
, but also Lagrangian **data** (FTLE field). Thus, the new ROMs are Lagrangian data-driven ROMs.In Sec-
tion 4.1, we construct the new Lagrangian ROMs. In Section 4.2, we briefly 
contrast traditional Eulerian ROMs (built from Eulerian data) and the new 
Lagrangian ROMs (which are built from both Eulerian and Lagrangian data). 