Density Evolution

Density evolution studies the temporal change in probability density functions, aiming to understand and model how these distributions evolve over time. Current research focuses on developing efficient algorithms and model architectures, such as normalizing flows and physics-informed neural networks, to solve the underlying equations governing density evolution, often within the context of particle systems or stochastic processes. These advancements have significant implications for diverse fields, including robotics (safe motion planning), machine learning (out-of-distribution detection and generative models), and the analysis of complex systems (e.g., network dynamics and swarm behavior). Improved understanding and modeling of density evolution offers more accurate predictions and control strategies across these areas.