretization of an optimal control problem governed by a simplified linear gradient enhanced damage model. The model equations are of a…
Stochastic Galerkin methods offer unexplored potential for the numerical simulation of parabolic problems with random variables, in particular if they are combined with variational discretizations of the space and time variables. Due to the…
In this paper, we develop an efficient preconditioned unfitted finite element method for the elliptic interface problem, based on the reconstructed discontinuous approximation. The approximation method for interface problems is originally…
We present a new approach to using neural networks to approximate the solutions of variational equations, based on the adaptive construction of a sequence of finite-dimensional subspaces whose basis functions are realizations of a sequence…
We consider the estimation of parameter-dependent statistics of functional outputs of elliptic boundary value problems (BVPs) with parametrized random and deterministic inputs. For a given value of the deterministic paremeter, a stochastic…
In this paper, we propose an adaptive approach, based on mesh refinement or parametric enrichment with polynomial degree adaption, for numerical solution of convection dominated equations with random input data. A parametric system emerged…
We consider a linear parabolic problem with random elliptic operator in the usual Gelfand triple setting. We do not assume uniform bounds on the coercivity and boundedness constants, but allow them to be random variables. The parabolic…
In this work we recast parametrized time dependent optimal control problems governed by partial differential equations in a saddle point formulation and we propose reduced order methods as an effective strategy to solve them. Indeed, on one…
Understanding chemical mechanisms requires estimating dynamical statistics such as expected hitting times, reaction rates, and committors. Here, we present a general framework for calculating these dynamical quantities by approximating…
This work introduces a stochastic model predictive control scheme for dynamic chance constraints. We consider linear discrete-time systems affected by unbounded additive stochastic disturbance. To synthesize an optimal controller, we solve…