Reinforcement Operator Learning (ROL): A hybrid DeepONet-guided reinforcement learning framework for stabilizing the Kuramoto-Sivashinsky equation.

In the final 20% of the simulation (steps 64–80), DeepONet RL’s SEM band shows minimal overlap with Pure TD3’s, suggesting statistical significance ( p < 0.05), while LQR’s complete separation indicates a highly significant gap ( p < 0.001). 4.2.2 Spatio-temporal state consistency.

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