Related papers: Accurate error estimation for model reduction of n…
Developing accurate, efficient, and robust closure models is essential in the construction of reduced order models (ROMs) for realistic nonlinear systems, which generally require drastic ROM mode truncations. We propose a deep residual…
A posteriori error estimates are derived in the context of two-dimensional structural elastic shape optimization under the compliance objective. It is known that the optimal shape features are microstructures that can be constructed using…
We show how a posteriori goal oriented error estimation can be used to efficiently solve the subproblems occurring in a Model Predictive Control (MPC) algorithm. In MPC, only an initial part of a computed solution is implemented as a…
Many complex engineering systems consist of multiple subsystems that are developed by different teams of engineers. To analyse, simulate and control such complex systems, accurate yet computationally efficient models are required. Modular…
We develop a compact, reliable model order reduction approach for fast frequency sweeps in microwave circuits by means of the reduced-basis method. Contrary to what has been previously done, special emphasis is placed on certifying the…
A residual based {\em a posteriori} error estimator is derived for a quadratic finite element method (fem) for the elliptic obstacle problem. The error estimator involves various residuals consisting the data of the problem, discrete…
Linear reduced-order modeling (ROM) is widely used for efficient simulation of deformation dynamics, but its accuracy is often limited by the fixed linearization of the reduced mapping. We propose a new adaptive strategy for linear ROM that…
In this note, we extend the analysis for the residual-based a posteriori error estimators in the energy norm defined for the algebraic flux correction (AFC) schemes [Jha20.CAMWA] to the newly proposed algebraic stabilization schemes…
In this paper we introduce and analyze the residual-based a posteriori error estimation of the partially penalized immersed finite element method for solving elliptic interface problems. The immersed finite element method can be naturally…
This study presents incremental correction methods for refining neural network parameters or control functions entering into a continuous-time dynamic system to achieve improved solution accuracy in satisfying the interim point constraints…
For the numerical solution of the American option valuation problem, we provide a script written in MATLAB implementing an explicit finite difference scheme. Our main contribute is the definition of a posteriori error estimator for the…
We propose and analyze a posteriori error estimates for a control-constrained optimal control problem with bang-bang solutions. We consider a solution strategy based on the variational approach, where the control variable is not…
Discrete-time models are very convenient to simulate a nonlinear system on a computer. In order to build the discrete-time simulation models for the nonlinear feedback systems (which is a very important class of systems in many…
A novel residual-type {\it a posteriori} error analysis technique is developed for multipoint flux mixed finite element methods for flow in porous media in two or three space dimensions. The derived {\it a posteriori} error estimator for…
The importance of state estimation in fluid mechanics is well-established; it is required for accomplishing several tasks including design/optimization, active control, and future state prediction. A common tactic in this regards is to rely…
In this work, we aim at efficiently solving a parametrized family of optimal transport problems by using model order reduction methods. We propose a reduced-order model by adding to the primal (respectively dual) version of the…
Real world evolves in continuous time but computations are done from finite samples. Therefore, we study algorithms using finite observations in continuous-time linear dynamical systems. We first study the system identification problem, and…
We consider a control-constrained optimal control problem subject to time-harmonic Maxwell's equations; the control variable belongs to a finite-dimensional set and enters the state equation as a coefficient. We derive existence of optimal…
In this work, we further develop multigoal-oriented a posteriori error estimation with two objectives in mind. First, we formulate goal-oriented mesh adaptivity for multiple functionals of interest for nonlinear problems in which both the…
We derive a new residual-type a posteriori estimator for a singularly perturbed reaction-diffusion problem with obstacle constraints. It generalizes robust residual estimators for unconstrained singularly perturbed equations. Upper and…