Henrik Rosenberger developed a new exact approach to operator inference. It exactly recovers intrusive operators but in a non-intrusive way, while guaranteeing that a minimum number of snapshots of the full order model is needed. The key lies in a smart selection of initial conditions at which the FOM is evaluated. As a consequence, the least-squares problem becomes an interpolation problem and the associated matrix is square and full-rank.
As the recovered operators are exact, there is no need to employ any additional structure-preserving techniques: any structure is automatically preserved.
You can find the full preprint here, and the associated software here.
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