DeepAI
Log In Sign Up

Online adaptive basis construction for nonlinear model reduction through local error optimization

05/04/2021
by   Jun-Geol Ahn, et al.
0

The accuracy of the reduced-order model (ROM) mainly depends on the selected basis. Therefore, it is essential to compute an appropriate basis with an efficient numerical procedure when applying ROM to nonlinear problems. In this paper, we propose an online adaptive basis technique to increase the quality of ROM while decreasing the computational costs in nonlinear problems. In the proposed method, the adaptive basis is defined by the low-rank update formulation, and two auxiliary vectors are set to implement this low-rank condition. To simultaneously tackle the issues of accuracy and the computational cost of the ROM basis, the auxiliary vectors are algebraically derived by optimizing a local residual operator. As a result, the reliability of ROM is significantly improved with a low computational cost because the error information can be contained without inverse operations of the full model dimension required in conventional approaches. The other feature of the proposed iterative algorithm is that the number of the initial incremental ROM basis could be varied, unlike in the typical online adaptive basis approaches. It may provide a fast and effective spanning process of the high-quality ROM subspace in the iteration step. A detailed derivation process of the proposed method is presented, and its performance is evaluated in various nonlinear numerical examples.

READ FULL TEXT

page 29

page 30

page 31

page 32

page 33

page 34

page 35

page 37

07/26/2020

Rank-adaptive structure-preserving reduced basis methods for Hamiltonian systems

This work proposes an adaptive structure-preserving model order reductio...
11/13/2019

Adaptive Basis Construction and Improved Error Estimation for Parametric Nonlinear Dynamical Systems

An adaptive scheme to generate reduced-order models for parametric nonli...
05/01/2022

Adaptive auxiliary reduced model reanalysis-based efficient topology optimization method

Efficient topology optimization based on the adaptive auxiliary reduced ...
01/30/2021

Metalearning: Sparse Variable-Structure Automata

Dimension of the encoder output (i.e., the code layer) in an autoencoder...
02/27/2019

Online adaptive basis refinement and compression for reduced-order models

In many applications, projection-based reduced-order models (ROMs) have ...
02/27/2019

Online adaptive basis refinement and compression for reduced-order models via vector-space sieving

In many applications, projection-based reduced-order models (ROMs) have ...
10/15/2019

Adaptive Low-Rank Approximations for Operator Equations: Accuracy Control and Computational Complexity

The challenge of mastering computational tasks of enormous size tends to...