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Most physical systems of interest are chaotic in nature. Quick and reasonably accurate solutions for these systems are essential to various fields such as the effective control mechanism construction and early-stage design. However, their chaotic nature also leads to them being computationally expensive to model using traditional numerical techniques. Reduced Order Modelling (ROM) is an umbrella term that describes any method wherein a system state is projected into a ‘simplified’ state space in order to extract meaningful information about its dominant components. Traditional ROMs whilst effective in capturing statistical information, tend to neglect smaller-energy components responsible for short-term dynamics. With the advances seen in data-driven approaches over the past decade, namely in machine learning (specifically deep learning), these methods seem to offer attractive alternatives to traditional ROM techniques and are the focus of this thesis. It is found that in existing literature there is no consensus on which ML models to use and no real extensive comparative studies either. Further, there is no unified approach to training the different RNN models, and only one surveyed study utilises an auto-regressive optimization strategy. This is a major pitfall, since the RNNs are only trained for single-step prediction but tested on multi-step prediction - a clear contradiction in the training and testing objectives. Additionally, no studies have been performed on true Runge-Kutta methods-inspired layering architectures, which show initial promise in increasing prediction horizons at little additional compute cost. As such, an extensive comparative study is performed, pitting long-short term memory networks, gated recurrent unit networks and echo state networks against each other. Further, the effect of RK-inspired layering is tested against a standard single-layer network. The effect of incorporating contractive losses in the auto-encoders is also investigat, Aerospace Engineering