An algorithm for discovering Lagrangians automatically from data

TL;DR

This paper introduces an algorithm that automatically discovers Lagrangians from data, enabling the modeling of mechanical systems without prior knowledge, based on the principle of least action.

Contribution

It presents a novel, automated method for deriving Lagrangians directly from observed data, facilitating model building and system understanding.

Findings

Successfully predicts system evolution from trajectories

Generates human-interpretable Lagrangians

Works without prior knowledge or parameter tuning

Abstract

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 also provides insight into the working of the system.