Adaptive ODE Solver Selection for Combustion Simulations Using Reinforcement Learning

Computational fluid dynamics (CFD) simulations of combustion processes employ operator-splitting schemes separating chemistry and transport calculations. The chemistry component, involving stiff ordinary differential equations (ODEs), represents a significant computational bottleneck. Traditional approaches use a single ODE solver throughout simulation, which may not be optimal across diverse thermochemical states in multi-dimensional combustion simulations. This work presents a novel reinforcement learning (RL) framework for dynamic ODE solver selection in combustion simulations, optimizing computational efficiency and solution accuracy. The framework employs Proximal Policy Optimization (PPO) trained on a custom Open AI Gymnasium environment integrated with Cantera for chemical kinetics. The state space includes temperature, species mass fractions, and gradients, while the action space comprises various ODE solvers (RK23, Adams, BDF) with different tolerance settings. Initial investigations using methane-oxygen combustion (54 species) demonstrate adaptive selection between explicit and implicit solvers based on local solution characteristics. The RL agent balances computational cost against accuracy through a reward function incorporating integration time and solution error metrics. Results show robust performance across combustion regimes, particularly during pre-ignition, ignition, and post-ignition phase transitions. Comparative analyses against single-solver approaches demonstrate computational speedup while maintaining accuracy within specified tolerances. The framework identifies optimal solver transitions during critical phenomena like ignition events. The methodology shows promise for multi-dimensional reactive flow simulations, where different domain regions benefit from different integration strategies based on local conditions. This spatially adaptive approach enables significant computational savings while maintaining solution accuracy, with broader implications for improving detailed chemistry calculations in practical combustion systems.