Methods for data-driven multiscale model discovery for materials

Despite recent achievements in the design and manufacture of advanced materials, the contributions from first-principles modeling and simulation have remained limited, especially in regards to characterizing how macroscopic properties depend on the heterogeneous microstructure. An improved ability to model and understand these multiscale and anisotropic effects will be critical in designing future materials, especially given rapid improvements in the enabling technologies of additive manufacturing and active metamaterials. In this review, we discuss recent progress in the data-driven modeling of dynamical systems using machine learning and sparse optimization to generate parsimonious macroscopic models that are generalizable and interpretable. Such improvements in model discovery will facilitate the design and characterization of advanced materials by improving efforts in (1) molecular dynamics, (2) obtaining macroscopic constitutive equations, and (3) optimization and control of metamaterials.