Author Correction: Reinforcement learning-based estimation for spatio-temporal systems
Saviz Mowlavi, Mouhacine Benosman · Scientific Reports · 2025
The original version of this Article contained errors in the Figures. Figure 4 was published as Figure 3 and Figure 3 was published as Figure 4. The Figure legends were correct at the time of publication. Fig. 3 Flow past a cylinder. ( a ) Normalized L 2 error of the RL-ROE and KF-ROE state estimates for values of Re not seen during training, using p = 3 sensors. ( b ) Ground-truth velocity magnitude at t = 50 for values of Re not seen during training and corresponding RL-ROE and KF-ROE estimates using p = 3 sensors. The black crosses in the contours of the reference solutions indicate the sensor locations. ( c ) Left: Normalized L 2 error, averaged over time, versus μ when using p = 3 sensors. Values of μ belonging to the training set S are shown by large circles while the testing values are displayed by small circles. Right: Normalized L 2 error, averaged over time and over the testing values of Re , versus number of sensors p . In ( a ) and ( c ) the error metrics are averaged over 5 trajectories with randomly-sampled initial true states z 0 , and the shaded areas denote the standard deviation. Full size image Fig. 4 Chaotic vorticity flow. ( a ) Normalized L 2 error of the RL-ROE and KF-ROE state estimates for trajectories not seen during training, using p = 3 sensors. ( b ) Ground-truth velocity magnitude at t = 15 for trajectories not seen during training and corresponding RL-ROE and KF-ROE estimates using p = 3 sensors. The black crosses in the contours of the ground truth plots indicate the sensor locations. ( c ) Left: Normalized L 2 error, averaged over time, versus trajectory number when using p = 3 sensors. Trajectories belonging to the training set S are shown by large circles while the testing trajectories are displayed by small circles. Right: Normalized L 2 error, averaged over time and over testing trajectories, versus number of sensors p . In ( a ) and ( c ) the error metrics are averaged over 5 randomly-sampled initial true states z 0 along each trajectory, and the shaded areas denote the standard deviation. Full size image