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Open Access

ARTICLE

Large-Scale Formation Energy Prediction in One Million Crystalline Materials Using Deep Learning and Principal Component Analysis

Muhammad Imran1, Javed Ferzund2, Ateeq Ur Rehman Butt1, Abdul Noman1, Hessa Alfraihi3, Mohamad Khairi Ishak4,*
1 Department of Computer Science, Faculty of Computing, Engineering & Technology, University of Kamalia, Toba Tek Singh, Pakistan
2 Department of Computer Science, Comsats University Islamabad, Sahiwal Campus, Sahiwal, Pakistan
3 Department of Information Systems, College of Computer and Information Sciences, Princess Nourah Bint Abdulrahman University, Riyadh, Saudi Arabia
4 Department of Computer Engineering, College of Computing and Informatics, University of Sharjah, Sharjah, United Arab Emirates
* Corresponding Author: Mohamad Khairi Ishak. Email: email

Computers, Materials & Continua https://doi.org/10.32604/cmc.2026.089520

Received 21 July 2026; Accepted 04 September 2026; Published online 20 September 2026

Abstract

Predicting the formation energy of crystalline materials with high accuracy and low computational cost is important for accelerating large-scale materials screening. This study presents a systematic comparison of four deep learning architectures multi-layer perceptron (MLP), deep neural network (DNN), recurrent neural network (RNN), and long short-term memory (LSTM) and three classical machine-learning regressors, namely random forest, support vector regression, and gradient boosting. The models were evaluated using one million DFT-computed crystalline-material records containing nine structural and electronic descriptors, with an 80:10:10 train/validation/test split. Principal component analysis (PCA) reduced the numerical descriptor space from nine variables to six components retaining 95.1% of the variance. Under the original descriptor configuration, the DNN showed the lowest error among the evaluated models, and PCA was associated with a further reduction in error and faster convergence. However, energy_per_atom is included among the predictors and is mathematically related to formation_energy_per_atom; therefore, the very low absolute errors obtained in this configuration may be affected by target leakage and should not be interpreted as leakage-free estimates of generalization performance. Feedforward architectures consistently outperformed recurrent models on the tabular descriptor representation. The reliability of the comparative workflow was further assessed through independent held-out testing, training-set-only preprocessing, repeated-run statistical evaluation, and comparison across seven algorithms spanning deep and classical machine-learning paradigms. The study therefore provides a large-scale comparative benchmark and a preprocessing analysis, while highlighting the need for leakage-controlled descriptors, categorical treatment of crystallographic labels, and source-aware validation in future evaluations.

Keywords

Formation energy prediction; deep learning; materials informatics; DNN; LSTM; PCA; big data; chemical stability; surrogate modelling; high-throughput screening

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