A.1 Initial Value Problem518 We use the datasets from Pfaff et al. (2021), and take the first and last frames of each trajectory as the519 input and output data for the initial value problem.520 Cylinder The dataset includes computational fluid dynamics (CFD) simulations of the flow around521 a cylinder, governed by the incompressible Navier-Stokes equation. These simulations were generated522 using COMSOL software, employing an irregular 2D-triangular mesh. The trajectory consists of 600523 timestamps, with a time interval of t =0 .01s between each timestamp.524 Airfoil The dataset contains CFD simulations of the flow around an airfoil, following the com-525 pressible Navier-Stokes equation. These simulations were conducted using SU2 software, using an526 irregular 2D-triangular mesh. The trajectory encompasses 600 timestamps, with a time interval of527 t =0 .008s between each timestamp.528 A.2 Dynamics Modeling529 2D-Navier-Stokes (Navier-Stokes) We consider the 2DNavier-Stokes equation as presented in Li530 et al. (2021); Yin et al. (2022).

We have provided baseline models, comprehensive experimental observations, and analysis to accelerate future research.

Effective airfoil geometry optimization requires exploring a diverse range of designs using as few design variables as possible. This study introduces AirDbM, a Design-by-Morphing (DbM) approach specialized for airfoil optimization that systematically reduces design-space dimensionality. AirDbM selects an optimal set of 12 baseline airfoils from the UIUC airfoil database, which contains over 1,600 shapes, by sequentially adding the baseline that most increases the design capacity. With these baselines, AirDbM reconstructs 99 % of the database with a mean absolute error below 0.005, which matches the performance of a previous DbM approach that used more baselines. In multi-objective aerodynamic optimization, AirDbM demonstrates rapid convergence and achieves a Pareto front with a greater hypervolume than that of the previous larger-baseline study, where new Pareto-optimal solutions are discovered with enhanced lift-to-drag ratios at moderate stall tolerances. Furthermore, AirDbM demonstrates outstanding adaptability for reinforcement learning (RL) agents in generating airfoil geometry when compared to conventional airfoil parameterization methods, implying the broader potential of DbM in machine learning-driven design.

This work is open-source under Open Data Commons Open Database License v1.0.

Surrogate models are necessary to optimize meaningful quantities in physical dynamics as their recursive numerical resolutions are often prohibitively expensive. It is mainly the case for fluid dynamics and the resolution of Navier-Stokes equations. However, despite the fast-growing field of data-driven models for physical systems, reference datasets representing real-world phenomena are lacking.

The main objective of this paper is to introduce a transfer learning-enhanced deep reinforcement learning (DRL) methodology that is able to optimise the geometry of any airfoil based on concomitant aerodynamic and structural integrity criteria. To showcase the method, we aim to maximise the lift-to-drag ratio $C_L/C_D$ while preserving the structural integrity of the airfoil -- as modelled by its maximum thickness -- and train the DRL agent using a list of different transfer learning (TL) strategies. The performance of the DRL agent is compared with Particle Swarm Optimisation (PSO), a traditional gradient-free optimisation method. Results indicate that DRL agents are able to perform purely aerodynamic and hybrid aerodynamic/structural shape optimisation, that the DRL approach outperforms PSO in terms of computational efficiency and aerodynamic improvement, and that the TL-enhanced DRL agent achieves performance comparable to the DRL one, while further saving substantial computational resources.