## 9 Practical Application and Future Work  
Figure 6 gives the error in microns (\(\upmu\)m) against ground truth, for estimates of peak amplitude time of flight as provided by CSDI models trained on \(\mathcal{X}_{0.95}\) and \(\mathcal{X}_{0.70}\) partitioned datasets. For the UT NDE inspection of nuclear CANDU PT, the minimum deviation from nominal that must be reported is 100 \(\upmu\)m. In practice, the minimum reportable deviation sits at the edge of human cognitive abilities, and for anomalies in this range the data are often unclear, which causes analysis to be somewhat subjective. To support this point of view we note that, in the best conditions, subject matter experts consider the accuracy of manual analysis to be within a 40 \(\upmu\)m band. This suggests that the CSDI-based estimates are at least on par with manual analysis. To be sure, a further study and quantification of the delta between model-based estimates and manual analysis in the low range <100 \(\upmu\)m is required. Figure 5: The top plot shows peak amplitude time of flight data, and the three color-coded vertical bars mark the final datum of three increasingly large data sets; with sizes of 111,222, 219,438, and 435,369 elements. The second row plot shows the color-coded MAE error of CSDI model trained with 50% missing data ratio on the three datasets of increasingly large size. We use the VAE MSE threshold procedure to construct 28 unique partitions for each dataset size and train on each. In-the-field usage of DPM-based estimates would require some means for fault diagnosis without reference to ground truth. There are numerous avenues for engineering solutions that involve the use of agreement between multiple independent estimation techniques. One opportunity for a second estimation technique, currently being investigated, involves the use of a dynamic nominal partition that changes in response to a self-supervised signal provided during training. Though this may improve the robustness of results, without ground truth we see no opportunity to provide concrete guarantees on model performance. Given that this is the case, we think it likely that automation and decision support for UT NDE data analysis will necessarily involve a human in the loop, driving an iterative process of training, verification, and reclassification. So for instance, a practical procedure might assign a well chosen partition to a UT NDE dataset and train a model on it, and after sampling allow an analyst to verify the classification of data in regions where the sampled estimates vary, beyond some bound, from observed data. The analyst might then tweak the partition and retrain the model to achieve superior results. This process of training and directed manual reclassification would continue, until some quantifiable error objective was achieved; this process would almost surely force the nominal partition in the direction of ground truth and ensure satisfactory performance across the dataset. A number of opportunities exist for improving results. Figure 7 shows in detail the fit of CSDI estimates, as well as the support of \(\mathcal{X}_{0.95}^{n}\) on which the model was trained. What is clear is that the SGF fit on estimates overshoots the weight of the data in and around regions where its derivative is close to zero. This wig way could in part be due to the Gaussian prior distribution used by CSDI models, and could also in part be due to the nature of SGF curve fitting. A post-processing step that introduced weight to the SGF from  
Figure 6: The practical error in \(\upmu\)m of a CSDI model trained on the \(\mathcal{X}_{0.95}\) and \(\mathcal{X}_{0.70}\) partitioned datasets of size 435,369, as shown in Figure 5, for 5 epochs. For these results, CSDI estimates for \(t_{pq}\) are multiplied by the speed of sound in \(D_{2}O\) to arrive at the estimated nominal round-trip distance from the UT probe to the calibration fixture inner diameter.