Adaptive Filtering Strategies for Convection-Dominated flows through Reinforcement Learning
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Simulations of convection-dominated flows in under-resolved regimes often require numerical stabilization to improve accuracy and mitigate spurious oscillations. One of the possibilities is the evolve–filter (EF) approach, which consists of evolving the solution by solving discretized Navier-Stokes equations, and applying a filtering step (with an elliptic filter [1]) to remove high-frequency noise. The EF accuracy strongly depends on a parameter, the filter radius delta, which determines the filtering entity. A standard literature choice for delta is related either to the grid size or to the Kolmogorov n-width. However, both choices may result in over-diffusive solutions, especially in the case of laminar-to-turbulent transition. To overcome this issue, we introduce time-dependent parameters (delta(t)), which are adaptively optimized in a data-driven way, namely considering a fully-resolved simulation as reference [2]. A first approach, introduced in [2], performs the parameter optimization every k time steps, by minimizing the discrepancy of the optimized-EF solution with respect to the reference. Despite their effectiveness, the algorithms introduced in [2] rely entirely on expensive high-fidelity simulation data and lack predictive capabilities. To overcome this limitation, in this talk we propose the use of reinforcement learning (RL) techniques that learn the timing and extent of filtering. The filtering action is learned exclusively from reference data within a limited temporal window, allowing the model to make informed decisions without relying on the entire simulation history. These approaches exhibit strong predictive capabilities and robust generalizability. We will show the evidence of these techniques in the under-resolved simulation of a turbulent flow past a cylinder at Re=1000. The results obtained with our approach are significantly more accurate than standard EF techniques and better capture the underlying dynamics of the system. References: [1] Germano, M., Differential filters of elliptic type. The Physics of fluids, (1986) 29(6), 1757-1758. [2] Ivagnes, A., Strazzullo, M., Girfoglio, M., Iliescu, T., & Rozza, G., Data-driven Optimization for the Evolve-Filter-Relax regularization of convection-dominated flows. arXiv preprint arXiv:2501.03933, (2025), accepted for publication.