Machine Learning for Predicting Magnetization from X-ray Diffraction of Iron Oxide Nanoparticles Using Simple Physics-Based Data Generation

TL;DR

ML models are developed to predict magnetization from X-ray diffraction for iron oxide nanoparticles, showing that the RF model excels at predicting the high magnetic field values, which is key for determining the success of an iron oxide nanoparticle synthesis for applications like magnetic particle imaging, thermal magnetic particle imaging (T-MPI), and hyperthermia.

Abstract

Automation and high-throughput characterization and synthesis for material development are becoming increasingly common; these approaches require machine learning (ML) tools to assess material properties, ideally based on a single measurement. Here, ML models are developed to predict magnetization from X-ray diffraction (XRD) for iron oxide nanoparticles. Our approach is to first develop a set of simulated data that links modulated XRD, based on a crystallographic information file (CIF), to a simple magnetic model to determine magnetization at a given magnetic field, thereby enabling us to train Random Forest and Gradient Boosting regression models on a large amount of simulated data. The models are validated by synthesizing iron oxide nanoparticles and measuring their crystal structure via XRD and room-temperature magnetization curves. In doing so, we can fine-tune both the training hyperparameters and the optimal size of the simulated datasets used to train the models. Through this optimization, the best models can achieve an $R^2$ greater than 0.9 for five experimental samples, used for tuning, for predicting the max magnetization (at 2.8 T) of the measurement. Lastly, we demonstrate reasonable predictions on the full magnetization vs. magnetic field curve, showing that the RF model excels at predicting the high magnetic field values, which is key for determining the success of an iron oxide nanoparticle synthesis for applications like magnetic particle imaging (MPI), thermal magnetic particle imaging (T-MPI), and hyperthermia.

Figures (5)

• Figure 1: Workflow schematic of simulated data generation, model validation, and tuning based on inference using experimental datasets.
• Figure 2: Possible pairs of XRD and magnetization (M) vs. magnetic field (B) for iron oxide nanoparticles that could be generated in a given dataset of size N. XRD and magnetization vs. magnetic field for Fe$_3$O$_4$ (a,c), FeO (b,d), and mixture of FeO/Fe$_3$O$_4$ (e,f).
• Figure 3: RF regression model predictions of max magnetization vs. true max magnetization value on 20 % holdout data on N = 1000 dataset with R$^2$, MAE, and RMSE metrics, ideal line to indicate 1:1 correspondence (a), corresponding RF feature importance analysis, looking at change in $R^2$ with 2$\theta$ (b). GB regression model predictions of max magnetization vs. true max magnetization value on 20 % holdout data on N = 1000 dataset with $R^2$, MAE, and RMSE metrics, ideal line to indicate 1:1 correspondence (c), corresponding GB feature importance analysis, looking at change in R$^2$ with 2$\theta$ (d).
• Figure 4: Raw experimental XRD (background subtraction only) data of five iron oxide nanoparticle samples (a), experimental XRD after pre-processing for inference (b), RF model prediction of max magnetization vs. experimentally measured max magnetization (c), GB model prediction of max magnetization vs. experimentally measured max magnetization (d), in both cases the error in prediction is taken as the RMSE of the models prediction of holdout simulated data and the error in experimental max magnetization is estimated as 10 % of the sample mass. Experimental measurements of magnetization vs. magnetic field, the max magnetization corresponds to the value at maximum magnetic field about 2.8 T (e).
• Figure 5: Prediction metrics for the RF model at each magnetic field value for holdout simulated data (a), full M-B curve RF prediction on holdout simulated data (b, c), and full M-B curve RF prediction compared to the experimentally measured M-B curves for the five iron oxide nanoparticle samples (d-h).