NONE 20260421094643879 wseas/wseas content-registration-form+ja@crossref.org content-registration-form WSEAS TRANSACTIONS ON INFORMATION SCIENCE AND APPLICATIONS 1790-0832 2224-3402 Mohamed El-Bahnasawi nstitute for Smart Systems Technologies, Universität Klagenfurt, AUSTRIA Witesyavwirwa Vianney Kambale Faculty of Information and Communication Technology, Tshwane University of Technology, Pretoria, SOUTH AFRICA Kyandoghere Kyamakya nstitute for Smart Systems Technologies, Universität Klagenfurt, AUSTRIA This paper presents a fully analytic, neuro-symbolic forecasting pipeline that automatically extracts symbolic rules from multivariate time-series and embeds them as differentiable constraints in an Extreme Learning Machine (ELM) predictor. An ELM-based auto-encoder (ELM-AE) first learns latent descriptors in closed form; these descriptors are discretised and mined for frequent temporal patterns. Association-rule and inductive-logic discovery yield a library of Answer Set Programming (ASP) clauses. The clauses are re-encoded as hinge-loss penalties inside a second closed-form ELM forecaster (ELM-F), yielding long-horizon predictions that are both accurate and rule-consistent. The entire system trains rapidly on commodity hardware and runs in real time on microcontrollers, making it attractive for safety-critical digital-twin applications such as those for battery management systems. Beyond its novel algorithmic contributions, this paper also provides a hands-on tutorial on applying analytic ELM methods and symbolic rule integration to practical forecasting problems. 04 21 2026 04 21 2026 276 21 https://creativecommons.org/licenses/by/4.0/deed.en_US 10.37394/23209.2026.23.21 https://wseas.com/journals/isa/2026/a425109-009(2026).pdf Haoyi Zhou, Shanghang Zhang, Jieqi Peng, Shuai Zhang, Jianxin Li, Hui Xiong, and Wancai Zhang, “Informer: Beyond efficient transformer for long sequence time-series forecasting,” Proceedings of AAAI, vol. 35, no. 12, pp. 11 106–11 115, 2021, DOI: 10 . 1609/aaai.v35i12.17325. Meire Fortunato, Charles Blundell, and Oriol Vinyals, “Bayesian recurrent neural networks,” arXiv preprint arXiv:1704.02798, 2017, DOI: 10.48550/arXiv.1704.02798. 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