Model Reduction for Large Scale Systems

@inproceedings{Keil2021ModelRF,
  title={Model Reduction for Large Scale Systems},
  author={Tim Keil and Mario Ohlberger},
  booktitle={LSSC},
  year={2021}
}
Projection based model order reduction has become a mature technique for simulation of large classes of parameterized systems. However, several challenges remain for problems where the solution manifold of the parameterized system cannot be well approximated by linear subspaces. While the online efficiency of these model reduction methods is very convincing for problems with a rapid decay of the Kolmogorov n-width, there are still major drawbacks and limitations. Most importantly, the… 
1 Citations

Guided Probabilistic Simulation of Complex Systems Toward Rare and Extreme Events

A framework is developed to identify rare and extreme events and enabling the use of reverse trajectories to trace failures to causes for potential mitigation actions, to control the growth of the “scenario tree” and to efficiently identify important scenarios that meet single or multiple criteria.

References

SHOWING 1-10 OF 20 REFERENCES

Localized model reduction for parameterized problems

In detail, it is shown how optimal local approximation spaces can be constructed and approximated by random sampling and an overview of possible conforming and non-conforming couplings of the local spaces is provided.

REDUCED BASIS METHOD FOR FINITE VOLUME APPROXIMATIONS OF PARAMETRIZED LINEAR EVOLUTION EQUATIONS

This work introduces a new offline basis-generation algorithm based on the derivation of rigorous a-posteriori error estimates in various norms for general linear evolution schemes such as finite volume schemes for parabolic and hyperbolic evolution equations.

Error Control for the Localized Reduced Basis Multiscale Method with Adaptive On-Line Enrichment

This contribution is considering error estimators that are based on conservative flux reconstruction and provide an efficient and rigorous bound on the full error with respect to the weak solut...

Reduced Basis Methods: Success, Limitations and Future Challenges

This contribution discusses what is known about the convergence properties of these methods: when they succeed and when they are bound to fail, and highlights some recent approaches employing nonlinear approximation techniques which aim to overcome the current limitations of reduced basis methods.

Chapter 2: Reduced Basis Methods for Parametrized PDEs—A Tutorial Introduction for Stationary and Instationary Problems

A class of model reduction techniques for parametric partial differential equations, the so-called Reduced Basis (RB) methods, allow to obtain low-dimensional parametric models for various complex applications, enabling accurate and rapid numerical simulations.

Non-conforming Localized Model Reduction with Online Enrichment: Towards Optimal Complexity in PDE Constrained Optimization

This work proposes an iterative enrichment procedure that refines and locally adapts the surrogate model specifically for the parameters that are depicted during the outer optimization loop.

Reduced Basis Approximation for Nonlinear Parametrized Evolution Equations based on Empirical Operator Interpolation

A new algorithm is introduced, the PODEI-greedy algorithm, which constructs the reduced basis spaces for the empirical interpolation and for the numerical scheme in a synchronized way, and it is shown that the resulting reduced scheme is able to capture the evolution of both smooth and discontinuous solutions.

Localized Model Reduction in PDE Constrained Optimization

We present efficient localized model reduction approaches for PDE constraint optimization or optimal control. The first approach focuses on problems where the underlying PDE is given as a locally

An adaptive projected Newton non-conforming dual approach for trust-region reduced basis approximation of PDE-constrained parameter optimization

A new proof of convergence of the TR-RB method based on infinite-dimensional arguments is presented, not restricted to the particular case of an RB approximation and an a posteriori error estimate for the approximation of the optimal parameter is provided.

A Certified Trust Region Reduced Basis Approach to PDE-Constrained Optimization

The reduced basis (RB) model reduction method is used in conjunction with a trust region optimization framework to accelerate PDE-constrained parameter optimization.