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Machine Learning in Electronic-Structure Theory


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Machine learning (ML) approaches are transforming the field of electronic structure calculations. This is particularly true for Density Functional Theory (DFT), the most widely used quantum mechanical approach in computational materials science. It allows to recast the search for the ground state of the Schrödinger operator into the minimization of a functional of the electronic density of the system, a function in three variables only. The caveat is that the form of the functional is unknown. The very efficient Kohn-Sham (KS) scheme proposed in the 60’s, in which only the exchange-correlation (XC) energy needs to be approximated, still faces some limitations, despite intense efforts in the physics and chemistry communities. Machine learning (ML) is promising for improving density-functional approximations, either to find the best combination of current XC approximations, or to construct new XC functionals or even to produce pure density functionals to bypass the need to solve KS equations. Besides tackling the total energy in that way, ML can also be used to predict the electronic structure from higher-level methodology like Green-function approaches. Moreover, ML is also very promising for other complementary electronic structure methods, e.g. to solve the bottleneck of the parametrization of tight-binding Hamiltonians on DFT calculations or to improve the efficiency of the highly-accurate Quantum Monte Carlo methods that have prohibitive computational cost for large systems.


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Claudia Draxl Humboldt-Universität zu Berlin
Giulia Galli University of Chicago
Lin Lin University of California Berkeley
Francois Willaime CEA Saclay