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In practice, we can classify materials by how well we can solve their corresponding Schr\"odinger equation. For the class of compounds encompassing simple metals, insulators and semiconductors, termed weakly correlated materials, we have a well-developed theory of their excitation spectra called Fermi liquid theory. From a practical viewpoint, the theoretical framework of density functional theory (DFT) naturally lends itself to computational implementations for modeling properties. Materials which are not well-described by DFT are colloquially termed strongly correlated materials.  For weakly correlated materials, DFT has become the underlying workhorse of the scientific community. Extensive benchmarks of software implementations~\cite{Lejaeghere_2016} have shown that DFT reliably produces the total energy of a given configuration of atoms, enabling comparisons of stability between different chemical polymorphs. The maturity of DFT, combined with searchable repositories of experimental data (ICDD, ICSD, NIMS) data, has fostered the growth of databases of computed materials properties (Materials Project, AFLOWlib, NIMS). The field of weakly correlated systems to has  advanced to the point where one can successfully design materials~\cite{Fennie_2008, Gautier_2015, Fredeman_2011}. A clear example that theoretical approaches are coming of age is the recent prediction of superconductivity in H$_3$S under high pressure near 190~K~\cite{Duan_2014}. Subsequently, hydrogen sulfide was observed to superconduct near 200~K, the highest temperature superconductor discovered so far~\cite{Drozdov_2015}. In contrast, materials design for strongly correlated systems is less mature, stemming from the fundamental challenge of understanding the physics of electron correlations. Correlated systems exhibit novel phenomena not observed in weakly-correlated materials: metal-insulator transitions, magnetic order and unconventional superconductivity are salient examples. While designing and optimizing materials with these properties would advance both technology and our understanding of the underlying physics, in practice we lack a tool akin to DFT capable of reliably modeling properties and scaling up to the thousands of calculations necessary.