## 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:

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

- Publication Date:

- Research Org.:
- Los Alamos National Lab. (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

### Citation Formats

```
Taverniers, Soren, Haut, Terry S., Barros, Kipton, Alexander, Francis J., and Lookman, Turab. Physics-based statistical learning approach to mesoscopic model selection. United States: N. p., 2015.
Web. doi:10.1103/PhysRevE.92.053301.
```

```
Taverniers, Soren, Haut, Terry S., Barros, Kipton, Alexander, Francis J., & Lookman, Turab. Physics-based statistical learning approach to mesoscopic model selection. United States. doi:10.1103/PhysRevE.92.053301.
```

```
Taverniers, Soren, Haut, Terry S., Barros, Kipton, Alexander, Francis J., and Lookman, Turab. Mon .
"Physics-based statistical learning approach to mesoscopic model selection". United States. doi:10.1103/PhysRevE.92.053301. https://www.osti.gov/servlets/purl/1457240.
```

```
@article{osti_1457240,
```

title = {Physics-based statistical learning approach to mesoscopic model selection},

author = {Taverniers, Soren and Haut, Terry S. and Barros, Kipton and Alexander, Francis J. and Lookman, Turab},

abstractNote = {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.},

doi = {10.1103/PhysRevE.92.053301},

journal = {Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics},

number = 5,

volume = 92,

place = {United States},

year = {2015},

month = {11}

}

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