mlsanityData to 14 Oct 2026

Soft Actor-Critic with Backstepping-Pretrained DeepONet for control of PDEs

arXiv 2507.04232 ↗First posted 6 Jul 2025math.OCcited by 0

On the map: Deep reinforcement learning methods → RL theory and sample complexity

Abstract (arXiv)

This paper develops a reinforcement learning-based controller for the stabilization of partial differential equation (PDE) systems. Within the soft actor-critic (SAC) framework, we embed a DeepONet, a well-known neural operator (NO), which is pretrained using the backstepping controller. The pretrained DeepONet captures the essential features of the backstepping controller and serves as a feature extractor, replacing the convolutional neural networks (CNNs) layers in the original actor and critic networks, and directly connects to the fully connected layers of the SAC architecture. We apply this novel backstepping and reinforcement learning integrated method to stabilize an unstable ffrst-order hyperbolic PDE and an unstable reactiondiffusion PDE. Simulation results demonstrate that the proposed method outperforms the standard SAC, SAC with an untrained DeepONet, and the backstepping controller on both systems.

Key facts. No citing papers in the map yet (data through 14 Oct 2026). Placed in RL theory and sample complexity, one of 15 directions in Deep reinforcement learning methods. Builds on 14 of its 20 references that are in the map. First posted on arXiv 6 Jul 2025.

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14 of 20 references.

Closest ancestors · 2

Same direction, newest first

  1. 2024Stochastic Reinforcement Learning with Stability Guarantees for Control of Unknown Nonlinear Systems12 Sep
  2. 2024PDE Control Gym: A Benchmark for Data-Driven Boundary Control of Partial Differential Equations18 May

Other references · 12

  1. 2019DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operatorscited by 2,018
  2. 2017Safe Model-based Reinforcement Learning with Stability Guaranteescited by 366
  3. 2022LyaNet: A Lyapunov Framework for Training Neural ODEscited by 44
  4. 2023Neural Operators for Bypassing Gain and Control Computations in PDE Backsteppingcited by 29
  5. 2023Neural Operators of Backstepping Controller and Observer Gain Functions for Reaction-Diffusion PDEscited by 18
  6. 2023Neural Operators for PDE Backstepping Control of First-Order Hyperbolic PIDE with Recycle and Delaycited by 13
  7. 2024Control-Informed Reinforcement Learning for Chemical Processescited by 9
  8. 2023Deep Learning of Delay-Compensated Backstepping for Reaction-Diffusion PDEscited by 8
  9. 2024Adaptive Neural-Operator Backstepping Control of a Benchmark Hyperbolic PDEcited by 8
  10. 2023Online identification and control of PDEs via Reinforcement Learning methodscited by 5
  11. 2024Adaptive control of reaction-diffusion PDEs via neural operator-approximated gain kernelscited by 5
  12. 2024Neural Operator Feedback for a First-Order PIDE with Spatially-Varying State Delaycited by 2

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  8. 2026CINOC: Cardinality-Invariant Neural Operator Policies for Scalable PDE Control ↗