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Strongly-correlated compounds have many unusual properties. For example, there are very sensitive 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. 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, while the remaining electrons form bands; their interplay poses special challenges for theory. 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. [ I MOVED THIS  For understanding the electronic properties of a material given a crystal structure, DMFT and GW perform remarkably well. However, only LDA+U can currently scale to produce total energies for simulations involving thousands of compounds. Thus we adopt a hybrid workflow correlated materials, one where structural prediction is performed using LDA+U and then, once the final structure has been obtain, detailed analysis is performed using DMFT or GW. ]  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.