Dynamical model reduction method for solving parameter-dependent dynamical systems
For computational scientists solving parameterized dynamical systems, this method offers a new approach to reduce computational cost while maintaining accuracy, though it is an incremental improvement over existing low-rank approximation techniques.
The paper proposes a projection-based model order reduction method for parameter-dependent dynamical systems, achieving uniform error control over the parameter set via a greedy algorithm with a posteriori error estimates.
We propose a projection-based model order reduction method for the solution of parameter-dependent dynamical systems. The proposed method relies on the construction of time-dependent reduced spaces generated from evaluations of the solution of the full-order model at some selected parameters values. The approximation obtained by Galerkin projection is the solution of a reduced dynamical system with a modified flux which takes into account the time dependency of the reduced spaces. An a posteriori error estimate is derived and a greedy algorithm using this error estimate is proposed for the adaptive selection of parameters values. The resulting method can be interpreted as a dynamical low-rank approximation method with a subspace point of view and a uniform control of the error over the parameter set.