🔬 materials science

Ordered-to-disordered transfer learning with graph neural networks for formation-energy and HOMO-LUMO gap prediction in high-entropy perovskite oxides

This study demonstrates that ordered-to-disordered transfer learning with graph neural networks effectively predicts formation energies in high-entropy perovskite oxides but requires supplementary HEPO-specific data and three-body geometric representations to accurately model HOMO-LUMO gaps due to their sensitivity to local chemical environments.

Original authors: Panupol Untarabut, Narjes Jomaa, Sylvian Cadars, Olivier Masson, Samuel Bernard, Assil Bouzid, Santanu Saha

Published 2026-08-03

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CC BY 4.0

Original authors: Panupol Untarabut, Narjes Jomaa, Sylvian Cadars, Olivier Masson, Samuel Bernard, Assil Bouzid, Santanu Saha

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine you are a master chef trying to invent the ultimate soup. You have a pantry full of ingredients, but instead of just picking one or two, you decide to throw in a chaotic mix of five different spices, three types of vegetables, and a handful of herbs all at once. This is the world of "high-entropy" materials: a super-complex kitchen where scientists mix many different atoms together to create new substances with amazing powers, like super-strong ceramics or materials that can conduct electricity in weird ways. The problem is, this "soup" is so messy and unpredictable that even the smartest computer simulations struggle to taste it before it's cooked. It's like trying to guess the flavor of a soup by looking at a single, perfectly arranged spoonful of ingredients, when the real pot is a swirling storm of chaos.

To solve this, scientists use a clever trick called "transfer learning." Think of it like learning to drive a car. You don't start by driving a chaotic, off-road monster truck through a mud pit; you start on a smooth, orderly highway with clear lane markers. Once you've mastered the rules of the road on that simple highway, you might be able to handle the messy mud pit with just a little extra practice. This paper asks a burning question: If we teach a computer how to predict the properties of materials using simple, orderly "highway" recipes, can it then instantly predict the properties of the messy "mud pit" high-entropy soups? And if not, how much extra practice does it actually need?

The researchers, a team from the University of Limoges in France, set out to test this idea using a specific type of material called perovskite oxides. These are like the building blocks of many modern technologies. They created a massive digital library of these materials, containing thousands of "orderly" recipes (where atoms are neatly arranged) and thousands of "disordered" recipes (where atoms are mixed up randomly, like in high-entropy perovskites). They then trained four different types of "AI chefs" (called Graph Neural Networks) to predict two things: how stable the material is (formation energy) and how it handles electricity (the HOMO-LUMO gap, which is a fancy way of saying how hard it is to make electrons jump around).

Here is what they found, and it's a tale of two very different results. First, the AI chefs were fantastic at predicting stability. When they were trained only on the neat, orderly highway recipes, they could look at the messy mud-pit high-entropy soups and guess their stability with almost the same accuracy. It turns out that the rules for how atoms stick together to stay stable are surprisingly similar, whether the kitchen is tidy or chaotic. The AI learned the "physics of sticking" so well that it didn't need to see the messy soup to know if it would hold together.

However, the story changed completely when they tried to predict the electrical properties (the HOMO-LUMO gap). The AI chefs, even the smartest ones, were terrible at guessing the electrical behavior of the messy soups if they had only seen the tidy ones. The error jumped up by about ten times! It seems that electricity is incredibly sensitive to the exact, chaotic arrangement of atoms. A tiny shift in where an atom sits in the mess changes the electrical flow, and the AI couldn't figure that out just by looking at the orderly highways.

But there is a happy ending. The researchers discovered that the AI didn't need to see all the messy soups to get good at predicting electricity. They only needed to show the AI a tiny taste—just 20% of the messy training data—mixed in with the orderly data. With this small "tasting session," the AI's predictions for the electrical properties improved dramatically, dropping the error rate from a huge 0.28 eV down to a very accurate 0.07 eV.

The team also tested different types of AI architectures. They found that the best chef was one called ALIGNN. This model is special because it doesn't just look at which atoms are neighbors; it also pays attention to the angles between them, like noticing if a bond is bent or straight. This "angle-aware" chef was much better at understanding the complex geometry of these materials than the others, proving that to understand these materials, you have to pay attention to the shape of the connections, not just the ingredients.

In short, this paper suggests that we can use simple, orderly materials to train AI to predict the stability of complex, messy high-entropy materials without much trouble. But if we want to predict how they conduct electricity, we can't just rely on the orderly training; we need to give the AI a small, specific sample of the messy reality to fine-tune its taste. It's a powerful strategy: learn the basics on the highway, then take a quick detour into the mud to master the rest.

Technical Summary: Ordered-to-Disordered Transfer Learning with Graph Neural Networks for High-Entropy Perovskite Oxides

Problem Statement
High-entropy perovskite oxides (HEPOs) represent a chemically complex class of materials with promising functional properties. However, their vast compositional space and inherent chemical/structural disorder pose significant challenges for accurate property prediction. While first-principles calculations based on density functional theory (DFT) provide a reliable framework, modeling chemical disorder is computationally prohibitive due to the need for large supercells and extensive structural relaxations. Machine learning (ML) offers a pathway to accelerate discovery, but its application to HEPOs is often limited by the scarcity of representative training data. A critical gap exists in understanding whether models trained on chemically ordered perovskites can effectively transfer knowledge to the chemically disordered HEPO domain, particularly for properties sensitive to local atomic environments.

Methodology
The authors constructed a unified DFT dataset comprising:

Ordered Domain: 10,898 relaxed structures of single ( $ABO_3$ ) and double ( $A_2BB'O_6$ ) perovskites.
Disordered Domain (HEPO): 1,810 relaxed structures generated using Special Quasirandom Structures (SQS) with nominal compositions of $A_5TiZrHfSnGeO_{15}$ (where $A \in \{Ca, Sr, Ba\}$ ).
The elemental pools for A-site ($Ca, Sr, Ba$) and B-site ($Ti, Zr, Hf, Sn, Ge$) cations were identical across both domains, isolating the effect of local chemical disorder from the introduction of new elements.

Four representative Graph Neural Network (GNN) architectures were evaluated:

CGCNN: Atom-bond graph representation (pairwise interactions).
GATGNN: Graph-based modeling with attention mechanisms.
ALIGNN: Joint operation on atomic graphs and line graphs to explicitly encode bond angles (three-body interactions).
M3GNet: Geometric three-body features and message passing for many-body environments.

The study employed two primary evaluation strategies:

Blind Transfer Test: Models trained exclusively on the ordered domain were tested on the held-out HEPO test set to assess direct transferability.
Fine-Tuning and Data Efficiency: Models were retrained by combining the ordered dataset with varying fractions (0.0 to 1.0) of the HEPO training data to determine the minimal amount of disorder-specific data required for accurate prediction.

The target properties were formation energy ( $E_f$ ) relative to binary oxides and the electronic HOMO-LUMO gap ( $E_g$ ).

Key Results

Model Performance on Ordered Domain: ALIGNN consistently outperformed other architectures for both $E_f$ and $E_g$ prediction on the ordered test set (MAE of 2.47 meV/atom for $E_f$ and 0.03 eV for $E_g$ ). This superiority is attributed to its explicit incorporation of bond-angle information, which is critical for capturing perovskite tilting and octahedral distortions.
Transferability of Formation Energy: The prediction of formation energy demonstrated strong transferability. Models trained solely on ordered perovskites achieved a blind-transfer MAE of 1.98 meV/atom on HEPOs, comparable to their performance on the ordered test set. This suggests that the structural patterns governing thermodynamic stability in ordered systems are sufficient to predict stability in disordered HEPOs.
Transferability of HOMO-LUMO Gap: In contrast, HOMO-LUMO gap prediction showed limited transferability. Blind-transfer models exhibited a systematic underestimation and a significant error increase (MAE rising from ~0.03 eV in ordered domains to ~0.28 eV in HEPOs). This indicates that electronic structure is highly sensitive to the local chemical disorder present in HEPOs, which is not fully captured by ordered-domain training.
Impact of Fine-Tuning: Incorporating a small fraction of HEPO-specific training data (20%) substantially improved HOMO-LUMO gap prediction, reducing the MAE to 0.07 eV. Full HEPO training further reduced the error to 0.04 eV. Conversely, formation energy prediction saw minimal improvement with additional HEPO data, confirming its robust transferability.
Representation Analysis: UMAP analysis of graph embeddings revealed that ALIGNN's angle-aware representation creates more compact and chemically distinct clusters compared to CGCNN. Furthermore, ALIGNN embeddings better organized structures according to octahedral tilting angles, a key structural descriptor in perovskites.

Significance and Claims
The paper claims that ordered perovskite oxides serve as an effective training foundation for screening the thermodynamic stability of high-entropy perovskite oxides, as formation energy transfers reliably across the ordered-to-disordered boundary. However, for electronic property screening (specifically HOMO-LUMO gaps), the authors assert that models trained only on ordered data are insufficient due to the sensitivity of electronic states to local disorder.

The study concludes that a practical strategy for HEPO discovery involves training graph neural networks (specifically angle-aware models like ALIGNN) on ordered perovskite datasets and then applying a small, targeted HEPO-specific calibration dataset when electronic properties are the primary target. This approach aims to reduce the computational cost of expensive HEPO DFT calculations while maintaining a clear physical connection between ordered structures, local chemical disorder, and material property prediction. The work highlights the importance of encoding three-body geometric information (bond angles) in GNNs to capture complex structure-property relationships in perovskite systems.

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