Infinitesimal Generator

Infinitesimal generators describe the instantaneous rate of change of a dynamical system, providing a fundamental tool for analyzing stochastic processes and Lie groups. Current research focuses on learning these generators from data, particularly addressing challenges posed by high-dimensional spaces and biased datasets, employing techniques like energy-based risk metrics and kernel methods. This work has significant implications for diverse fields, enabling more accurate modeling of complex systems in areas such as molecular dynamics and facilitating the discovery of sparse representations for Lie group symmetries. Improved generator estimation promises advancements in simulations and the understanding of underlying physical processes.