## 4 Results and Experimental Evaluation
### Stochastic Property Validation  
Table 4 presents the detailed statistical properties comparison between ground truth and predictions for different sampling rates. The analysis reveals that our model maintains excellent distributional fidelity across all sampling rates, with JS divergences ranging from 0.140697 to 0.231409, indicating very close distributional alignment. Notably, the model shows improving performance in capturing distributional properties as sampling rate decreases, with JS divergence improving from 0.231409 at SR = 1 to 0.140697 at SR = 4.  
Table 5 provides a comprehensive performance comparison including both accuracy and uncertainty metrics across all sampling rates.  
The detailed performance analysis reveals that our StochasticTrajectory model achieves the best accuracy for dense sampling conditions (SR = 1 and SR = 2) while maintaining superior uncertainty quantification across all conditions. At SR = 1, our model achieves MSE of 0.0000678, outperforming all baselines while providing substantial uncertainty benefits. At SR = 2, our model again achieves the best performance with MSE of 0.000849. For the most challenging sparse sampling condition (SR = 4), while GRU achieves slightly better point accuracy (0.0177 vs. our 0.0218), our method provides significantly better calibrated  
\begin{table}
\begin{tabular}{l c c c c c c c} \hline \hline \multirow{2}{*}{**Sampling Rate**} & \multicolumn{2}{c}{**Mean**} & \multicolumn{2}{c}{**Std. Dev.**} & \multicolumn{2}{c}{**Variance**} & \multirow{2}{*}{**JS Divergence**} \\ \cline{2-2} \cline{5-7}  & **Ground Truth** & **Prediction** & **Ground Truth** & **Prediction** & **Ground Truth** & **Prediction** & **JS Divergence** \\ \hline SR = 1 & 0.4838 & 0.4857 & 0.4087 & 0.4090 & 0.1670 & 0.1672 & 0.2314 \\ SR = 2 & 0.5612 & 0.5598 & 1.3637 & 1.3573 & 1.8596 & 1.8421 & 0.1634 \\ SR = 4 & 0.3576 & 0.3353 & 1.4065 & 1.3869 & 1.9783 & 1.9235 & 0.1407 \\ \hline \hline \end{tabular}
\end{table}
Table 4: Statistical properties comparison: ground truth vs. StochasticTrajectory predictions.  
\begin{table}
\begin{tabular}{l c} \hline \hline \multicolumn{2}{c}{**Sampling Rate = 1**} \\ \hline \hline \multicolumn{2}{c}{**Model Variant**} & \multicolumn{2}{c}{**Test MSE**} \\ \hline Full Model & 0.0000678 \\ Deterministic & 0.000118 \\ Small Latent Space & 0.000391 \\ w/o Weather Attention & 0.000482 \\ w/o Lyapunov & 0.000494 \\ Small Hidden Size & 0.000636 \\ \hline \hline \multicolumn{2}{c}{**Sampling Rate = 2**} \\ \hline \hline \multicolumn{2}{c}{**Model Variant**} & \multicolumn{2}{c}{**Test MSE**} \\ \hline Full Model & 0.000849 \\ Deterministic & 0.001323 \\ w/o Lyapunov & 0.007042 \\ Small Latent Space & 0.008853 \\ w/o Weather Attention & 0.009302 \\ Small Hidden Size & 0.010158 \\ \hline \hline \multicolumn{2}{c}{**Sampling Rate = 4**} \\ \hline \hline \multicolumn{2}{c}{**Model Variant**} & \multicolumn{2}{c}{**Test MSE**} \\ \hline Deterministic & 0.0133 \\ Full Model & 0.0218 \\ Small Hidden Size & 0.0525 \\ w/o Lyapunov & 0.0544 \\ Small Latent Space & 0.0569 \\ w/o Weather Attention & 0.0588 \\ \hline \hline \end{tabular}
\end{table}
Table 3: Ablation study results across different sampling rates.  
uncertainty estimates with 95% coverage of 0.982 compared to GRU's 0.554, demonstrating the critical importance of proper uncertainty quantification in safety-critical applications.