Adaptive time step control using reinforcement learning for stiff chemical kinetic systems

This work focuses on identifying an adaptive time step size for the integration of stiff chemistry ordinary differential equations (ODEs) encountered in reactive flow simulations. Identifying the right time step size in high-fidelity numerical simulations is an expensive task, which requires eigen-decomposition of the chemical Jacobian to identify the smallest timescales. An incorrect specification of time step size results in numerical instability and eventually leads to a blowup of the ODE integrator. To tackle these challenges, backward difference ODE integrators have been developed, which rely on a trial-and-error or predetermined criterion-based time-step control process. This study employs machine learning techniques for time step size control in explicit integration methods for stiff chemical systems. The proposed approach involves a model-based Reinforcement Learning (RL) algorithm to learn an optimized policy for time step control in an explicit ODE integrator. The RL agent's primary goal is to minimize interactions with the environment while maintaining near-optimal performance through efficient time step size control. The effectiveness of this method is evaluated through tests involving a constant pressure batch reactor with H₂-air mixture and contrasted with time step size control algorithms used for integrating the system with stiff chemical kinetics. The results highlight the potential of the RL-based time step size control technique to enhance the performance of explicit integration methods in the realm of chemical kinetics and reacting flow simulations.