Improving Flow-Function Learning by Means of Linear Approximation

Sammanfattning

Artificial neural networks have revolutionised the modelling of dynamic systems, offering a data-driven alternative to traditional differential equations. In this thesis, we study how to improve a state-of-the-art RNN-based architecture for learning flow functions of continuous-time control systems by integrating linearised system dynamics knowledge in the hypothesis space. The core problem addressed is whether embedding such prior knowledge can reduce the volume of required training data while improving prediction accuracy and training efficiency. This problem is significant in its complexity and impact. Learning models of high-dimensional nonlinear systems requires a large amount of data and computational resources. This project attempts to bridge the gap between theoretical modelling and practical implementation by combining data-driven learning with insights from linear system theory. To tackle the problem, we analyse in detail the RNN structure proposed in the baseline work. We then implemented a new architecture with a custom RNN cell which incorporates both hidden and system states. The cell update integrates the linearised dynamics, enabling the model to combine physics-informed and learned representations. The experimental results, validated on benchmark systems such as the Van der Pol oscillator, support our hypothesis. The modified architecture achieved comparable or improved accuracy using fewer training epochs, and outperformed the baseline architecture in test loss. These outcomes confirm that embedding approximate system knowledge within the network’s architecture enhances learning efficiency and generalisation. This work contributes to a hybrid modelling framework that can be extended to more complex dynamic systems.