Transfer-Learning-Enhanced Regression Generative Adversarial Networks for Optimal eVTOL Takeoff Trajectory Prediction

Electric vertical takeoff and landing (eVTOL) aircraft represent a crucial aviation technology to transform future transportation systems. The unique characteristics of eVTOL aircraft include reduced noise, low pollutant emission, efficient operating cost, and flexible maneuverability, which in the meantime pose critical challenges to advanced power retention techniques. Thus, optimal takeoff trajectory design is essential due to immense power demands during eVTOL takeoffs. Conventional design optimizations, however, adopt high-fidelity simulation models in an iterative manner resulting in a computationally intensive mechanism. In this work, we implement a surrogate-enabled inverse mapping optimization architecture, i.e., directly predicting optimal designs from design requirements (including flight conditions and design constraints). A trained inverse mapping surrogate performs real-time optimal eVTOL takeoff trajectory predictions with no need for running optimizations; however, one training sample requires one design optimization in this inverse mapping setup. The excessive training cost of inverse mapping and the characteristics of optimal eVTOL takeoff trajectories necessitate the development of the regression generative adversarial network (regGAN) surrogate. We propose to further enhance regGAN predictive performance through the transfer learning (TL) technique, creating a scheme termed regGAN-TL. In particular, the proposed regGAN-TL scheme leverages the generative adversarial network (GAN) architecture consisting of a generator network and a discriminator network, with a combined loss of the mean squared error (MSE) and binary cross-entropy (BC) losses, for regression tasks. In this work, the generator employs design requirements as input and produces optimal takeoff trajectory profiles, while the discriminator differentiates the generated profiles and real optimal profiles in the training set. The combined loss facilitates the generator training in the dual aspects: the MSE loss targets minimum differences between generated profiles and training counterparts, while the BC loss drives the generated profiles to share analogous patterns with the training set. We demonstrated the utility of regGAN-TL on optimal takeoff trajectory designs for the Airbus A3 Vahana and compared its performance against representative surrogates, including the multi-output Gaussian process, the conditional GAN, and the vanilla regGAN. Results showed that regGAN-TL reached the 99.5% generalization accuracy threshold with only 200 training samples while the best reference surrogate required 400 samples. The 50% reduction in training expense and reduced standard deviations of generalization accuracy achieved by regGAN-TL confirmed its outstanding predictive performance and broad engineering application potential.