A Posteriori Error Estimation for Model Order Reduction of Parametric Systems

Abstract

This survey discusses a posteriori error estimation for model order reduction of parametric systems, including linear and nonlinear, time-dependent and steady systems. We focus on introducing the error estimators we have proposed in the past few years and comparing them with the most related error estimators from the literature. For a clearer comparison, we have translated some existing error bounds proposed in function spaces into the n-dimensional complex coordinate space and provide the corresponding proofs. Some new insights into our proposed error estimators are explored. Moreover, we review our newly proposed error estimator for nonlinear time-evolution systems, which is applicable to reduced-order models solved by arbitrary time-integration solvers. Our recent work on multi-fidelity error estimation is also briefly discussed. Finally, we derive a new inf-sup-constant-free output error estimator for nonlinear time-evolution systems. Numerical results for two examples show the robustness of the new error estimator.

Fast and reliable reduced‐order models for cardiac electrophysiology

“…For the cardiac electrophysiology model, the quality of approximation of the output quantities (ECG or flux) is of particular interest, as these are the ones of medical consequence. A posteriori error estimation for output quantities has received considerable attention in the reduced basis community [18,23,31,34,66]. We use the residual-based primal-dual a posteriori output error estimator proposed in [18].…”