Metric-Based Machine-Learning Forecast of Non-Stationary Process Dynamics

This paper addresses the challenge of online forecasting for inherently unstable technological processes—such as chaotic gas- and hydrodynamic flows—by leveraging metric-based machine-learning algorithms. Traditional models, including the Wold decomposition and stationary Gaussian noise assumptions, fail to capture the complex interplay of deterministic chaos and stochastic fluctuations present in turbulent environments. To overcome these limitations, the authors propose a precedent-based forecasting framework in which the current state is compared, via a chosen similarity metric, against historical segments ("analogs") drawn from a high-dimensional retrospective database. Forecasts are then generated by extrapolating the observed evolution following the most similar past situations, with accuracy improvements achieved through multi-analog averaging and similarity-weighted ensembles. Empirical validation on real-world oil-refining process data demonstrates that the metric approach can maintain relative prediction errors within 2–3% over one-hour horizons. The paper further discusses the extension to multivariate series using Mahalanobis and information-theoretic metrics, highlighting the method’s adaptability to nonstationary, heteroskedastic data. This work illustrates a promising, data-driven alternative to classical statistical and deterministic chaos models for real-time control of complex industrial processes.