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