A FOM/ROM Hybrid Approach for Accelerating Numerical Simulations

Abstract

The basis generation in reduced order modeling usually requires multiple high-fidelity large-scale simulations that could take a huge computational cost. In order to accelerate these numerical simulations, we introduce a FOM/ROM hybrid approach in this paper. It is developed based on an a posteriori error estimation for the output approximation of the dynamical system. By controlling the estimated error, the method dynamically switches between the full-order model and the reduced-oder model generated on the fly. Therefore, it reduces the computational cost of a high-fidelity simulation while achieving a prescribed accuracy level. Numerical tests on the non-parametric and parametric PDEs illustrate the efficacy of the proposed approach.

arXiv comment17 pages, 10 figures

References in corpus (5)

• Reduced-order modeling of advection-dominated systems with recurrent neural networks and convolutional autoencoders
• Adaptive $h$-refinement for reduced-order models
• Online adaptive basis refinement and compression for reduced-order models via vector-space sieving
• Efficient nonlinear manifold reduced order model
• POD-DL-ROM: enhancing deep learning-based reduced order models for nonlinear parametrized PDEs by proper orthogonal decomposition