An algorithm for discovering Lagrangians automatically from data

An activity fundamental to science is building mathematical models. These models are used to both predict the results of future experiments and gain insight into the structure of the system under study. We present an algorithm that automates the model building process in a scientifically principled way. The algorithm can take observed trajectories from a wide variety of mechanical systems and, without any other prior knowledge or tuning of parameters, predict the future evolution of the system. It does this by applying the principle of least action and searching for the simplest Lagrangian that describes the system’s behaviour. By generating this Lagrangian in a human interpretable form, it can also provide insight into the workings of the system