(477d) Inverse Learning of Material Physics through Image Data and Continuum Modeling

The advent of big data in spatio-temporal microscopic images as well as large-scale atomistic simulations offers a tremendous amount of hidden information about the physical chemistry at the continuum level. Using a framework of PDE-constrained optimization, we extract multiple unknown constitutive relations simultaneously from a small set of images of pattern formation. Compared to the data-driven modeling approach, our approach provides clear physical interpretability by prescribing a general governing equation while faithfully achieving quantitative matching between data and continuum model prediction through highly expressive nonlinear and/or nonlocal (integro-differential) constitutive relations.

We present examples of learning state-dependent properties such as the diffusivity, kinetic prefactor, free energy, and direct correlation function from Cahn-Hilliard equation, Allen-Cahn equation, and Phase Field Crystal Model. Applying the method to experimental images of lithium concentration field in lithium-iron phosphate (LFP) particles during charge and discharge, we are able to extract its free energy and reaction kinetics, and “image” its reaction kinetics heterogeneity map. In addition, we also demonstrate its ability to coarse-grain molecular simulations and hence provide acceleration by learning functions of free energy and diffusivity and achieving quantitative matching of the patterns of spinodal decomposition.