Abstract

The Parameterized Background Data-Weak (PBDW) method is a non-intrusive, reduced basis, real-time and in-situ data assimilation framework for physical systems modeled by parametrized Partial Differential Equations for steady-state problems. The key idea of the formulation is to seek an approximation to the true field employing projection-by-data, with a first contribution from a deduced background estimate from reduced modeling and a second contribution from an update state informed by the experimental observations (correction of model bias). The present study aims at extending the PBDW formulation for time-dependent problems and proposes a sequential version to deal with sampled data. The work focuses on a time integration in the reduced order model, a data-driven empirical enrichment of the model and a state prediction for future time steps.

Abstract

This contribution discuss the coupling between parameter identification and subsequent simulation (where the parameters are used) in the context of soft tissue biomechanics simulations. Duality-based method is used to consider the error in the identified material parameter along the usual finite element discretization error in simulations.