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\section{Introduction}  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 intuition-guided serendipity being the most fruitful path. For example, all major classes of superconductors--from elemental mercury in 1911, to the heavy fermions, cuprates, iron-based superonductors and most recently, hydrogen sulfide in late 2014--have been discovered by chance.  The dream of materials design is to leverage our theories of electronic structure, rather than ignoring them, combined with our increasing computational and storage abilities to discover new materials. Beyond its technological implications, the challenge of materials design is also one of great intellectual depth. In principle, we know all the fundamental equations needed to model the behavior of electrons and nuclei. Solving these equations is another matter.  For a large class of materials called weakly-correlated compounds, encompassing simple metals, insulators and semiconductors, implementations of density functional theory (DFT) performs extremely well. DFT is a workhorse of the materials science community, providing efficient and accurate computations of the total energy and distribution of electrons of a compound, requiring only the coordinates of the atoms in its crystal lattice as input. From the total energy, one can obtain lattice constants, equations of state and the spectrum of lattice vibrations. Furthermore, one can obtain electronic properties such as band gaps, electric polarization and topological numbers, which are by no means trivial for these "simple" compounds. Using DFT, several groups have been constructing databases spanning large swaths of the space of known compounds, containing these computed properties which can then be data mined for specific properties. Successes include the prediction of multiferroics~\cite{Fennie_2008}, intermetallic semiconductors\cite{Gautier_2015} and even heavy fermion materials\cite{Fredeman_2011}.  However, there is another large class of materials called strongly-correlated compounds, whose distinguishing phenomenological feature is sensitivity to external perturbation, which makes them technologically useful. Small changes in pressure, temperature or chemical doping often drives large changes in electronic or structural behavior. 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.  The basic feature of correlated materials is their electrons cannot be described as non-interacting particles, posing special challenges for theory. Often, this occurs because the material contains atoms with partially-filled $d$ or $f$ orbitals. The electrons occupying these orbitals retain a strong atomic-like character to their behavior, which when combined with the band-like behavior of the remaining electrons, makes for a challenging problem. Consequently current implementations of DFT cannot describe their properties accurately. This led to the development of extensions to DFT such as LDA+U, and entirely more sophisticated approaches such as dynamical mean field theory (DMFT) and the GW approximation.  [Describe the intersection of materials design with correlated materials]  % Only LDA+U can produce energies at scale.  % Materials design also necessarily involves handling and organizing large bodies of data since the process of check => machine learning.  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 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.  % 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. %  However, the road to saying "I want a material that has these mechanical %  properties combined with these optical properties with these specific thermal %  switching characteristics" and being able to design a new material satisfying %  those properties from nothing more than the constituent elements is a long one. %  Why is it so difficult? %  Ingredients of materials design. %  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. %  \begin{itemize} %  \item define the material design challenge %  \item say that in weakly correlated systems it has been fulfilled within DFT. Can mention Zunger’s Heussler compound. %  \item define strongly correlated materials %  \item they do interesting things and pose special challenges for the material, %  and we want to summarize outsanding problems in this area and possible %  directions to overcome them. %  \end{itemize}