Quantitative reconstruction of the magnetic connectivity between the ionosphere and the vast volume of distant magnetosphere has traditionally been the principal goal of the data-based empirical modeling. Introduction of advanced mathematical architectures (N. A. Tsyganenko & Sitnov, 2007, henceforth TS07; N. A. Tsyganenko, Andreeva, Kubyshkina, et al., 2021, and references therein), the continuing growth of volume/quality of archived data, and the development of new methods of data ingestion into the models (Sitnov et al., 2008, 2020, and refs. therein) resulted in significant progress, making it eventually possible to model not only average magnetospheric states, quantified by ad hoc driving functions (e.g., N. A. Tsyganenko & Andreeva, 2015; henceforth TA15), but also to reproduce the dynamics of individual events (