## 3 Results  
### Evaluation of Predictive Models  
To select the most precise prediction model for the hysteresis and sensitivity of the sensing material, we analysed the correlation coefficients of the four models, as presented in Table 5. The optimal prediction model for the hysteresis of the sensing material is HKOA-LSTM, with three hidden layers with 80 neurones each, achieving an R\({}^{2}\) of 0.981. The HKOA-LSTM model, featuring three hidden layers and 70 neurones per layer, has the highest sensitivity prediction accuracy, with an R\({}^{2}\) value of 0.9803, indicating superior accuracy and generalisation relative to the other three models. The other three models exhibit superior accuracy and generality. Our study reveals that the sensing properties of nanocomposites exhibit complexity, influenced by the three filler contents and MT examined, which affect the hysteresis and sensitivity of the composite sensing materials. This complexity arises from factors such as the adhesion between the matrix and filler, the interaction among filler particles, the modulus of elasticity of the matrix, and the degree of dispersion of nanofillers. Furthermore, the proposed HKOA-LSTM prediction model demonstrates a strong adaptability to the intricacies of the data. Figure 7 depicts the correlation between the predicted and measured values of the hysteresis and sensitivity characteristics of the examined composite sensing materials. Ten simulations were conducted under identical optimal conditions to evaluate the reproducibility of the HKOA-LSTM model. The graphs demonstrate a strong correlation between the projected values and the observed data since the points are closely aligned with the diagonal line, indicating an excellent model fit. The slope of the graph, consistently approaching 1 in all instances, further substantiates this observation.  
To evaluate the precision of the HKOA-LSTM prediction model presented in this paper, the root mean square error (RMSE) and mean absolute error (MAE) of the four models were compared, with the results displayed in Table 6. The HKOA-LSTM model exhibits the lowest RMSE (0.0225) for hysteresis, signifying a superior predictive accuracy relative to that of the other models. Nonetheless, for MAE, the LSTM model exhibits a slightly lower value (0.0079), indicating that the average discrepancy between its projected and experimental values is reduced. The HKOA-LSTM model exhibits the lowest RMSE (0.1285) and MAE (0.0547) for sensitivity, signifying that its results align more with the experimental values. Regarding the hysteresis and sensitivity of the sensing material, the  
\begin{table}
\begin{tabular}{c l c c c c} \hline \hline  & **Determination Coefficient** & **RSM** & **RF** & **LSTM** & **HKOA-LSTM** \\ \hline Hysteresis & R\({}^{2}\) training & - & 1.0000 & 0.9987 & 1.0000 \\  & R\({}^{2}\) testing & 0.8961 & 0.8277 & 0.8864 & 0.9810 \\ Sensitivity & R\({}^{2}\) training & - & 0.9999 & 0.9968 & 1.0000 \\  & R\({}^{2}\) testing & 0.8955 & 0.8046 & 0.8440 & 0.9803 \\ \hline \hline \end{tabular}
\end{table}
Table 5: R\({}^{2}\) values for training and test datasets of various predictive models regarding hysteresis and sensitivity performance.  
HKOA-LSTM demonstrates superior data fitting and prediction outcomes relative to the other three predictive models.