Modeling temporal evolution is a fundamental challenge in machine learning and scientific computing, particularly in domains where data is continuous and dynamic. Traditional deep learning models, such as recurrent neural networks (RNNs) and transformers, struggle with capturing smooth temporal transitions and irregularly sampled data. Neural Differential Equations (NDEs), including Neural ODEs, Neural CDEs, and Neural SDEs, offer a principled framework to model temporal processes by leveraging differential equations. This study introduces the mathematical foundations of NDEs, explores their relationship to classical differential equation models, and presents state-of-the-art advancements in neural time series modeling. This study discusses their applications in a diverse domain, focusing on how NDEs provide an interpretable and flexible approach to learning from continuous data.

#Bio 

Dr. YongKyung Oh serves as a postdoctoral researcher at the University of California, Los Angeles (UCLA) Health - David Geffen School of Medicine. He contributes as a member of the UCLA Medical & Imaging Informatics (MII) group, under the leadership of Dr. Alex Bui. Prior to joining UCLA MII, he held a postdoctoral researcher position at the Industry Intelligentization Institute at the Ulsan National Institute of Science and Technology (UNIST). He received his Ph.D. in Industrial Engineering from UNIST, under the supervision of Dr. Sungil Kim. Prior to pursuing his Ph.D., he earned his Master's degree in Technology and Innovation Management and his B.Sc. in Physics, both from UNIST.