  Electronic density of states (DOS) is a key factor in condensed matter
physics and material science that determines the properties of metals.
First-principles density-functional theory (DFT) calculations have typically
been used to obtain the DOS despite the considerable computation cost. Herein,
we report a fast pattern learning method for predicting the DOS patterns of not
only bulk structures but also surface structures in multi-component alloy
systems by a principal component analysis. Within this framework, we use only
four features to define the composition, atomic structure, and surfaces of
alloys, which are the d-orbital occupation ratio, coordination number, mixing
factor, and the inverse of miller indices. While the DFT method scales as
O(N^3) in which N is the number of electrons in the system size, our pattern
learning method can scale as O(1) regardless of N. Furthermore, our method
provides a pattern similarity of 91~98% compared to DFT calculations. This
reveals that our learning method will be an alternative that can break the
trade-off relationship between accuracy and speed that is well known in the
field of electronic structure calculations.
