Physics-based statistical learning approach to mesoscopic model selection.

Area of Science:

• Materials Science
• Statistical Physics
• Computational Modeling

Background:

• Models in materials science often lack generalization to new data.
• Coarse-grained models are crucial for simulating complex systems.
• Statistical learning offers a data-driven approach to model development.

Purpose of the Study:

• To develop an optimally predictive coarse-grained model using statistical learning.
• To assess the generalization capability of learned models on unseen data.
• To compare statistical learning models against standard phenomenological descriptions.

Main Methods:

• Applied statistical learning with cross-validation to a 2D kinetic Ising model with Glauber dynamics (GD).
• Learned a coarse-grained model (stochastic Ginzburg-Landau equation - sGLE) from GD training data via log-likelihood analysis.
• Tested predictive accuracy on independent GD test data using magnetization time trajectory error metrics.

Main Results:

• The learned sGLE model demonstrated predictive capability on unseen data.
• Standard quartic free energy models were not always the most predictive.
• Increased training data shifted optimal model complexity to higher values.
• Model performance was analyzed for both equilibrium and out-of-equilibrium training data.

Conclusions:

• Statistical learning provides a powerful, generalizable tool for materials modeling.
• Optimizing model complexity is key for accurate predictions.
• This data-driven approach advances materials discovery and simulation.