Surrogate Optimization

In this chapter, we take up our first instance of using machine learning for high-dimensional functional representation. Of interest here—and one that we will return to in a subsequent chapter—is the representation of free energy surfaces. The application in this chapter is the identification of precipitate morphologies in alloy systems. The traditional approach to this problem in continuum materials physics has been to combine phase field models with elasticity to traverse a free energy landscape in search of minima at which equilibrium precipitate morphologies occur. The twist in this chapter is the exploitation of machine learning methods to represent high-dimensional data and to combine it with surrogate optimization, sensitivity analysis, and multifidelity modelling as an alternate framework to explore extrema of a function in these large dimensions. A number of phenomena in physics are governed by extremization, and often the function of interest is not an energy, of course, but the ideas carry over. This chapter is based upon work that was described in Teichert and Garikipati (Comput Methods Appl Mech Eng 344:666–693, 2019).