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

Nadim Ahmed1, Md Ashraful Babu1, Muhammad Sajjad Hossain2

  • 1Department of Physical Sciences, Independent University, Bangladesh, Dhaka, Bangladesh.

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Summary
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Reinforcement Operator Learning (ROL), a hybrid control method, significantly stabilizes chaotic systems. This approach combines Deep Operator Networks and Twin-Delayed Deep Deterministic Policy Gradient for superior performance and efficiency.

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Area of Science:

  • Control Theory
  • Machine Learning
  • Applied Mathematics

Background:

  • Complex systems often exhibit chaotic behavior, making them difficult to control.
  • Traditional control methods struggle with high-dimensional, non-linear dynamics.

Purpose of the Study:

  • To introduce Reinforcement Operator Learning (ROL), a novel hybrid control paradigm.
  • To demonstrate ROL's effectiveness in stabilizing spatio-temporal chaos using the Kuramoto-Sivashinsky equation.

Main Methods:

  • ROL integrates Deep Operator Networks (DeepONet) for offline control law acquisition.
  • A Twin-Delayed Deep Deterministic Policy Gradient (TD3) residual is used for online adaptation.
  • The framework is tested on the 1D Kuramoto-Sivashinsky equation, a benchmark for spatio-temporal chaos.

Main Results:

  • ROL reduced system energy by 99.1% compared to LQR and 64.3% vs. pure TD3.
  • DeepONet achieved a low training loss (7.8 × 10-6) in 200 epochs.
  • ROL restricted state amplitudes threefold tighter than TD3 and stabilized chaos faster.

Conclusions:

  • Combining operator learning with residual policy optimization offers state-of-the-art control.
  • ROL provides a sample-efficient method for stabilizing chaotic partial differential equations.
  • This approach is scalable for applications like turbulence suppression and combustion control.