Learning the Physics of Pattern Formation from Images
Author(s)Zhao, Hongbo; Storey, Brian D.; Braatz, Richard D.; Bazant, Martin Z.
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Using a framework of partial differential equation-constrained optimization, we demonstrate that multiple constitutive relations can be extracted simultaneously from a small set of images of pattern formation. Examples include state-dependent properties in phase-field models, such as the diffusivity, kinetic prefactor, free energy, and direct correlation function, given only the general form of the Cahn-Hilliard equation, Allen-Cahn equation, or dynamical density functional theory (phase-field crystal model). Constraints can be added based on physical arguments to accelerate convergence and avoid spurious results. Reconstruction of the free energy functional, which contains nonlinear dependence on the state variable and differential or convolutional operators, opens the possibility of learning nonequilibrium thermodynamics from only a few snapshots of the dynamics.
DepartmentMassachusetts Institute of Technology. Department of Chemical Engineering; Massachusetts Institute of Technology. Department of Mathematics
Physical Review Letters
American Physical Society
Zhao, Hongbo et al. "Learning the Physics of Pattern Formation from Images." Physical Review Letters 124, 6 (February 2020): 060201 © 2020 American Physical Society
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