Ground truth data was obtained by capturing the 3-D position of nine control points selected on the shape sensor surface, which were distributed evenly along its four edges, along with one located in the center. During the data capture, one corner control point was fixed in position and the remaining eight control points were each measured at 40 Hz with 5-DoF electromagnetic (EM) tracking markers (Aurora® V3, NDI) attached to the shape sensor surface (Figure. 2a), while the FBG strain data was simultaneously captured. All the data for model training was obtained in a single session of hands-on sensor deformation, which took  over 100 seconds and ~20 different ‘key-frame’ poses. The nine tracked control points were enriched to a grid of 11×7 positional nodes through FE-based data enrichment, and then used for the ensemble model output. The 29 strain-measuring FBGs were integrated into the shape sensor in a single optical fiber placed in a dog-bone layout (Figure. 2a), with center-to-center spacings of approximately 22 mm between FBGs. A total of 1,500 sets of FBG and node data were captured, with 1,000 used for training the learning model, 200 for model validation, and 300 for testing of reconstruction accuracy (described in the following section).  
Ensemble learning configuration parameters in terms of (i) the node density (total nodes in the A4 size) and (ii) the sub-model size (window size) were tested to evaluate their effect on prediction accuracy and processing time. As shown in Figure. 2b, three different node densities (i.e., 7×5, 11×7 and 21×13 nodes) and eight window sizes (ranging from 1/16 to 1 times the A4 size) were compared. As for a specified node density, smaller window sizes would result in more windows (sub-models) for prediction, thereby increasing the processing time but slightly reducing the prediction error. The denser the node on the A4, the longer the prediction time due to the increased number of sub-models as well as the higher output data size for each sub-model. To maintain a reasonably high update frequency at >100 Hz, we have to limit the processing time per time step <10 ms; therefore, 11×7 nodes with 24 sub-models (6×4 nodes) was selected for this A4-size surface model training, taking account of a trade-off among the FE-based nodes density, the learning-based prediction error and the sensing frequency.
The integration of FE-based data enrichment highly relaxes the amount of ground truth that needs to be captured in a data-driven approach, where position-tracked control points data were imported into the FE model as displacement constraints to generate a rich amount of surface nodes data offline. Although we utilized an EM-based tracking system for ground truth capturing, other tracking modalities can be used with this sensing framework, provided that they are capable of accurately measuring node data on the shape sensor surface even in the case of complex or overlapping deformation. For example, camera-based motion capture systems can be used to obtain the original node data and then become enriched via FE modeling, thus reducing the number of motion reflective markers needed.\cite{Rendl_2014,Saunders_2011,Dobrzynski_2011}
Simulated environment was used to evaluate the accuracy of the FE-enrichment method in comparison to two commonly used surface approximation methods (Figure. 3a), namely bilinear and non-linear interpolations. A virtual A4-sized sensor was placed on a reference cylinder object (with radius of R = 115 mm), which acted as the ground truth shape. Each method used the 9 tracked sensor nodes as inputs/query points and displacement errors were calculated against the cylinder ground truth. The FE-enrichment method demonstrated a maximum displacement error of 3.2 mm, which outperformed the piecewise bilinear interpolation method (max. error ~ 19.7 mm) and triangle-based nonlinear surface interpolation (max. error ~ 16.8 mm).\cite{Cuomo_2014}The performance of the FE-based data enrichment method can be attributed to its use of the real sensor’s geometric and material properties in the FE model.