MAGNDATA-Trained Classifiers Overview

• MAGNDATA-trained classifiers are supervised models that leverage experimental magnetic data to predict zero versus nonzero propagation vectors.
• They employ ensemble methods like LightGBM, XGBoost, and Random Forest using compositional, structural, and electronic descriptors to optimize predictions.
• The models demonstrate high accuracy in identifying systematic ferromagnetic bias in DFT workflows, enabling scalable screening of magnetic materials.

MAGNDATA-trained classifiers are supervised learning models built from the MAGNDATA database, which provides experimentally validated magnetic structures. These classifiers are designed to diagnose and predict magnetic order in crystalline compounds using compositional, structural, and electronic descriptors sourced from high-throughput materials databases such as the Materials Project. By leveraging ground-truth physical labels, MAGNDATA-trained classifiers identify systematic biases in density functional theory (DFT) workflows and facilitate reliable large-scale screening for magnetic materials.

1. Classifier Construction and Training Strategy

MAGNDATA-trained classifiers are constructed using experimental entries from the MAGNDATA database, where each compound's magnetic ground state is well characterized. To train these models, materials from MAGNDATA are enriched with descriptors derived from the Materials Project database, forming a structured dataset suitable for machine learning.

The principal target variable is the "binary propagation vector," indicating whether the magnetic structure has a zero (ferromagnetic) or nonzero (antiferromagnetic or modulated) propagation vector. Binary classification is preferred for balance and physical relevance, as nonzero propagation vectors signal non-ferromagnetic or complex arrangements.

Learning algorithms include ensemble methods such as LightGBM, XGBoost, and Random Forest, which are trained using stratified data splits and five-fold cross-validation. Hyperparameter optimization is performed using RandomizedSearchCV to ensure robust generalization to unseen materials.

2. Descriptor Types and Feature Importance

Three primary types of descriptors are used for training:

• Compositional: One-hot encoding of elemental composition, emphasizing magnetic elements (3d transition metals, lanthanides, actinides). Feature importance analysis consistently identifies elemental composition, particularly memberships containing Mn, Fe, Co, Cr, Ni, and O, as critical.
• Structural: Crystal system labels (e.g., cubic, tetragonal), atomic density, unit cell volume, and mass density contribute to capturing symmetry and atomic packing, which affect magnetic interactions.
• Electronic: Density functional theory-derived metrics such as band gap, conduction band minimum (CBM), valence band maximum (VBM), and Fermi energy are included to account for electron localization and itinerancy.

Feature importance in ensemble models is quantified using gain-based metrics. For LightGBM, feature importance for a given feature $f$ is defined as:

$I_\text{gain}(f) = \sum_{s \in S(f)} \Delta L(s)$

where $S(f)$ contains all splits using feature $f$ and $\Delta L(s)$ is the loss function reduction at split $s$.

3. Model Performance

MAGNDATA-trained classifiers, particularly using ensemble techniques, attain high accuracy and macro F$_1$ scores:

Training Set	Model	Accuracy (%)	Macro F$_1$ Score (%)
MAGNDATA (experimental)	XGBoost	>92	~91–93
Materials Project (DFT labels)	LightGBM/XGBoost	84–86	63–66
DummyClassifier (baseline)	Dummy	$\sum_k p_k^2$	$1/C$

Performance is measured against stratified baselines: the DummyClassifier yields accuracy equal to the sum of squared class priors ($\sum_k p_k^2$) for $k$ classes, with macro F$_1$-score $1/C$ for $C$ classes.

Comparisons with prior literature confirm that these propagation-vector classifiers outperform recent machine learning efforts in distinguishing zero vs. nonzero propagation vectors. For Materials Project labels, MAGNDATA-trained classifiers reach or exceed state-of-the-art, although macro F$_1$ scores are lower due to DFT labeling bias.

4. Diagnosis of Systematic Ferromagnetic Bias

A key result of MAGNDATA-trained classifier deployment is the identification of systematic ferromagnetic (FM) bias in the Materials Project database. High-throughput DFT workflows typically default to FM initialization, leading to persistent FM labeling even for materials whose true ground states are antiferromagnetic or exhibit modulated magnetic order.

By applying MAGNDATA-trained propagation vector classifiers to the MP database, thousands of cases (7,843 compounds in the intersecting set) are flagged where the MP label is FM but the classifier predicts a nonzero propagation vector, implicating likely misclassification. This diagnosis is enabled by the contrast in label origin: MAGNDATA uses neutron-diffraction-derived physical truth, while MP relies on DFT self-consistency protocols.

5. Large-Scale Applications and Implications

MAGNDATA-trained classifiers have substantial utility for:

• Large-scale screening of magnetic classes in databases, facilitating identification of candidate materials for experimental follow-up.
• Diagnostic correction of artifacts in DFT-generated datasets, enhancing the reliability of high-throughput materials informatics.
• Detailed understanding of structure–property relationships, enabled by interpretable descriptor selection.
• Accelerating the discovery of materials with targeted magnetic properties by flagging and correcting database label errors.

A plausible implication is that continued integration of experimentally curated databases (such as MAGNDATA) and machine learning workflows will increase the trustworthiness of computational materials design, particularly where DFT methods alone are prone to initialization artifacts.

6. Mathematical Formulations

Performance analysis and feature selection in MAGNDATA-trained classifiers rely on specific mathematical structures:

• DummyClassifier accuracy: $\text{Accuracy}_\text{dummy} = \sum_k p_k^2$, $p_k$ being class prior.
• DummyClassifier macro F$_1$: $1/C$ for $C$ classes.
• LightGBM gain-based feature importance: $I_\text{gain}(f) = \sum_{s \in S(f)} \Delta L(s)$.

These formulations underpin rigorous quantification of classifier performance and feature relevance.

7. Significance for Database Construction and Future Work

MAGNDATA-trained classifiers expose and quantify labeling biases in large-scale electronic-structure databases, contributing directly to the development of more accurate materials informatics pipelines. Their application enables a corrective mechanism for systematic errors, particularly those stemming from DFT workflow choices.

The use of simple, physically motivated descriptors ensures model interpretability and makes the approach scalable to increasingly complex magnetic phenomena. Future research is likely to exploit these classifiers in database curation, automated label validation, and active learning frameworks for targeted discovery of novel magnetic materials.

This suggests an expanding role for machine learning techniques trained on high-quality experimental data in both the correction and exploration of materials databases.