Understanding the dynamical system governing neuronal activity is crucial for unraveling how the brain performs cognitive functions. Historically, various forms of recurrent neural networks (RNNs) have been suggested as simplified models of the cortex. Recently, owing to remarkable advancements in the field of machine learning, RNNs' inherent ability to capture temporal dependencies has been leveraged to develop tools for approximating unknown dynamical systems directly by training on observed time-series data. Concurrently, improvements in electrophysiological recording techniques have enabled the simultaneous recording of hundreds of neurons in animals performing complex behavioral tasks. These parallel developments present a unique opportunity to characterize comprehensively population dynamics and parametrize the neuronal manifold, thereby constructing functional models of cognitive functions. The objective of this research project is to further refine RNN-based algorithms, tailoring them to investigate neuronal dynamics, and applying them to experimental data.