Physics-Constrained Generative Artificial Intelligence for Rapid Takeoff Trajectory Design

TL;DR

This work tackles the high computational cost of designing rapid takeoff trajectories for eVTOL aircraft by introducing physicsGAN, a physics-constrained generative adversarial network augmented with surrogate models. The framework uses a twinGAN to parameterize realistic power and wing-angle trajectories, LSTM-based surrogates to predict time-series states, and a physicsGAN that transforms the original design space into a feasible, lower-dimensional space, ensuring all constraints are satisfied. In quantitative tests on the Airbus A³ Vahana, physicsGAN achieves about 99.6% optimization accuracy and 100% feasibility, with a dramatic 200× reduction in computation time to around 2.2 s, outperforming data-driven GAN-based approaches that struggle with feasibility or require longer runtimes. Overall, the method enables fast, robust, and feasible trajectory optimization, representing a novel integration of physics constraints into generative surrogate-based optimization for UAM applications.

Abstract

To aid urban air mobility (UAM), electric vertical takeoff and landing (eVTOL) aircraft are being targeted. Conventional multidisciplinary analysis and optimization (MDAO) can be expensive, while surrogate-based optimization can struggle with challenging physical constraints. This work proposes physics-constrained generative adversarial networks (physicsGAN), to intelligently parameterize the takeoff control profiles of an eVTOL aircraft and to transform the original design space to a feasible space. Specifically, the transformed feasible space refers to a space where all designs directly satisfy all design constraints. The physicsGAN-enabled surrogate-based takeoff trajectory design framework was demonstrated on the Airbus A3 Vahana. The physicsGAN generated only feasible control profiles of power and wing angle in the feasible space with around 98.9% of designs satisfying all constraints. The proposed design framework obtained 99.6% accuracy compared with simulation-based optimal design and took only 2.2 seconds, which reduced the computational time by around 200 times. Meanwhile, data-driven GAN-enabled surrogate-based optimization took 21.9 seconds using a derivative-free optimizer, which was around an order of magnitude slower than the proposed framework. Moreover, the data-driven GAN-based optimization using gradient-based optimizers could not consistently find the optimal design during random trials and got stuck in an infeasible region, which is problematic in real practice. Therefore, the proposed physicsGAN-based design framework outperformed data-driven GAN-based design to the extent of efficiency (2.2 seconds), optimality (99.6% accurate), and feasibility (100% feasible). According to the literature review, this is the first physics-constrained generative artificial intelligence enabled by surrogate models.

Figures (7)

• Figure 1: The original design requirement space (left) is represented by the cube. The cube's dimension is reduced to a realistic design requirement space (middle) by generating only realistic shapes, which can be achieved using the twinGAN model. The realistic space contains irregular feasible (tan) and infeasible (blue) regions. The physicsGAN delivers the feasible design requirement space (right) where all constraints are satisfied.
• Figure 2: The eVTOL model used in this work: (a) the Airbus $A^3$ Vahana eVTOL drone; (b) the model process diagram shows the flow of information through the simulation model. The simulation model (b) propagates the position ($X$) and velocity ($V$) by calculating the change for each time step. To do so, it calculates the lift and drag ($L$ and $D$), using the aerodynamics subsystem where $\alpha$ is the angle of attack, and the thrust and normal force ($T$ and $N$), using the propulsion subsystem, on the aircraft. The dynamics subsystem calculates the acceleration due to the forces acting on the aircraft and returns the change in position and velocity.
• Figure 3: The twinGAN model serves as an intelligent parametrization method for realistic power and wing angle trajectories. The separate generators ensure the trajectories are generated independently. The inputs to the generators are the random noise variables ($\mathbf{z}_t$) . The reference data ($\mathbf{x}$) are passed to the discriminator along with the generated power ($\mathbf{g_1}$) and wing angle ($\mathbf{g}_2$) control points. The predicted probabilities ($p_g$ and $p_x$) are used by the optimizer to update the network weights ($\mathbf{W}_{g_1}$, $\mathbf{W}_{g_2}$, and $\mathbf{W}_d$).
• Figure 4: The LSTM cell is differentiated from a neural network node by the internal memory state of the cell, as well as the gates which modify the memory of the cell. These adaptations allow LSTM cells to retain information from long time steps back, which aids their ability to predict time-series data.
• Figure 5: The inputs to the generators ($\mathbf{z}$, $\eta$, and $m$) are the random noise variables, efficiency, and mass. The predicted twinGAN noise variables ($\mathbf{z}_t$) are passed to the twinGAN generators to predict the generated power and wing angle control points. The reference data and labels ($\mathbf{x}$, $\eta$, and $m$) are passed to the discriminator along with the predicted flight time ($t$), generated power ($\mathbf{g}_1$), and wing angle ($\mathbf{g}_2$) control points. The penalty ($\lambda$) is based on the surrogate-predicted feasibility of the trajectory. The predicted probabilities ($p_g$ and $p_x$) are used by the optimizer to update the network weights ($\mathbf{W}_{g_{con}}$ and $\mathbf{W}_d$).