This study explores the integration of machine learning with space mapping techniques to enhance the mapping of optimal control sequences between low- and high-fidelity flight mechanic models. Space mapping is a methodology that simplifies the control optimisation process by approximating a high-fidelity model using less computationally demanding low-fidelity models, which are then iteratively corrected to converge towards high-fidelity outputs. The main research question investigates how the integration of space mapping with sequence-to-sequence neural networks can improve control sequence mapping compared to traditional model predictive control (MPC) methods, particularly in managing the trajectory differences in non-linear flight regimes.

In the pursuit of sustainable aviation, with a sharp focus on reducing emissions through innovative designs and enhanced flight mechanics, the computational cost of high-fidelity models becomes a significant limitation. These models, crucial for capturing complex interactions in advanced aircraft designs, often require simplification to reduce computational demands. This research proposes a novel approach by combining the strengths of machine learning, particularly sequence-to-sequence neural networks like Gated Recurrent Units (GRUs) and transformers, with space mapping techniques to bridge the gap between low- and high-fidelity models effectively.

The study delves into two main machine learning architectures: GRUs and transformers. GRUs excel in managing sequences with fewer changes, maintaining stable predictions with minimal error. Transformers on the other hand are well suited at handling complex sequences with frequent changes, thanks to their ability to process entire sequences simultaneously through self-attention mechanisms. This capability makes transformers particularly suitable for dynamic scenarios where anticipating future states is crucial.

A significant contribution of this study is the implementation of the Prior Knowledge Input-Difference (PKI-D) architecture, which uses the low-fidelity model output as a baseline that the neural network corrects, providing a robust framework for the machine learning models to accurately predict trajectory adjustments. This architecture not only enhances the predictive accuracy but also optimises computational efficiency by reducing the dependency on extensive high-fidelity simulations.

Comparative analyses reveal that MPC methods typically provides superior mapping performance for trajectories requiring no anticipation, while the hybrid machine learning-space mapping approach offers improved performance comparably or better in complex scenarios requiring advanced anticipation. This study highlights the critical role of active learning in adapting the machine learning models to new data dynamically, a feature that proves essential in maintaining accuracy over prolonged operational periods.

In conclusion, this research demonstrates that integrating space mapping with machine learning can significantly enhance the mapping of control sequences in aerospace applications. It provides a starting point for future studies to explore tailor made machine learning solutions using extremely small data sets in situations where data availability is sparse. This research could further open up avenues where the advanced capabilities of machine learning can be applied to problems in aerospace engineering previously inaccessible.