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All Journal Jurnal Edukasi Elektro JURNAL NASIONAL TEKNIK ELEKTRO Journal of Energy, Mechanical, Material and Manufacturing Engineering JOMLAI: Journal of Machine Learning and Artificial Intelligence Engineering Science Letter Jurnal Pengabdian Masyarakat Bangsa Indonesian Journal of Electronics, Electromedical Engineering, and Medical Informatics Jurnal Teknik Elektro
Tengku Reza Suka Alaqsa
Universitas Islam Negeri Sultan Syarif Kasim Riau
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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 Altof, Muhammad Sayid Arbi, Arbi Ardila, Melati Eng, Ewe Win Fadilah Fadilah, Fadilah Farhan, Aulia Muhammad Juliana Juliana Liliana Liliana Liliana Lindasari, Ewil Maulana, Hamsah Muhammad Guido Randa Febiant Guido Nanda Putri Miefthawati Rahmadeni Safka, Lutvi Nabilla Sri Basriati Syarifah Adriana Zahra, Annisa Zulfatri Aini