Fokker Planck Equation

The Fokker-Planck equation is a partial differential equation describing the time evolution of the probability density function of a stochastic process, primarily used to model systems with both deterministic and random forces. Current research focuses on developing efficient numerical solutions, particularly for high-dimensional problems, employing techniques like deep learning (e.g., physics-informed neural networks, normalizing flows), and score-based methods. These advancements are improving the accuracy and speed of solving the Fokker-Planck equation across diverse fields, including physics, finance, and machine learning, with applications ranging from generative modeling to the analysis of stochastic optimization algorithms.