Webinar: Scientific Machine Learning is a rapidly evolving field that combines machine learning, artificial intelligence, and traditional scientific computing. Its application in Neuroscience is at the forefront of this field, bridging the gap between classical computational modeling and state-of-the-art AI. These applications range from replacing traditional partial differential equation solvers with neural surrogates to evaluating the computational complexity of single neurons. In this talk, we will examine some of these methodologies, highlighting their inherent strengths and limitations, as well as the emerging pathways being defined within this growing field.