Abstract: Computational modeling of dynamic behavior in neurons is quickly becoming a fundamental tool in both research and clinical applications. This is due in part to improvements in physical computation capabilities as well as in part to improvements in mathematical modeling techniques both in respect to the physical models and the computational models. In this talk, we will cover some recent advances in these areas that contribute to modeling the dynamic behavior at multiple time and spatial scales, including adapting classical model reduction techniques to computational settings, constructing efficient numerical methods for these reduced models, and employing modern machine learning techniques to reduce simulation time and move toward clinical applications. We will then look at recent applications and preliminary results of these techniques to studying neuronal response to transcranial magnetic stimulation (TMS), a noninvasive therapeutic treatment for a variety of neurological disorders.