A deep reinforcement learning framework for dynamic optimization of numerical schemes for compressible flow simulations

Marginal or under-resolved simulations of compressible flow configurations that often occur in practical applications classically are enabled by administering sufficient numerical dissipation to keep the simulation stable. Such measures, however, often are physically inconsistent due to non-selectively altering of dynamics across scales. Sustaining physically consistent large scale dynamics requires the numerical solution to effectively model non-resolved small scale dynamics. In this work, we propose a general deep-reinforcement-learning framework for devising an agent to interact with high-resolution scheme in order to balance dissipation and dispersion such that physically consistent modeling of non-resolved scales is achieved. A densely distributed reward function without involving labeled data is defined. The agent is trained on low-resolution uniform grids that capture the dominant flow structures. We demonstrate that it can be applied directly to high-resolution simulations without the need for retraining or fine-tuning, thereby, demonstrating significantly improved modeling performance compared to empirically designed high-resolution schemes. The proposed methodology opens a new path for self-adaptive numerical solutions whose truncation errors act as physically consistent model for unresolved scales of widely differing flow configurations.