  Predicting the behavior of AI-driven agents is particularly challenging
without a preexisting model. In our paper, we address this by treating AI
agents as nonlinear dynamical systems and adopting a probabilistic perspective
to predict their statistical behavior using the Perron-Frobenius (PF) operator.
We formulate the approximation of the PF operator as an entropy minimization
problem, which can be solved by leveraging the Markovian property of the
operator and decomposing its spectrum. Our data-driven methodology
simultaneously approximates the PF operator to perform prediction of the
evolution of the agents and also predicts the terminal probability density of
AI agents, such as robotic systems and generative models. We demonstrate the
effectiveness of our prediction model through extensive experiments on
practical systems driven by AI algorithms.
