ELM meets ASP – Automatic Rule Discovery for Real-Time Long-Term Time-Series Forecasting using ELM Auto-Encoders and Rule-Aware ELM Predictors

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.