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Learning the Physics of Pattern Formation from Images.

Hongbo Zhao¹, Brian D Storey^2,3, Richard D Braatz¹

¹Department of Chemical Engineering, Massachusetts Institute of Technology 77 Massachusetts Avenue, Cambridge, Massachusetts 02139, USA.

Physical Review Letters

|February 29, 2020

Summary

This summary is machine-generated.

This study introduces a novel optimization framework to extract multiple material properties simultaneously from pattern formation images. This method enables learning nonequilibrium thermodynamics from limited dynamic snapshots.

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Area of Science:

Materials Science
Computational Physics
Thermodynamics

Background:

Phase-field models describe pattern formation but often require known material properties.
Extracting these properties from experimental or simulation images is challenging.

Purpose of the Study:

To develop a computational framework for simultaneously extracting multiple constitutive relations from limited image data.
To enable learning of nonequilibrium thermodynamics from sparse dynamic snapshots.

Main Methods:

Utilizing partial differential equation-constrained optimization.
Applying the framework to phase-field models like Cahn-Hilliard and Allen-Cahn equations, and dynamical density functional theory (phase-field crystal model).
Incorporating physical constraints to improve convergence and accuracy.

Main Results:

Demonstrated simultaneous extraction of state-dependent properties: diffusivity, kinetic prefactor, free energy, and direct correlation function.
Successfully reconstructed complex free energy functionals with nonlinear dependencies and differential operators.
Showcased the ability to learn from a small set of pattern formation images.

Conclusions:

The developed optimization framework offers a powerful tool for material property discovery from limited data.
This approach facilitates the learning of nonequilibrium thermodynamics, advancing materials modeling and simulation.