title: Physics-based statistical learning approach to mesoscopic model selection.
abstract: In materials science and many other research areas, models are frequently inferred without considering their generalization to unseen data. We apply statistical learning using cross-validation to obtain an optimally predictive coarse-grained description of a two-dimensional kinetic nearest-neighbor Ising model with Glauber dynamics (GD) based on the stochastic Ginzburg-Landau equation (sGLE). The latter is learned from GD "training" data using a log-likelihood analysis, and its predictive ability for various complexities of the model is tested on GD "test" data independent of the data used to train the model on. Using two different error metrics, we perform a detailed analysis of the error between magnetization time trajectories simulated using the learned sGLE coarse-grained description and those obtained using the GD model. We show that both for equilibrium and out-of-equilibrium GD training trajectories, the standard phenomenological description using a quartic free energy does not always yield the most predictive coarse-grained model. Moreover, increasing the amount of training data can shift the optimal model complexity to higher values. Our results are promising in that they pave the way for the use of statistical learning as a general tool for materials modeling and discovery.
authors.affiliation: Department of Mechanical and Aerospace Engineering, University of California, San Diego, 9500 Gilman Drive, La Jolla, California 92093, USA.
authors.forename: Søren
authors.initials: S
authors.lastname: Taverniers
authors.affiliation: Computer, Computational, and Statistical Sciences Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA.
authors.forename: Terry S
authors.initials: TS
authors.lastname: Haut
authors.affiliation: Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA.
authors.forename: Kipton
authors.initials: K
authors.lastname: Barros
authors.affiliation: Computer, Computational, and Statistical Sciences Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA.
authors.forename: Francis J
authors.initials: FJ
authors.lastname: Alexander
authors.affiliation: Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA.
authors.forename: Turab
authors.initials: T
authors.lastname: Lookman