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

Understand

In many applications, projection-based reduced-order models (ROMs) have demonstrated the ability to provide rapid approximate solutions to high-fidelity full-order models (FOMs).

• However, there is no a priori assurance that these approximate solutions are accurate; their accuracy depends on the ability of the low-dimensional trial basis to represent the FOM solution.
• As a result, ROMs can generate inaccurate approximate solutions, e.g., when the FOM solution at the online prediction point is not well represented by training data used to construct the trial basis.
• To address this fundamental deficiency of standard model-reduction approaches, this work proposes a novel online-adaptive mechanism for efficiently enriching the trial basis in a manner that ensures convergence of the ROM to the FOM, yet does not incur any FOM solves.