This is the code to reproduce the result of the paper "High order expansion of neural ODEs flows" published in Science Advances in 2025. We report below the abstract of the paper: "Artificial neural networks, widely recognised for their role in machine learning, are also transforming the study of ordinary differential equations (ODEs), bridging data-driven modelling with classical dynamical systems as well as enabling the development of infinitely deep neural models. However, their practical applicability remains, in this context, constrained by the opacity of the learned dynamics, which operate as black-box systems with limited explainability, thereby hindering trust in their deployment. Existing approaches for the analysis of neurally driven dynamical systems are currently scarce and anyway restricted to first-order gradient information due to computational constraints, thereby limiting the depth of achievable insight. In this paper we introduce Event Transition Tensors as a new tool containing high-order differential information that provides a rigorous mathematical description of neural ODE dynamics on event manifolds. We demonstrate its versatility across diverse applications: characterising uncertainties in a data-driven prey-predator control model, analyzing neural optimal feedback dynamics, and mapping landing trajectories in a three-body neural Hamiltonian system. In all cases, our method allow for the interpretability of neural ODEs and their analytical verification by expressing their behaviour through new explicit mathematical structures. The neural dynamics are thereby fully encapsulated within a set of compact, computationally efficient tensors, which retain all the necessary information for rigorous system analysis and certification.Our findings contribute to a deeper theoretical foundation for event-triggered neural differential equations and provide a mathematical construct for explaining complex system dynamics."