Fig. 7: Forecasting error analysis indicating that accurate forecasts are generated by the MH-HDMD algorithm.

a–c Spatial MAE across detector locations and its average across all detectors for the I-10, I-5, and Los Angeles network. The SMAE is evidently stable across different highways and networks of highways and is on average between 1 and 2 miles per hour. d–f Temporal MAE and its time average. Again, it is evident that our method is not only stable across differing highways and spatial scales but also stable across a wide range of time scales (days, week, month). g–i Normalized histograms of highway velocities for both true and forecasted data sets. The near-perfect matches for low and high speeds indicate that despite the unpredictability present in a highway system the statistics of our forecasts are nearly identical with the real physical system. A complete summary of the error analysis for all highways can be referenced in Supplementary Table 2.