DeepONet for the stabilization of stochastic PDE-ODE systems

A Python implementation of a numerical solver for coupled Stochastic PDEs-ODEs with Markov chain mode switching. System parameters switch between multiple modes according to a continuous-time Markov chain with time-dependent transition rates. The solver implements a Neural Operator(NO)-based feedback control to stabilize the system.

The code reproduces the experiment in the paper K. Lyu, U. Biccari, J. Wang - Robust stabilization of hyperbolic PDE-ODE systems via Neural Operator-approximated gain kernels

Code Structure

The implementation follows a modular design with clear separation of concerns:

Core Components

• Kernel Estimator: Computes feedback gain functions for the control system
• Markov Chain Handler: Manages mode transitions and probability evolution
• PDE Solver: Implements finite difference schemes for the coupled system
• Visualization Suite: Creates comprehensive plots for analysis