## 3 Results
### Predictions Aided via Machine Learning  
To evaluate the accuracy of each of the ML algorithms in the forecasting of the elastic displacements of CCAJs with LFHs, the error margins between predicted and simulated values were calculated. In Table 2, the predicted displacements are presented along with their respective error margins. Here, the ML algorithm with the lowest margin of error was the GPR, with a maximum error of 0.03% for one of the predictions. On the other hand, the  
Figure 14: Comparison between the higher and lower displacements obtained from the studied latticed compliant cross-axis joints with a force applied of 0.04905 N. (**a**) Latticed compliant cross-axis joint with re-entrant lattice-flexure hinges with the unit cell at 60° orientation. (**b**) Latticed compliant cross-axis joint with square lattice-flexure hinges with the unit cell at 0° orientation. Figure 13: Force-displacement curves from experimental, simulated, and ML predictions. (**a**) Stiffest responses from the compliant cross-axis joints with hexagonal lattice-flexure hinges. (**b**) Least stiff responses from the compliant cross-axis joints with hexagonal lattice-flexure hinges. (**c**) Stiffest responses from the compliant cross-axis joints with re-entrant lattice-flexure hinges. (**d**) Least stiff responses from the compliant cross-axis joints with re-entrant lattice-flexure hinges. (**e**) Stiffest responses from the compliant cross-axis joints with square lattice-flexure hinges. (**f**) Least stiff responses from the compliant cross-axis joints with square lattice-flexure hinges. worst ML algorithm was the SVM, with a maximum error of 86% for one of the predictions. This first attempt allowed us to evaluate how these ML algorithms might adapt to specific parameters and mechanical properties. The predictions obtained with each algorithm are compared with the experimental and FE data in Figure 13.  
The stiffness of each case tested as a function of the orientation of the lattice is presented in Figure 15. FEA and ML predictions are also included in Figure 15a-c for the hexagonal, re-entrant, and square topologies, respectively. This helped to analyze and compare each lattice CCAJ based on the lattice configuration implemented with its respective lattice orientation. In some cases, the displacement obtained was higher or lower depending on the type of lattice and its orientation. Variations in stiffness were more significant for the square lattice. This was due to the fact that the square lattice, when oriented at 0\({}^{\circ}\), was stretch-dominated. Once the orientation for the square lattice was changed, its deformation mechanism changed to bending-dominated. Having the same relative density, stretch-dominated cellular structures are stiffer than bending-dominated ones. Stiffness was predicted with the ML algorithms mentioned previously. As seen in Table 3, the predictions demonstrated behavior similar to the displacements from FE simulations presented in Figure 13. Yet again, the best ML algorithm was the GPR algorithm, with a maximum error of 0.12%, and the worst algorithm was the SVM, with a maximum error of 18.98% in one of the predictions. Finally, as seen in Figure 15, the data obtained were compared and analyzed for each one of the lattice orientations tested. \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline  & \multicolumn{6}{c}{**Displacement FEA and ML (mm)**} \\ \hline
**Lattice-Flexure** & \multirow{2}{*}{**ANN1**} & \multicolumn{2}{c}{**\%E**} & \multicolumn{2}{c}{**\%E**} & \multirow{2}{*}{**SVM**} & \multicolumn{2}{c}{**\%E**} & \multirow{2}{*}{**ANN2**} & \multicolumn{2}{c}{**\%E**} \\
**Hinges** & & **ANN1** & & & & **GPR** & & **SVM** & **ANN2** \\ \hline RH-5.5-0\({}^{\circ}\) & 0.5785 & 0.08\% & 0.579 & 0.00\% & 0.5766 & 0\% & 0.5793 & 0.05\% \\ RH-5.5-20\({}^{\circ}\)  
Figure 15: Stiffness as a function of the orientation angle, with data from experimental findings, simulation, and ML predictions. (**a**) Hexagonal lattice-flexure hinges. (**b**) Re-entrant lattice-flexure hinges.