Predicting the Mpemba Effect Using Machine Learning

Abstract

The Mpemba Effect can be studied with Markovian dynamics in a non-equilibrium thermodynamics framework. The Markovian Mpemba Effect can be observed in a variety of systems including the Ising model. We demonstrate that the Markovian Mpemba Effect can be predicted in the Ising model with several machine learning methods: the decision tree algorithm, neural networks, linear regression, and non-linear regression with the LASSO method. The positive and negative accuracy of these methods are compared. Additionally, we find that machine learning methods can be used to accurately extrapolate to data outside the range which they were trained. Neural Networks can even predict the existence of the Mpemba Effect when they are trained only on data in which the Mpemba Effect does not occur. This indicates that information about which coefficients result in the Mpemba Effect is contained in coefficients where the results does not occur. Furthermore, neural networks can predict that the Mpemba effect does not occur for positive $J$, corresponding to the ferromagnetic ising model even when they are only trained on negative $J$, corresponding to the anti-ferromagnetic ising model. All of these results demonstrate that the Mpemba Effect can be predicted in complex, computationally expensive systems, without explicit calculations of the eigenvectors.

References in corpus (23)

• Anomalous cooling and heating - the Mpemba effect and its inverse
• When the Hotter Cools More Quickly: Mpemba Effect in Granular Fluids
• The Mpemba index and anomalous relaxation
• The Mpemba effect in spin glasses is a persistent memory effect
• Pre-Cooling Strategy Allows Exponentially Faster Heating
• Large Mpemba-like effect in a gas of inelastic rough hard spheres
• Exact Coarse Graining Preserves Entropy Production out of Equilibrium
• Relaxation shortcuts through boundary coupling
• Paths towards equilibrium in molecular systems: a mesoscopic Mpemba-like effect in water
• Deep Learning on the 2-Dimensional Ising Model to Extract the Crossover Region with a Variational Autoencoder
• Anomalous cooling and overcooling of active systems
• Eigenvalue crossing as a phase transition in relaxation dynamics
• Memory effects in a gas of viscoelastic particles
• The metastable Mpemba effect corresponds to a non-monotonic temperature dependence of extractable work
• Kovacs memory effect with an optically levitated nanoparticle
• S- and p-wave structure of $S=-1$ meson-baryon scattering in the resonance region
• Slow growth of magnetic domains helps fast evolution routes for out-of-equilibrium dynamics
• Towards the Minimal Spectrum of Excited Baryons
• Mpemba effect in anisotropically driven inelastic Maxwell gases
• Strong non-exponential relaxation and memory effects in a fluid with non-linear drag
• Model selection for amplitude analysis
• Sampling algorithms for validation of supervised learning models for Ising-like systems
• Relaxation-speed crossover in anharmonic potentials

Cited by in corpus (1)

• Speedups in nonequilibrium thermal relaxation: Mpemba and related effects