Aerodynamic shape optimization of airfoils across rarefied to continuum regimes using deep reinforcement learning

Vehicles operating over wide altitude ranges, such as reusable spaceplanes and atmospheric reentry vehicles, face complex aerodynamic environments spanning from continuum to rarefied flow regimes. Conventional aerodynamic designs, typically optimized for a single regime, tend to struggle to maintain consistent performance across such a wide range of flow conditions. This challenge motivates the development of design frameworks capable of accommodating variable flow physics throughout the mission envelope. To this end, we propose CrossAero, a deep reinforcement learning-based framework for aerodynamic optimization that operates directly on a continuous design space of the Knudsen number (Kn), thus removing the need to manually select discrete design points. This capability is facilitated by introducing a probability density function of Kn, which encodes the relative importance of different flow conditions and can be tailored to mission requirements or operation time fractions. Leveraging deep reinforcement learning, CrossAero learns directly from the entire Kn distribution, effectively capturing cross-regime aerodynamic effects within a unified framework. The framework's capabilities are first demonstrated through two single-regime optimization tasks, thereby confirming its reliability under distinct aerodynamic conditions. Building upon this, CrossAero optimizes a fixed-geometry airfoil to maximize average performance over a prescribed Kn distribution, achieving a 5.9% drag reduction relative to the baseline airfoil. Finally, the third case trains a flow-conditioned airfoil generator capable of rapidly producing near-optimal designs for given Kn values without retraining, demonstrating the framework's efficiency in condition-adaptive design and its potential for application in morphing platforms. These results demonstrate CrossAero's robustness, efficiency, and adaptability for the cross-regime aerodynamic design.