Differential Equation

Differential equations (DEs) describe the rates of change in systems, enabling predictions of future states. Current research focuses on developing efficient and accurate methods for solving DEs, particularly those involving complex systems or high-dimensional data, using machine learning techniques such as neural ordinary differential equations (NODEs), physics-informed neural networks (PINNs), and deep operator networks. These advancements are significantly impacting diverse fields, from finance and engineering to climate modeling and healthcare, by providing powerful tools for simulating complex dynamics and solving inverse problems where the underlying equations are unknown. The development of robust and efficient algorithms for solving various types of DEs, including stochastic and fractional DEs, remains a key area of ongoing investigation.