# Entity Embeddings in Remote Sensing: Application to Deformation Monitoring for Infrastructure
## 4 Results and Discussion  
### Prediction Performance of EE-DL Model  
Deep learning experiments were successfully undertaken on the embeddings of the InSAR deformation metadata. The temporal behaviour of the EE-DL predictions is given in Figure 6. It presents the error between InSAR measurements and the predicted deformations from a variety of experiments. The input timescale and prediction horizon (i.e., forecast steps into the future) of the experiments are detailed in Table 3. In these experiments, the steps correspond to the number of dates at which prediction was performed, and each step equals the temporal resolution of the SAR data, which is every 12 days over Cadia. In the case of one-step-ahead prediction, the inference starts from \(n+1\), where \(n\) represents the last date used in training. Similarly, in the context of four-step-ahead prediction (as seen in Run-C), following the completion of the four-step-ahead prediction, the data at \(n+4\) were inserted back into the training dataset, and the model was re-trained. Therefore, it is important to note that training occurred after the introduction of each new set of predictions. For a typical stable location not experiencing deformation in Figure 6a, the absolute error between predictions and measurements was within 6 mm for all experiments, independent of the time frame and prediction horizons. However, the variation in the absolute error was significantly different for a typical measurement from the failure area, as plotted  
Figure 5: Comparison of GPR kernels in capturing the InSAR deformation behaviour: (**a**) Radial Basis Function kernel (RBF) and (**b**) combined RBF and linear kernels. The addition of a linear kernel gets rid of the tendency of the RBF to return to zero. in Figure 6b. The absolute error was within 8 mm, which is \(\pm\)4 mm, before almost doubling in the last three dates (2018-01-20 onwards) immediately before failure (2018-02-25). This is a clear sign of anomalous deformation behaviour arising from the TSF foundation issues attributed to the failure [19]. The minimum number of temporal data points required as training data for an acceptable EE-DL model performance was also explored. Figure 7 plots the global RMSE for InSAR measurements and the predictions for each inference date. The shortest number of input dates used for training was in Run-A, which had an input of 21 dates (2015-12-02 to 2016-08-10). The RMSE for Run-A was noisy for the first 13 predictions until 2017-02-06, after which the RMSE variability was significantly less in time, plateauing at approximately \begin{table}
\begin{tabular}{c c c c c} \hline \hline  & **Start** & **End** & **Total Dates** & **Steps** \\ \hline Run-A & 2015-12-02 & 2016-08-10 & 21 & 1 \\ Run-B & 2015-12-02 & 2017-01-25 & 35 & 1 \\ Run-C & 2015-12-02 & 2017-01-25 & 35 & 4 \\ Run-D & 2015-12-02 & 2017-10-04 & 56 & 1 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: EE-DL input training data with different lengths of temporal data points as described by the start and end dates. The total number of dates used in the training and the prediction horizon, i.e., forecast steps into the future, are also specified. There is a 12-day interval between each date. Figure 6: The absolute error between the EE-DL prediction and the InSAR deformation measurements (grey) is plotted. The dashed lines mark the absolute error associated with the background noise level in the data. (**a**) An example of an InSAR measurement not experiencing deformation. (**b**) A measurement displaying a deformation of 40 mm and a clear anomalous deformation behaviour immediately preceding failure. Note the sudden jump in the absolute error for the last four dates. 3 mm. This implies that a minimum of 35 dates, from 2015-12-02 to 2017-01-25, is required to obtain a stable deformation prediction. The data up to 2017-02-06 were used for training Run-B and Run-C.