Adaptive Reduced Basis Trust Region Methods for Parameter Identification Problems

by   Michael Kartmann, et al.

In this contribution, we are concerned with model order reduction in the context of iterative regularization methods for the solution of inverse problems arising from parameter identification in elliptic partial differential equations. Such methods typically require a large number of forward solutions, which makes the use of the reduced basis method attractive to reduce computational complexity. However, the considered inverse problems are typically ill-posed due to their infinite-dimensional parameter space. Moreover, the infinite-dimensional parameter space makes it impossible to build and certify classical reduced-order models efficiently in a so-called "offline phase". We thus propose a new algorithm that adaptively builds a reduced parameter space in the online phase. The enrichment of the reduced parameter space is naturally inherited from the Tikhonov regularization within an iteratively regularized Gauß-Newton method. Finally, the adaptive parameter space reduction is combined with a certified reduced basis state space reduction within an adaptive error-aware trust region framework. Numerical experiments are presented to show the efficiency of the combined parameter and state space reduction for inverse parameter identification problems with distributed reaction or diffusion coefficients.


page 20

page 23


Robust Parameter Inversion using Adaptive Reduced Order Models

Nonlinear parametric inverse problems appear in many applications and ar...

In-situ adaptive reduction of nonlinear multiscale structural dynamics models

Conventional offline training of reduced-order bases in a predetermined ...

A Perturbation Scheme for Passivity Verification and Enforcement of Parameterized Macromodels

This paper presents an algorithm for checking and enforcing passivity of...

A globally convergent method to accelerate large-scale optimization using on-the-fly model hyperreduction: application to shape optimization

We present a numerical method to efficiently solve optimization problems...

On a Dynamic Variant of the Iteratively Regularized Gauss-Newton Method with Sequential Data

For numerous parameter and state estimation problems, assimilating new d...

Computational Homogenization of Concrete in the Cyber Size-Resolution-Discretization (SRD) Parameter Space

Micro- and mesostructures of multiphase materials obtained from tomograp...

Please sign up or login with your details

Forgot password? Click here to reset