TY - JOUR
T1 - On the Criteria for Online Updating of Basis Functions for Model Order Reduction Techniques
AU - Zhang , Han
AU - Wang , Zhiyong
AU - Mou , Zihao
AU - Niu , Taidong
AU - Gong , Helin
JO - Numerical Mathematics: Theory, Methods and Applications
VL - 3
SP - 619
EP - 649
PY - 2025
DA - 2025/09
SN - 18
DO - http://doi.org/10.4208/nmtma.OA-2024-0127
UR - https://global-sci.org/intro/article_detail/nmtma/24321.html
KW - POD, model order reduction, data assimilation, parameterized dynamical restriction, 2D LWR problem.
AB - <p style="text-align: justify;">The model order reduction and data assimilation techniques have been
extensively applied to construct surrogate models as core models for digital twins
in different industries. However, in most applications, the online phases rely on
a single offline basis construction within the parameter domain, which is computationally expensive and often overlooks local parameter variations due to anisotropic
behavior. Consequently, this poses challenges for real-time monitoring where parameters vary dynamically. To address this, we introduce a relative deviation score of
reduced basis coefficients, represented by $\mathcal{W},$ to assess the reconstruction capability
of basis functions under current parameters. Additionally, we provide a quantitative
threshold $\overline{\mathcal{W}}$ for $\mathcal{W}.$ Using the reconstruction of a two-dimensional reactor core field
distribution as a case study, we demonstrate that if $\mathcal{W}$ remains below the threshold $\overline{\mathcal{W}}=1,$ the average reconstruction error can be maintained within the same order of
magnitude as the fundamental error limit $ε (κ ≤ 10).$ Furthermore, we compare $\mathcal{W}$ with the traditional one-time reduced basis selection method and the metric $C_{R2F}$ [F. Bai and Y. Wang, SN Applied Sciences, 2 (2020), p. 2165], confirming the lower
computational cost and enhanced robustness of our proposed algorithm.</p>