Abdolbaghi Malihe, Tabatabaei Seyed Amir Hossein, Keyanpour Mohammad
Department of Applied Mathematics, Faculty of Mathematical Sciences, University of Guilan, Rasht, Iran.
Department of Computer Science, Faculty of Mathematical Sciences, University of Guilan, Rasht, Iran.
Sci Rep. 2025 Aug 12;15(1):29479. doi: 10.1038/s41598-025-14090-0.
This paper presents a novel data-driven framework for designing observers and controllers in coupled ODE-PDE systems of reaction-diffusion type. Leveraging the DeepONet architecture as a neural operator, the method directly approximates nonlinear mappings between function spaces, eliminating the need for analytical solutions of kernel equations. The observer is first constructed to estimate the system states, followed by the design of the controller based on the estimated states. Simulation results, validated against exact solutions of Goursat equations and evaluated through metrics such as convergence rate, estimation error, and control effort, demonstrate the high accuracy and computational efficiency of the proposed approach. Finally, an ablation study was conducted as well to evaluate the building blocks of the proposed method.
本文提出了一种新颖的数据驱动框架，用于设计反应扩散型常微分方程-偏微分方程（ODE-PDE）耦合系统中的观测器和控制器。该方法利用深度算子网络（DeepONet）架构作为神经算子，直接逼近函数空间之间的非线性映射，无需核方程的解析解。首先构建观测器来估计系统状态，然后基于估计状态设计控制器。通过与古尔萨方程的精确解进行对比验证，并通过收敛速度、估计误差和控制量等指标进行评估的仿真结果表明，该方法具有很高的精度和计算效率。最后，还进行了对比研究以评估所提方法的各个组成部分。
