## 4 Evaluation
### Gulf Stream
Figure 5 depicts how the FP-GENN interpolator performs using nadir data (a) or their joint use with SWOT (b), according to the input and target data used for the training. Within this part-GULFSTREAM domain, we clearly see the best performance is obtained by the unsupervised configuration of FP-GENN: it is a key result because the learning network's abilities seem to be better when it is fully data-driven, meaning that it benefits from its knowledge of the spatio-temporal location and occurrence of the data, which is a fairly new avenue for data assimilation-related problems. The use of the OI as a covariate improve the FP-GENN's behavior but not systematically. Intriguingly, if the joint use of nadir and SWOT data generally improves the results, using only nadir in the unsupervised FP-GENN may yield a better reconstruction the days where no SWOT data are available. We hope that a longer training period could help the network to learn from the masking periodicity of 2D wide-swath data. Based on these first results, the FP-GENN interpolator is used in its unsupervised configuration with OI used as a covariate. FP-ConvAE generally shows lower performance, probably because auto-encoders may not be relevant for the reconstruction of fine-scale processes, so it was used in the following in the supervised 2 configuration as a low-rated NN-scheme among the NN-based interpolators. Figure 6 presents the daily nRMSE of the different interpolators: it can be seen how FP-GENN significantly outperforms the conventional OI-based interpolator, but also the other data-driven algorithms used in the experiment. In addition, the FP-GENN mapping error seems to be more stable across time than the OI, meaning that in case of a missing altimetric mission, the error would also remain more stable. AnDA still remains quite efficient at the very beginning of the four 20-days validation period, which is probably related to a strong persistence of the mesoscale dynamics of the SSH over the region. In other words, the one-year catalog (minus the 4 \(\times\) 20 validation days) obviously enable to build a good analog forecasting operator when knowing the short-term dynamics, but its accuracy quickly decays afterwards, which may not be fair for AnDA that probably requires \begin{table}
\begin{tabular}{l l c c c} \hline \hline \multicolumn{1}{c}{**Configurations**} & \multicolumn{3}{c}{**Data**} \\  & & **Observations** & **Gap-Free Maps** & **DUACS OI** \\ \hline \multirow{3}{*}{**Supervised 1**} & Input & & ✓ & yes/no \\  & Target & & ✓ & yes/no \\ \multirow{3}{*}{**Supervised 2**} & Input & ✓ & & yes/no \\  & Target & & ✓ & \\ \multirow{3}{*}{**Unsupervised**} & Input & ✓ & & yes/no \\  & Target & ✓ & & \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Specifications of GENN learning-based strategies. longer simulations-based catalog in this low-latitude GULFSTREAM region with large Rossby radius of deformation. The Taylor diagram in Figure 7a, here calculated over the four 20 validation days and focusing only on small-scale structures by applying a high-pass filter that spectrally separates the horizontal scales ranging in the order of 150 km, also confirms our first findings. In Table 3, R/I/AE-scores are applied to both SSH (after application of a retrieving high-pass filter to keep only the small scales information) and its gradient (module). Regarding the R-scores, AnDA and VE-DINEOF are often the best ways to keep track of the known areas, which is not surprising since these two methods make explicit use of the observational altimetric data in their mapping processes. When looking at the I-scores, where no data are available, FP-GENN clearly stands out from the other interpolators, which should drive its future use for irregularly-sampled data with large missing data rates. In addition, because its reconstruction scores remain overall satisfactory, in particular when considering the joint learning on nadir and SWOT data, these results are supplementary arguments on account of this Markovian-related NN-based formulation.