Electric vertical takeoff and landing (eVTOL) aircraft have attracted tremendous attention nowadays due to their flexible maneuverability, precise control, cost efficiency, and low noise. The optimal takeoff trajectory design is a key component of cost-effective and passenger-friendly eVTOL systems. However, conventional design optimization is typically computationally prohibitive due to the adoption of high-fidelity simulation models in an iterative manner. Machine learning (ML) allows rapid decision making; however, new ML surrogate modeling architectures and strategies are still desired to address large-scale problems. Therefore, we showcase a novel regression generative adversarial network (regGAN) surrogate for fast interactive optimal takeoff trajectory predictions of eVTOL aircraft. The regGAN leverages generative adversarial network architectures for regression tasks with a combined loss function of a mean squared error (MSE) loss and an adversarial binary cross-entropy (BC) loss. Moreover, we introduce a surrogate-based inverse mapping concept into eVTOL optimal trajectory designs for the first time. In particular, an inverse-mapping surrogate takes design requirements (including design constraints and flight condition parameters) as input and directly predicts optimal trajectory designs, with no need to run design optimizations once trained. We demonstrated the regGAN on optimal takeoff trajectory designs for the Airbus (Formula presented.) Vahana. The results revealed that regGAN outperformed reference surrogate strategies, including multi-output Gaussian processes and conditional generative adversarial network surrogates, by matching simulation-based ground truth with 99.6% relative testing accuracy using 1000 training samples. A parametric study showed that a regGAN surrogate with an MSE weight of one and a BC weight of 0.01 consistently achieved over 99.5% accuracy (denoting negligible predictive errors) using 400 training samples, while other regGAN models require at least 800 samples.


Mechanical and Aerospace Engineering

Publication Status

Open Access

Keywords and Phrases

eVTOL; generative adversarial networks; inverse mapping; machine learning; optimal takeoff trajectory design; regGAN; surrogate modeling

International Standard Serial Number (ISSN)


Document Type

Article - Journal

Document Version

Final Version

File Type





© 2024 The Authors, All rights reserved.

Creative Commons Licensing

Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 License.

Publication Date

01 Jan 2024