Stochastic Differential Equation

Stochastic differential equations (SDEs) model systems evolving continuously in time under the influence of randomness, aiming to capture both deterministic trends and stochastic fluctuations. Current research focuses on developing efficient algorithms for solving SDEs, particularly within machine learning contexts, including novel deep learning approaches for optimal control and generative modeling (e.g., diffusion models and neural SDEs). These advancements are impacting diverse fields, from image reconstruction and drug discovery to uncertainty quantification in complex systems and the analysis of large language models, by providing powerful tools for modeling and inference in stochastic environments.