Physics-constrained generative adversarial networks for rapid optimal takeoff trajectory designs

Abstract Electric vertical takeoff and landing (eVTOL) aircraft play an essential role in urban air mobility but suffer from excessive energy consumption, especially during the takeoff phase. Multidisciplinary analysis and optimization (MDAO) minimizes the energy consumption but is computationally expensive, while surrogates enable efficient MDAO at a potentially excessive training cost. Moreover, complex nonlinear design constraints (especially in practical applications) hinder MDAO search and convergence. To tackle the above challenges, this work proposes the physics-constrained generative adversarial networks (physicsGAN) to transform an original design space to a reduced, feasible space where all design constraints are inherently satisfied. Thus, unconstrained optimization can be conducted to handle the original constrained problem at reduced complexity and enhanced efficiency. To construct physicsGAN, this work first leverages data-driven generative adversarial networks (GAN) to generate only realistic control profiles and reduce the original design space to lower dimensions, which facilitate surrogate modeling. Then, the training loss of physicsGAN is penalized if any design constraints are violated according to surrogate predictions. This work demonstrates the physicsGAN-enabled surrogate-based optimizations on the Airbus A³ A 3 Vahana aircraft. Results present that physicsGAN reduces the original design space from 41 to 3 dimensions while maintaining over 99% variability and achieves over 98% feasibility coverage within the whole flight condition space. The physicsGAN-enabled approach achieves over 93% accuracy compared with the simulation-based optimal references. Besides, the physicsGAN-enabled approach reduces the total optimization time by around three and over two orders of magnitude compared with the simulation-based references and data-driven-GAN-enabled counterparts, respectively.