# Langevin equations from experimental data: the case of rotational diffusion in granular media

## TL;DR

This paper demonstrates how to derive Langevin equations from experimental rotational diffusion data in granular media, highlighting the method's power and limitations, especially in complex multiscale regimes.

## Contribution

It introduces a novel approach to extract Langevin equations from empirical data in granular systems, addressing challenges in multiscale scenarios.

## Key findings

- Successful derivation of Langevin equations from experimental data
- Identification of multiscale dynamics in dense granular regimes
- Development of innovative methods for slow variable extraction

## Abstract

A model has two main aims: predicting the behavior of a physical system and understanding its nature, that is how it works, at some desired level of abstraction. A promising recent approach to model building consists in deriving a Langevin-type stochastic equation from a time series of empirical data. Even if the protocol is based upon the introduction of drift and diffusion terms in stochastic differential equations, its implementation involves subtle conceptual problems and, most importantly, requires some prior theoretical knowledge about the system. Here we apply this approach to the data obtained in a rotational granular diffusion experiment, showing the power of this method and the theoretical issues behind its limits. A crucial point emerged in the dense liquid regime, where the data reveal a complex multiscale scenario with at least one fast and one slow variable. Identifying the latter is a major problem within the Langevin derivation procedure and led us to introduce innovative ideas for its solution.