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Machine learning has been effective at detecting patterns and predicting theresponse of systems that behave free of natural laws. Examples include learningcrowd dynamics, recommender systems and autonomous mobility. There also havebeen applications to the search for new materials that bear relations to bigdata classification problems. However, when it comes to physical systemsgoverned by conservation laws, the role of machine learning has been morelimited. Here, we present our recent work in exploring the role of machinelearning methods in discovering, or aiding, the search for physics.Specifically, we focus on using machine learning algorithms to representhigh-dimensional free energy surfaces with the goal of identifying precipitatemorphologies in alloy systems. Traditionally, this problem has been approachedby combining phase field models, which impose first-order dynamics, withelasticity, to traverse a free energy landscape in search of minima.Equilibrium precipitate morphologies occur at these minima. Here, we exploitthe machine learning methods to represent high-dimensional data, combined withsurrogate optimization, sensitivity analysis and multifidelity modelling as analternate framework to explore phenomena controlled by energy extremization.This combination of data-driven methods offers an alternative to the impositionof first-order dynamics via phase field methods, and represents one approach tomachine learning materials physics.

computer methods in applied mechanics and engineering

Machine learning materials physics: Surrogate optimization and  multi-fidelity algorithms predict precipitate morphology in an alternative to  phase field dynamics