Japanese team develops explainable AI for predicting high-dimensional material spectra

A team from the Tokyo Institute of Science in Japan has proposed an interpretable, deep learning-based method for material spectra, using the ALIGNN model to predict high-dimensional optical absorption spectra. The study constructed a first-principles computational dataset comprising 2,681 materials, achieving a mean absolute error (MAE) below 0.14 for predicted absorption spectra and an R² of 0.950 for onset energy prediction, significantly improving agreement with experimental spectra. The method successfully identified the key elemental types and coordination environments governing optical absorption properties, providing an interpretable framework for machine learning applications in materials science.

Article author and source: HyperAI

The calculated results show significantly improved agreement with reported experimental spectra.

A research team from the Tokyo Institute of Science in Japan has proposed an interpretation method for deep learning models that significantly improves the agreement between experimental spectra and high-dimensional spectral data in materials science.

In recent years, machine learning has garnered significant attention in the field of materials science, with applications evolving from early scalar property predictions—such as bandgap energy, point defect formation energy, and melting point—to more complex high-dimensional physical quantity modeling, one of the most challenging directions being the prediction and interpretation of material spectra.

Spectral data such as the dielectric function, spectra (absorption, reflection, and emission), and electron and phonon density of states are crucial for understanding and designing materials. However, compared to scalar properties, high-dimensional spectral data exhibit large output dimensions, complex structures, and strong physical constraints, making it difficult for traditional machine learning methods to simultaneously achieve both accuracy and interpretability. Although deep learning models have made some progress in predicting spectra, the lack of interpretability remains a key bottleneck limiting their further application in materials design.

Under this context, a research team from the Tokyo Institute of Science proposed an interpretation method for deep learning models that significantly improves the agreement between experimental spectra and high-dimensional spectral data in materials science.

Researchers also developed a high-accuracy predictive model for optical absorption spectra using this dataset and the ALIGNN algorithm. By combining feature extraction with clustering analysis, they successfully identified the key elemental species and their coordination environments that primarily determine the onset energy and intensity of optical absorption.

The related research findings were published in Advanced Intelligent Discovery under the title "Deep Learning–Based Extraction of Promising Material Groups and Common Features from High-Dimensional Data: A Case of Optical Spectra of Inorganic Crystals".

Research Highlights:

• This study proposes a method for material classification by extracting features from high-dimensional spectral data and performing clustering analysis to identify latent material groups and their common characteristics.
• The first-principles computational dataset and machine learning model developed in this study are expected to play a significant role in future materials discovery and materials informatics research.
• The method proposed in this study has broad applicability and can be used for the classification and interpretation of various types of spectral data, extending beyond the absorption spectra of inorganic crystals.

Paper URL: https://advanced.onlinelibrary.wiley.com/doi/10.1002/aidi.202600007

Researchers first screened oxides, chalcogenides, and related materials from the Materials Project database that met the following criteria: (1) the material contains at least one of O, S, or Se, and their oxidation states are not necessarily −2; (2) the material does not contain any of the following elements: H, halogens, noble gases, Mn–Ni, Tc–Rh, Os–Ir, Po, lanthanides (except La and Ce), or actinides; (3) the material does not exhibit spin polarization; (4) systems with space group P1 and/or more than 40 atoms in the primitive unit cell were excluded due to excessive computational cost or uncertainty in crystal structure.

A total of 9,808 materials were ultimately used for first-principles calculations, and the computational database was constructed according to the process shown below.

Workflow for constructing a first-principles calculation database of dielectric functions for metal oxides, chalcogenides, and related compounds

As shown, the computational workflow is highly complex. To perform high-throughput calculations while maintaining consistency and efficiently utilizing computational resources, researchers employed a custom-developed program and relied on tools such as pymatgen, FireWorks, Custodian, atomate, and vise to automate the process. All first-principles calculations were carried out using the VASP software package. This workflow generates optical absorption spectra and compound formation energies based on PBEsol(+U) calculations, and obtains band structures using the nsc-dd hybrid functional and PBEsol(+U) calculations.

Regarding the machine learning dataset, researchers removed: (1) materials that were unstable relative to competing phases in the local database; (2) materials with a PBEsol(+U) band gap less than 0.3 eV. The final dataset retained 2,681 materials.

Building a machine learning model based on light absorption spectra using ALIGNN and its prediction accuracy

At the model level, this study employs ALIGNN (Atomistic Line Graph Neural Network) as the core predictive framework for modeling high-dimensional optical absorption spectra. Compared to traditional crystal graph convolutional networks (CGCNN), ALIGNN’s key advantage lies in its dual representation—incorporating both an atomic graph and a bond line graph—to explicitly encode three-body angular information, enabling a more refined representation of local structural environments. The upper portion of the figure below illustrates the ALIGNN architecture.

Overall schematic of the ALIGNN model and the proposed interpretive method for optical absorption spectroscopy prediction

Within this framework, atoms are represented as nodes, bonds between atoms as edges, and the relationships between edges are further modeled as a line graph, transforming bond angle information into learnable structural features. This design enables the model to capture not only pairwise distance information but also three-body interactions, better reflecting realistic crystalline physical behavior.

Feature extraction and clustering

Researchers performed feature extraction on the first layer, ALIGNN, of the optimized model, averaged the feature vectors across all atomic sites for each material, and then conducted hierarchical clustering analysis, as shown in the lower part of the figure above. This approach aims to classify materials into groups that exhibit similarity in both input features (such as elemental composition and atomic coordination features, including the number of neighboring atoms, interatomic distances, and bond angles) and output properties (optical absorption spectra).

The figure below shows the optical absorption spectra of 96 groups obtained through hierarchical clustering; the spectral shapes within each cluster are indeed similar, confirming the effectiveness of the clustering method used in this study.

Spectral classification results obtained through hierarchical clustering

Researchers conducted a series of experiments to validate the capability of a new deep learning model in handling high-dimensional spectral data in materials science:

Predictive performance capability

In terms of predictive performance, the ALIGNN model demonstrates high overall accuracy on the test set, as shown in the figure below, where approximately 75% of the predicted material absorption spectra have a mean absolute error (MAE) below 0.14, indicating that the model can effectively reproduce complex spectral shapes.

Prediction results for the optical absorption spectra of the test set using the optimized ALIGNN model

The right panel of the figure above shows the prediction results for the four materials with the largest errors in each quartile range. For materials in the first three quartiles, the ALIGNN predictions (colored curves) agree well with the first-principles reference calculations (black curves). However, some compounds in the fourth quartile exhibit significant deviations at the onset of their optical absorption spectra; these outlier samples show poor prediction performance, primarily due to their unique electronic structures and insufficient representation of similar materials in the training dataset.

Ability to detect the starting position of the optical absorption spectrum

Although MAE is a global metric covering the entire spectrum, researchers further investigated whether the model could accurately reproduce the local spectral onset energy. The figure below presents a parity plot comparing the lowest photon energy at which log₁₀ α(ω) first exceeds 2.5, where α represents the absorption coefficient, between first-principles calculations and ALIGNN predictions.

Parity plot of the starting energy for the test set spectrum

The results show an R² of 0.950 and an MAE of 0.353 eV for the onset energy prediction, indicating that the ALIGNN model can accurately capture the onset position of the optical absorption spectrum.

Explainability Analysis

In terms of interpretability analysis, researchers extracted feature representations from the first layer of ALIGNN and performed hierarchical clustering on the materials, resulting in 96 material groups. The results showed that materials within the same cluster exhibit high consistency in spectral shape, particularly in terms of absorption onset and the steepness of the absorption edge, indicating that the model has learned spectral-relevant structural feature representations already in its early layers.

Further case analysis reveals distinct physical differences among material groups. For example, Cluster 74 typically consists of materials with a wide bandgap and a high absorption coefficient near the spectral onset. As shown in Figure a, all materials in this cluster contain V or Cr elements, with other cations primarily being alkali metals. These materials predominantly exist in the forms of VO₄³⁻, CrO₄²⁻, or Cr₂O₇²⁻, with the cations in a tetrahedral coordination environment.

Optical absorption spectrum of substances belonging to cluster 74, where α denotes the absorption coefficient.

Researchers used the CrystalFingerprintNN implementation in matminer to calculate the tetrahedral coordination index for cationic sites in each material within the cluster and analyzed the distribution of the maximum values across all cationic sites. As shown in Figure b, most materials indeed exhibit tetrahedrally coordinated sites.

Tetrahedral coordination similarity distribution between Cluster 74 material (red) and the full dataset (blue)

From the electronic density of states, sharp peaks near the conduction band minimum (CBM) can be observed, arising from V-d or Cr-d states. The high oxidation states of V⁵⁺ and Cr⁶⁺ provide a large number of unoccupied electronic states available for optical transitions. Therefore, from the perspectives of solid-state chemistry and physics, it is reasonable that these vanadates, chromates, and dichromates exhibit high optical absorption coefficients.

This process of inferring chemical mechanisms from "model clustering results" transforms machine learning outcomes from black-box predictions into actionable knowledge for materials design. Additionally, the study compared clustering results based directly on raw spectral data and found that, while it could identify similar spectra, it struggled to form clear chemical structure groupings, resulting in severe mixing of material types. This further demonstrates the advantage of the ALIGNN feature space in achieving consistent representation of structure–property relationships.

The significance of this study lies not only in the development of a high-precision optical absorption spectrum prediction model, but more importantly in proposing a framework that integrates "deep learning representation learning" with "physical interpretation of materials." By combining the ALIGNN model with hierarchical clustering analysis, the study enables the extraction of common patterns from high-dimensional spectral data, allowing machine learning models not only to predict outcomes but also to reveal the structural and electronic origins underlying those outcomes.

Ideally, electron-hole interactions, electron-phonon coupling, and the effects of point defects should be incorporated to accurately reproduce excitonic effects, phonon-assisted electronic transitions, and defect-related spectral features. However, high-throughput first-principles spectral calculations including these effects are computationally prohibitive, and thus were not implemented in this study. Nevertheless, as more accurate many-body computational methods continue to integrate with machine learning models, such approaches are expected to play an increasingly central role in materials discovery, advancing material design from experience-driven toward a new paradigm that fuses data-driven and mechanism-driven approaches.