Learning When and How to Filter: Reinforcement Learning for Convection-Dominated Flows
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Simulations of convection-dominated flows in under-resolved regimes often require numerical stabilization to improve accuracy and suppress spurious oscillations. A widely used strategy is the evolve–filter (EF) approach, in which the discretized Navier–Stokes equations are advanced in time in an evolve step, and a filtering step—typically based on an elliptic filter [1]—is applied to remove high-frequency components. The EF performance strongly depends on the choice of the filter radius δ, which controls the amount of numerical dissipation. Standard selections for δ, commonly linked to the grid size or to the Kolmogorov scale, may lead to overly diffusive solutions, especially in turbulent regimes. To address this issue, we consider a time-dependent filter radius δ(t) that is adaptively tuned during the simulation. Previous data-driven approaches optimize δ by minimizing the discrepancy between EF solutions and fully resolved reference data, but they rely heavily on high-fidelity data and lack predictive capabilities [2]. In this talk, we propose a reinforcement learning (RL) framework to learn the value of the filter radius. We investigate RL strategies based on both data-driven and data-free reward formulations. In the data-driven case, the agent is trained using reference data over a limited temporal window, corresponding to about the 25% of the global simulation. In the data-free setting, the reward is constructed from physically motivated indicators, including the residuals of the discretized equations and the time variation of the spatial velocity gradients, which quantify excessive diffusion and numerical noise. This enables the agent to make informed decisions without access to reference solutions. We demonstrate the effectiveness of the proposed RL-EF approach for marginally-resolved 2D simulations of the flow past a cylinder at Re=1000 and decaying homogeneous turbulence at Re=40000, achieving significantly improved accuracy compared to standard EF methods and a better representation of the flow dynamics. [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. International Journal for Numerical Methods in Engineering, (2025) 126(9), e70042.
