Ordinary Differential Equation

Ordinary differential equations (ODEs) describe the continuous change of systems over time, and their identification and solution are central to many scientific disciplines. Current research focuses on developing efficient and robust methods for discovering ODEs from data, often employing neural networks (including Physics-Informed Neural Networks and Neural ODEs), transformers, and probabilistic integrators, as well as refining existing numerical techniques like collocation methods. These advancements are significantly impacting fields like biomedical signal processing (e.g., ECG analysis), dynamical systems modeling, and machine learning, enabling more accurate and efficient analysis of complex systems.