Discovering optimal flapping wing kinematics using active deep learning

This paper focuses on the discovery of optimal flapping wing kinematics using a deep learning surrogate model for unsteady aerodynamics and multi-objective optimisation. First, a surrogate model of the unsteady forces experienced by a 3-D flapping wing is built, based on deep neural networks. The model is trained on a dataset of randomly generated kinematics simulated using direct numerical simulation (DNS). Once trained, the neural networks can quickly predict the unsteady lift and torques experienced by the wing, using sparse information on the kinematics. This fast surrogate model allows multi-objective optimisation to be performed. The resulting Pareto front consists of new kinematics that may be very different from the kinematics of the initial dataset. A few arbitrarily chosen kinematics on the Pareto front are thus simulated using DNS and used to enhance the database. The new dataset is used to train again the networks, and this active deep learning/optimisation framework is performed until convergence, obtained after only two iterations. Overall, this method reduced the cost of optimisation by 83 %. Results reveal two distinct families of motions. Kinematics promoting high efficiency are characterised by large stroke amplitudes and relatively low angles of attack, as observed for fruit flies, honeybees or hawkmoths. For those, lift production is driven by quasi-steady effects and the formation of a stable leading edge vortex. Kinematics promoting high lift are characterised by small stroke amplitudes and high angles of attack, reminiscent of mosquitoes. Lift production is driven by the rapid generation of vorticity at the trailing edge.