In this thesis, we introduce a novel framework specifically designed for generating data tailored to the relevant machine learning tasks, applicable to regular 1-d cellular automata, cellular automata with anticipation, and cellular automata with memory. This framework serves as the starting point for the investigations and analyses presented herein.

Due to their inherent locality, cellular automata necessitate an alternative approach to conventional physics-informed dynamical systems. In an effort to bridge the conceptual gap between machine-learning and dynamical system theory, a theoretical foundation for these topics is established. This groundwork aids in analyzing how these types of cellular automata integrate into the wider scope of both domains and facilitates novel means of learning.

A convolutional neural network variant is proposed and demonstrated, capable of accurately learning both the one-step anticipatory and n-step historic cellular automata, paving the way for new applications, particularly in the fields where temporal dynamics play a crucial role. The trained networks’ activation patterns are analyzed, and their performance is compared to Decision Trees, Random Forest, and XGBoost alternatives.