Nonlinear
optical (NLO) crystals are the key materials in modern
laser technology and science because of their intrinsic capability
to convert the wavelength of the light source. The search for new
NLO materials is still very active in both scientific and industrial
communities. Machine learning (ML) becomes a powerful tool to explore
new candidates of NLO materials and to reveal the underlying relationship
between structures and properties. In this work, we have proposed
multilevel features that are relevant to the atomic properties, the
characters of fundamental structural groups, and the crystal structures
to describe inorganic NLO crystals for machine learning. The first-level
and second-level descriptors can be obtained based on chemical compositions
of crystals without prior knowledge about crystal structures. Several
ML classifiers have been optimized using a database that consists
of hundreds of NLO crystals to identify the samples with desired birefringence
(Δn) and second-order nonlinear coefficients
(d
ij
). In particular,
almost all of the ML models that only involve the first-level and
second-level features, called as the crystal-structure-free model,
exhibit good classification performance. It is still far from perfect
but suitable to act as a filter in the first step of high-throughput
materials discovery. Using the optimized ML models, feature importance
analyses and virtual screening processes have been performed to understand
the relationship between the features and targeted properties and
to extract the statistical pictures on elements and fundamental structural
groups. Several unexplored crystals are also picked out as ML-proposed
candidates, and three of them are suggested as new potential NLO materials
based on further first-principle calculations. The present ML models
are expected to accelerate the inverse design for new NLO crystals
with desired properties.