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All Journal JURNAL NASIONAL TEKNIK ELEKTRO JOMLAI: Journal of Machine Learning and Artificial Intelligence Indonesian Journal of Electronics, Electromedical Engineering, and Medical Informatics Jurnal Teknik Elektro
Tengku Reza Suka Alaqsa
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Computer Science & IT Control & Systems Engineering Decision Sciences, Operations Research & Management Electrical & Electronics Engineering Engineering Health Professions Materials Science & Nanotechnology

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Journal : JOMLAI: Journal of Machine Learning and Artificial Intelligence

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Entropy-Regularized Nonlinear Auto-Regressive Network with eXogenous Inputs (ER-NARX): A Mathematical Framework for Scalable and Robust Big Data Forecasting Using ITL and Fractional Dynamics Zulfatri Aini; Tengku Reza Suka Alaqsa
JOMLAI: Journal of Machine Learning and Artificial Intelligence Vol. 4 No. 4 (2025): Desember 2025
Publisher : Yayasan Literasi Sains Indonesia

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.55123/jomlai.v4i4.6689

Abstract

This study proposes the Entropy-Regularized NARX (ER-NARX) model, which integrates nonlinear autoregressive modeling, entropy-based regularization, and information-theoretic learning for big data forecasting. The NARX model captures temporal dependencies between past outputs and exogenous inputs, while entropy regularization is incorporated to control the uncertainty of model predictions and prevent overfitting. The innovation of this model is its ability to control information flow through entropy regularization, which helps balance predictive accuracy with uncertainty, preventing the model from becoming overly deterministic. By combining these components, the ER-NARX model enhances the stability and robustness of the forecasts and improves its generalization to complex, high-dimensional data. Additionally, fractional dynamics are employed to model long-range memory effects in temporal data to enhancing the model's ability to handle datasets with extended dependencies. The resulting ER-NARX framework provides a mathematically grounded approach to big data forecasting improved performance in a computationally efficient manner. Future research may explore advanced entropy regularization techniques and apply the model to more diverse real-world data with intricate dependencies.
Quantum-Entropy NARX (Q-ENARX): A Mathematical Framework for Forecasting Based on Quantum Information Theory and Nonlinear Dynamic Regularization Tengku Reza Suka Alaqsa; Syarifah Adriana
JOMLAI: Journal of Machine Learning and Artificial Intelligence Vol. 4 No. 4 (2025): Desember 2025
Publisher : Yayasan Literasi Sains Indonesia

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.55123/jomlai.v4i4.6722

Abstract

This study addresses the limitations of conventional nonlinear autoregressive models, which struggle to maintain stability and generalization in high-dimensional, non-stationary forecasting environments. The research aims to develop a mathematical framework that integrates deterministic dynamics with probabilistic uncertainty through the proposed Quantum-Entropy NARX (Q-ENARX) model. The methodology combines nonlinear autoregressive modeling, entropy-based trust-region optimization, and quantum information theory to establish a unified formulation for dynamic forecasting. The model embeds NARX states into a quantum Hilbert space, introduces an entropy-regularized loss function to balance accuracy and uncertainty, and employs a quantum Fisher Information Matrix for curvature-aware optimization. Analytical derivations reveal that Q-ENARX achieves enhanced stability, improved generalization, and robust convergence by leveraging quantum state dynamics, entropy-energy duality, and fractional learning operators. The results shows that the integration of entropy and quantum principles transforms traditional NARX forecasting into a probabilistically interpretable and physically grounded framework capable of capturing complex temporal correlations with high mathematical precision.
Co-Authors Guido, Muhammad Guido Randa Febiant Liliana Nanda Putri Miefthawati Syarifah Adriana Zulfatri Aini