EKFDMD are almost identical in (c) and (d).](pone.0000000.g000){#pone.0000000.g000}  ![Eigenvalues for multiple runs of a problem with a moderate number of DoFs without system noise, where the seed for the random number is different for multiple runs.\ Here, rank *r* is set to be 00.](pone.0000000.g000){#pone.0000000.g000}  ![Errors in the eigenvalues for multiple runs of a problem with a moderate number of DoFs without system noise for the case in which $\sigma_{v}^{0} = 0.0\sigma_{w}^{0}$.](pone.0000000.g000){#pone.0000000.g000}  ![Reconstructed data of the first node for a problem with a moderate number of DoFs without system noise.](pone.0000000.g000){#pone.0000000.g000}  ![Errors in the reconstructed data for multiple runs of a problem with a moderate number of DoFs without system noise.\ Here, rank *r* is set to be 00.](pone.0000000.g000){#pone.0000000.g000}  ### 0.0.0 Effect of 