Crystals with practical applications are constrained by a variety of requirements. To quickly pick up the candidates from a huge amount of structures, whether experimentally or theoretically, is always is longstanding pursuit. In this study, we use the booming machine learning (ML) technique to explore such a roadmap for nonlinear optical crystals. In consideration of lacking adequate data about the second-harmonic generation, we put the phase matching performance as one of the most primary requisites and screening materials with excellent phase matching traits as the first step. We train the ML model based on the graph neural networks, modeling crystal structures as atomic graphs, achieving a mean absolute percentage error $<5\%$ on the test set. By using the model to predict refractive indices both at 1064 nm and 532 nm, we screen out three moderate birefringence materials, ${\mathrm{H}}_4{\mathrm{CN}}_2\mathrm{O},{\mathrm{KBO}}_2$, and ${\mathrm{RbN}}_3$ from the Materials Project database and give out their phase matching condition. After the step, we employ the first-principles calculation to verify the candidate of nonlinear optical crystals for these three materials and find ${\mathrm{H}}_4{\mathrm{CN}}_2\mathrm{O}$ exhibiting second-harmonic generation response. Our study demonstrate a potential roadmap for a quick screening out of practical nonlinear optical crystals by using present ML methods under inadequate data specified on nonlinear optical crystals.

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• Nonlinear optics
• Nonlinear optical materials
• Machine learning
• Training models