Perspectives of Machine Learning for Ligand-Field Analyses in Lanthanide-Based Single Molecule Magnets

Lanthanide-based single-molecule magnets are promising candidates for potential applications. Their magnetism is governed by ligand-field splittings, which may require up to 27 ligand-field parameters for accurate modeling. Determining these parameters reliably from measured data is a major challenge, for which machine learning approaches offer promising solutions. We provide an overview of these approaches and present our perspective on addressing the inverse problem relating experimental data to ligand-field parameters. Previously, a machine learning architecture combining a variational autoencoder (VAE) and an invertible neural network (INN) showed promise for analyzing temperature-dependent magnetic susceptibility data. In this work, the VAE-INN model is extended through data augmentation to enhance its tolerance to common experimental inaccuracies. Focusing on second-order ligand-field parameters, diamagnetic and molar-mass errors are incorporated by augmenting the training dataset with experimentally motivated error distributions. Tests on simulated experimental susceptibility curves demonstrate substantially improved prediction accuracy and robustness when the distributions correspond to realistic error ranges. When applied to the experimental susceptibility curve of the complex Al2IIIEr2III, the augmented VAE–INN recovers ligand-field solutions consistent with least-squares benchmarks. The proposed data augmentation thus overcomes a key limitation, bringing the ML approach closer to practical use for higher-order ligand-field parameters.