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. Here, 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:

Taverniers, Soren ^[1]; Haut, Terry S. ^[2]; Barros, Kipton ^[2]; Alexander, Francis J. ^[2]; Lookman, Turab ^[2]

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+ Show Author Affiliations

1. Univ. of California, San Diego, CA (United States). Dept. of Mechanical and Aerospace Engineering
2. Los Alamos National Lab. (LANL), Los Alamos, NM (United States)

Publication Date:

Mon Nov 09 00:00:00 EST 2015

Research Org.:

Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)

Sponsoring Org.:

USDOE National Nuclear Security Administration (NNSA); USDOE Laboratory Directed Research and Development (LDRD) Program

OSTI Identifier:

1457240

Alternate Identifier(s):

OSTI ID: 1225546

Report Number(s):

LA-UR-15-23538
Journal ID: ISSN 1539-3755; PLEEE8; TRN: US1901323

Grant/Contract Number:  

AC52-06NA25396; 20140013DR

Resource Type:

Accepted Manuscript

Journal Name:

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics

Additional Journal Information:

Journal Volume: 92; Journal Issue: 5; Journal ID: ISSN 1539-3755

Publisher:

American Physical Society (APS)

Country of Publication:

United States

Language:

English

Subject:

97 MATHEMATICS AND COMPUTING; 36 MATERIALS SCIENCE; stochastic partial differential equations; Ginzburg-Landau equation; Ising model; statistical learning