Integrating Mechanistic and Data-Driven Models for Neurological Disorders through Differentiable Programming

Advances in computational modeling, neuroimaging, and artificial intelligence are revolutionizing the modeling of neurological disorders for improved diagnostics, prognosis, and treatment planning. Mechanistic models provide valuable scientific insight into the disorders, but in practice they are often simplified with assumptions or computationally expensive and slow to solve. However, while purely data driven approaches provide speed and scalability, they require large, high quality data to train and generally suffer from interpretability and generalization issues. This perspective paper presents a structured overview of hybrid modeling strategies, which combine deep learning models with physics based solvers, and are categorized into parallel, series, and parallel-series architectures. Three main approaches that have been emphasized are residual modeling for missing or incomplete physics, Neural Ordinary Differential Equations (NODEs) for continuous time dynamics approximation, and solver in the loop that accelerates traditional solvers with neural approximations. These hybrid models integrate the governing differential equation based formulations and deep learning to characterize the evolution of neurological disorders, and promise advanced personalized neurological modeling. In addition, the study explores and proposes different hybrid configurations to improve diagnosis accuracy, predict disease progression, and inform treatment strategies across a range of neurological disorders. These capabilities outperform standalone mechanistic or purely data driven approaches, making hybrid modeling a powerful tool, especially in applications involving modeling the progression and treatment responses in neurological conditions such as brain tumors, Alzheimer's disease, and stroke.