Effective Equations in complex systems: from Langevin to machine learning

Abstract

The problem of effective equations is reviewed and discussed. Starting from the classical Langevin equation, we show how it can be generalized to Hamiltonian systems with non-standard kinetic terms. A numerical method for inferring effective equations from data is discussed; this protocol allows to check the validity of our results. In addition we show that, with a suitable treatment of time series, such protocol can be used to infer effective models from experimental data. We briefly discuss the practical and conceptual difficulties of a pure data-driven approach in the building of models.

References in corpus (9)

• Complex networks in climate dynamics - Comparing linear and nonlinear network construction methods
• Negative Absolute Temperature for Motional Degrees of Freedom
• Construction of microcanonical entropy on thermodynamic pillars
• The prediction of future from the past: an old problem from a modern perspective
• Cages and anomalous diffusion in vibrated dense granular media
• Statistical mechanics of systems with long-range interactions and negative absolute temperature
• Langevin equations from experimental data: the case of rotational diffusion in granular media
• About thermometers and temperature
• Derivation of a Langevin equation in a system with multiple scales: the case of negative temperatures