Occupation Kernel

Occupation kernels are a data-driven method used to learn differential equations, both ordinary and partial, from observed trajectories of dynamical systems. Current research focuses on extending this approach to high-dimensional systems and stochastic processes, often employing techniques like reproducing kernel Hilbert spaces and principal component analysis to improve efficiency and robustness. This methodology offers a powerful tool for system identification and fault detection in various applications, particularly where traditional model-based approaches are difficult or impossible to implement due to complexity or lack of prior knowledge.