This presentation will focus on the application of advanced computational methods in neuroscience, specifically exploring how machine learning and dynamical systems theory can be utilized to unravel the complexities of brain function. We will delve into the latest advancements in spectral methods and their role in interpreting neural data, emphasizing how these techniques facilitate a deeper understanding of brain dynamics. By employing models that integrate linear operators for spectral analysis, we aim to provide scalable and interpretable insights into neural processes. The talk will highlight how these computational strategies not only enhance our comprehension of neural network interactions but also open new avenues for developing innovative approaches in neurological disorder diagnosis and treatment. Through this exploration, we will demonstrate the potential of computational neuroscience in bridging the gap between intricate neural mechanisms and practical healthcare applications.