A reinforcement learning approach to airfoil shape optimization
Dimitri N. Mavris2023, Scientific Reports
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Abstract
Shape optimization is an indispensable step in any aerodynamic design. However, the inherent complexity and non-linearity associated with fluid mechanics as well as the high-dimensional design space intrinsic to such problems make airfoil shape optimization a challenging task. Current approaches relying on gradient-based or gradient-free optimizers are data-inefficient in that they do not leverage accumulated knowledge, and are computationally expensive when integrating Computational Fluid Dynamics (CFD) simulation tools. Supervised learning approaches have addressed these limitations but are constrained by user-provided data. Reinforcement learning (RL) provides a data-driven approach bearing generative capabilities. We formulate the airfoil design as a Markov decision process (MDP) and investigate a Deep Reinforcement Learning (DRL) approach to airfoil shape optimization. A custom RL environment is developed allowing the agent to successively modify the shape of an initially provided 2D airfoil and to observe the associated changes in aerodynamic metrics such as lift-to-drag (L/D), lift coefficient (C l ) and drag coefficient (C d ). The learning abilities of the DRL agent are demonstrated through various experiments in which the agent's objectivemaximizing L/D, maximizing C l or minimizing C d -as well as the initial airfoil shape are varied. Results show that the DRL agent is able to generate high performing airfoils within a limited number of learning iterations. The strong resemblance between the artificially produced shapes and those found in the literature highlights the rationality of the decision-making policy learned by the agent. Overall, the presented approach demonstrates the relevance of DRL to airfoil shape optimization and brings forward a successful application of DRL to a physics-based aerodynamics problem. As demand for air travel continues to grow, so are concerns regarding the environmental impacts of aviation. For aircraft, aerodynamic drag represents the main source of energy losses 1 . As such, its reduction could represent a 20 to 25% decrease in fuel burn 2 and lead to fewer emissions. An optimization process leading to an increase in the aerodynamic efficiency of aircraft components is needed. Here, we focus on the optimization of airfoil shapes. Relying on fluid mechanics, aerodynamic related problems exhibit non-linearity and are complex in nature 1,3 . Specifically, the problem at hand involves generating airfoils that achieve a desired performance. Formally, airfoil inverse design is described as the prediction of airfoil shapes based on given desired performance metrics 4 , making our problem an inverse design problem. Solving inverse problems is generally more difficult due to the non-injective nature of the physical phenomena 3 . In simpler terms, for a given desired performance, multiple shapes can exist 5 . Since there is a potentially infinite number of airfoil shapes, the problem is characterized by high-dimensionality. All together, airfoil shape optimization is a challenging task . In exploring the associated high-dimensional design space, current approaches iteratively evaluate the performance of a large number of airfoils through either physical testing (wind tunnel testing) or numerical simulations (Computational Fluid Dynamics or CFD). With numerical simulations, a gradient-based or gradient-free optimizer is used to guide the search towards the optimal shape. However, these approaches are limited due to the high dimension of the design space to be explored as well as the prohibitive computational cost of running a large number of high-fidelity aerodynamic simulations 9 . Moreover, both gradient-based and gradient-free approaches are data-inefficient since they do not utilize the knowledge gained from previous experiments 3 . To cope with this, supervised machine learning approaches to computational aerodynamic problems have been developed and have proven successful in addressing these limitations . In particular, a data-driven approach to the problem at hand could help alleviate the high complexity associated with the underlying physics 10 . However, since these methods rely on provided
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