Predictive Inorganic Synthesis based on Machine Learning using Small Data sets: a case study of size-controlled Cu Nanoparticles

TL;DR

This study demonstrates that high-quality small data can effectively drive quantitative size prediction for Cu nanoparticles synthesized via microwave-assisted polyol routes. Using Latin Hypercube Sampling, 25 in-house experiments and DLS/UV-Vis characterization form a compact dataset. An interpretable AMADEUS ensemble regression approach with a six-feature model outperforms a DoE baseline ($R^2 \approx 0.74$ vs $R^2 \approx 0.60$), enabling accurate size predictions and synthesis-route suggestions from limited data. The findings advocate data-efficient, closed-loop design of inorganic syntheses and offer a scalable pathway for broader materials synthesis optimization.

Abstract

Copper nanoparticles (Cu NPs) have a broad applicability, yet their synthesis is sensitive to subtle changes in reaction parameters. This sensitivity, combined with the time- and resource-intensive nature of experimental optimization, poses a major challenge in achieving reproducible and size-controlled synthesis. While Machine Learning (ML) shows promise in materials research, its application is often limited by scarcity of large high-quality experimental data sets. This study explores ML to predict the size of Cu NPs from microwave-assisted polyol synthesis using a small data set of 25 in-house performed syntheses. Latin Hypercube Sampling is used to efficiently cover the parameter space while creating the experimental data set. Ensemble regression models, built with the AMADEUS framework, successfully predict particle sizes with high accuracy ($R^2 = 0.74$), outperforming classical statistical approaches ($R^2 = 0.60$). Overall, this study highlights that, for lab-scale synthesis optimization, high-quality small datasets combined with classical, interpretable ML models outperform traditional statistical methods and are fully sufficient for quantitative synthesis prediction. This approach provides a sustainable and experimentally realistic pathway toward data-driven inorganic synthesis design.

Figures (16)

• Figure 1: Visualization of the workflow followed to create the data set and model the syntheses.
• Figure 2: The computational modeling starts with selecting the best performing data set. Next, the optimal value for the regularization strength $\alpha$ is selected. Then, $100$ model instances are trained on random subsets of the data set. From these an ensemble model is created through averaging over all instances. Finally, through an iterative application of feature engineering and selection next generation models are created.
• Figure 3: a) Plot of the experimentally measured particle size and their standard deviation in ascending order (black) with the corresponding predicted particle size of the fifth generation ensemble model (red); b) Parity plot of the actual, experimental size against the corresponding predicted size using the fourth generation ensemble model.
• Figure 4: a) Plot of the experimental measured particle sizes and their standard deviation (black) and the statistical model (red); b) Parity plot of the actual, experimental size against the corresponding predicted size using the statistical model.
• Figure 5: Hyperparameter optimization for size prediction with data set C. LASSO regularized polynomials up to order eight are compared, and MAE of the average ensemble models is shown for $\alpha$=1.0 (red), $\alpha$=0.1 (orange), $\alpha$=0.01 (green), and $\alpha$=0.001 (blue).