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\section{Introduction}  \label{sec:intro}  The ability to design new materials with a desired set of properties is crucial to the development of new technology. The design of silicon and lithium-ion based materials are well known examples which led to the proliferation of consumer hand-held devices today. However, materials discovery has historically proceeded via trial and error, with a mixture of serendipity and intuition being the most fruitful path. For example, all major classes of superconductors--from elemental mercury in 1911, to the heavy fermions, cuprates and most recently, the iron-based superconductors--have been discovered by chance~\cite{Greene_2012}.  % The ability to design new materials with desired properties is a key challenge.  % Its solution would have far-reaching implications in both fundamental science  % and technological applications. Whether it is a new class of semiconductors for  % the next generation of integrated circuits, superconductors for dissipationless  % transport of electricity, or thermoelectrics for efficient recovery of waste  % heat, advances in underlying materials results in advances in technology.  The dream of materials design is to leverage, rather than ignore, our theories of electronic structure and combine them with our increasing computational ability to discover new materials. Beyond its technological implications, the challenge of materials design is also one of great intellectual depth. In principle, we know the fundamental equation needed to model the behavior of a material: it is the Schr\"odinger equation describing electrons moving in the potential of a periodic lattice, mutually interacting via the Coulomb repulsion. Solving this equation is another matter.  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. % The underlying workhorse for all materials design is a box which takes as input  % the coordinates of the atoms within a unit cell and produces the total energy  % of the configuration. For materials without partially-filled $d$ or $f$ shells,  % density functional theory performs quite well, providing total energies that  % are accurate to within 50meV.  For weakly correlated materials, DFT has become the underlying workhorse of the scientific community. The maturity of its various software implementations means researchers can routinely compute the approximate atomic coordinates of a new compound, and compute its optimized structure and myriad of electronic properties. Combined with growing databases of experimental [ICSD] and computed data [MatProj, AFLOW, NIMS], the field of weakly correlated systems has advanced to the point where one can successfully design materials [Feenie 2008, Gautier 2015 and Fredeman 2011]. A clear example that theoretical approaches are coming of age is the recent prediction of superconductivity in H$_3$S under pressure at XXX~K. Indeed, hydrogen sulfide was recently observed to superconduct near 200 K, the highest temperature superconductor discovered so far.  In order to understand the challenges particular to correlations in materials design, we need to better define what we mean by a correlated material, which we do in Sec.~\ref{sec:correlations}.  %, and we start by examining DFT. Section~\ref{sec:correlations}.  % TODO: Define the problem: What IS design of correlated materials? Describe the intersection of materials design with correlated materials. Also describe the need for large computable databases.  For weakly correlated electron systems, the tools for predicting the properties of solids have advanced to the point that one can contemplate materials design using these tools and their extensions. [ %  Materials Project AFLOW, what else ] , and these methods are being currently used to predict new materials, as for example in Feenie 2008, Gautier 2015 design also necessarily involves handling  and Fredeman 2011. A clear example that theoretical approaches in the field organizing large bodies  of weakly correlated electron materials is coming of age, is data since  the recent prediction process  of superconductivity in HS3 under pressure, which was recently found to superconduct near 200 K, the highest temperature superconductor discovered so far. check => machine learning.  Strongly-correlated compounds have many unusual exhibit unique  properties. For example, there In particular, they  arevery  sensitive to external perturbation, perturbations,  which makes them technologically useful. naturally leads to technological applications.  Small changes in pressure, temperature or chemical doping often drives large changes in electronic or structural behavior. behavior, making them ideal for sensing applications.  For example, changing the temperature by only several degrees Kelvin can drive a transition between a metallic and insulating state, behavior not observed in weakly-correlated compounds. In addition to metal-insulator transitions, these compounds display unusual magnetic properties, high-temperature superconductivity and strange-metal behavior. To be precise, we can phrase the question of materials design concretely as follows: given a chemical system, determine the crystal structures and electronic properties of all stable compounds formed by the constituent elements. For To give a concrete  example, if the chemical system of interest is Li-Fe-P-O, determine all binaries, ternaries and quaternaries and compute their properties (turns out LiFePO$_4$ is a promising battery material). This problem involves coordinating many moving pieces, including structural prediction, determination of thermodynamic stability against competing phases and computation of electronic properties. In this article, we seek to summarize outstanding challenges in the area, especially as it pertains to correlated materials, and propose strategies to solve them.