Machine Learning for Second‐ and Third‐Harmonic Generation: Benchmarks, Challenges, and a Roadmap for Data‐Driven Photonic Materials

ABSTRACT

Nonlinear optical (NLO) processes, particularly second‐ and third‐harmonic generation (SHG and THG), are central to modern photonics, enabling frequency conversion, ultrafast signal processing, and nonlinear imaging technologies. The discovery and optimization of efficient NLO materials remain challenging due to the complex interplay between structural symmetry, electronic band structure, and higher‐order light‐matter interactions, as well as the high cost and limited scalability of conventional experimental and computational approaches. Machine learning (ML) is increasingly adopted as a complementary framework to accelerate the prediction, screening, and inverse design of nonlinear susceptibilities. However, existing efforts remain fragmented, often limited to χ ⁽²⁾ ‐dominated systems, constrained material classes, and non‐standardized benchmarking practices, while higher‐order nonlinearities such as χ ⁽³⁾ remain underexplored. In this review, ML methodologies applied to SHG and THG are critically synthesized, with emphasis on descriptor design, dataset construction, model architectures, performance evaluation, and uncertainty quantification. Key challenges, including data scarcity, dataset heterogeneity, limited transferability, and insufficient incorporation of physical constraints, are systematically analyzed. Benchmarking considerations are discussed, and a roadmap for physics‐informed and uncertainty‐aware ML frameworks is outlined to support reproducible and scalable discovery of advanced NLO materials.