Chemical compound space (CCS), the
set of all theoretically conceivable
combinations of chemical elements and (meta-)stable geometries that
make up matter, is colossal. The first-principles based virtual sampling
of this space, for example, in search of novel molecules or materials
which exhibit desirable properties, is therefore prohibitive for all
but the smallest subsets and simplest properties. We review studies
aimed at tackling this challenge using modern machine learning techniques
based on (i) synthetic data, typically generated using quantum mechanics
based methods, and (ii) model architectures inspired by quantum mechanics.
Such Quantum mechanics based Machine Learning (QML) approaches combine
the numerical efficiency of statistical surrogate models with an ab
initio view on matter. They rigorously reflect the underlying physics
in order to reach universality and transferability across CCS. While
state-of-the-art approximations to quantum problems impose severe
computational bottlenecks, recent QML based developments indicate
the possibility of substantial acceleration without sacrificing the
predictive power of quantum mechanics.