Abstract
Physics provides mathematical formalisations of phenomena, such as oscillatory motion, that prove particularly useful and effective in describing characteristics of network nodes such as robustness (or conversely, vulnerability) to perturbations. At the same time, neural networks constitute tools for solving differential equations without the use of training data and without discretizing the integration domain. In particular, neural networks can prove to be efficient in calculating the numerical solution of systems of non-linear and stiff differential equations, cases in which traditional methods can be computationally cumbersome and accumulate significantly large errors. In this study, we propose a neural network activation function model that includes the vibration centrality of the physical network nodes whose dynamics we wish to simulate. We show how this can be particularly useful for the simulation of oscillating systems and analyse the case study of cellular glycolytic oscillations and the challenges that systems like that pose.