Overcoming Small Data Limitations in Materials Informatics: Interpretable Predictive Modeling of Optical Limiting Efficiency Using the CORRELATO Algorithm

This work addresses the fundamental challenge of predicting the efficiency of optical limiters (OLs): a critical class of materials for protecting sensitive optical components from intense laser radiation. While traditional approaches, including quantum-chemical calculations and machine learning (ML), face limitations such as high computational cost, data scarcity, and poor interpretability, we introduce and validate a novel methodology based on the CORRELATO algorithm. This hybrid approach integrates principles of nonlinear regression, symbolic regression, and factor analysis and is specifically optimized for small data sets. It enables the discovery of complex, interpretable analytical relationships between the molecular structure and macroscopic functional properties. The study was systematically conducted on a series of 24 specially synthesized low-symmetry phthalocyanine dyes, including monomers and dimers. Their nonlinear optical (NLO) response was experimentally characterized using Z-scan measurements at 532 nm, while key electronic structure descriptors (HOMO-LUMO gap, dipole moment, polarizability, and first hyperpolarizability) were obtained from DFT/M06-2X calculations. Applying the CORRELATO algorithm to this unified data set, we derived, for the first time, explicit analytical expressions for predicting the integral OL activation speed, marking a transition from qualitative classification to precise quantitative forecasting. A key achievement is the development of an iterative optimization procedure based on CORRELATO, which significantly refines the predictive models and reduces the mean absolute percentage error (MAPE). Furthermore, a clustering strategy utilizing the local nonlinear response density was implemented, enabling the construction of highly accurate cluster-specific models (MAPE <5% for one cluster). The obtained analytical criteria provide deep insights into the structure-property relationships, identifying polarizability, dipole moment, and the charge-transfer integral as the most critical parameters governing OL performance. Thus, this research establishes a comprehensive framework for the targeted design of high-performance optical limiters, demonstrating the CORRELATO algorithm as a powerful and interpretable tool for accelerated material screening and optimization, particularly under the constraints of limited experimental data.