Keeping the Whole Model Family: Bootstrap-Aggregated Phenomenological Ensembles for Mining and Industrial Process Data

Abstract

Industrial practice fits a family of candidate phenomenological models to process data and then keeps one winner, selected by R2 or an information criterion. That discards the evidence about model form and leaves the reported prediction without the uncertainty that model form carries. We define BAPE, bootstrap-aggregated phenomenological ensembles: the random-forest recipe with curated closed-form process models as base learners, crossing three diversity axes (model family, parameter multistart, data resample) and adding a fourth borrowed from Ensemble-SINDy, random subsampling of the family library itself. The ensemble returns a calibrated predictive distribution together with per-family inclusion probabilities, so the output is which mechanism the evidence supports and how wide the prediction is, inside and outside the operating envelope. We implement a bank of 48 cited families across seven unit processes (flotation, comminution, thickening, leaching, process dynamics, thermal power and plant utilities), and evaluate twelve methods (from single-best-fit to Bayesian model averaging, Gaussian-process discrepancy hybrids, deep ensembles and a mixture of phenomenological experts) over 137 case variants that include a real 737,453-row iron ore flotation circuit, digitized published laboratory series, real Bond grindability tests, reaction curves from an industrial process-control benchmark, and eleven years of measured national water and electricity records. On unit-free rank aggregation over 1,627 method-variant rows, 6 methods place ahead of the single-best-fit control under extrapolation; Bayesian model averaging is the best calibrated (interval-score rank 3.85, coverage 0.82 against a nominal 0.90); and Bayesian model averaging identifies the generating family most often (62.0 percent exact recovery). BAPE itself ranks 6.42 against 6.09 for the control and leads on the published settling series; the stable conclusion is about the class of methods, not about one rung. Deep ensembles and Ensemble-SINDy, implemented with unit-consistent constants, place behind the control. The real plant yields the sharpest industrial result: its residence time varies by about five percent while recovery moves ten points, so kinetics are not identifiable from normal operation and equifinality, not a rate constant, is the correct answer. Engine (MIT, PyPI phenoforge): https://pypi.org/project/phenoforge/ ; https://github.com/fsantibanezleal/CAOS_PhenoForge . The case registry, extraction scripts and benchmark are held in a private repository and are available from the author on request.