Equation-Free Screening of Mittag-Leffler-Compatible Dynamics from Scalar Time Series via kNN Multi-Horizon Profiles
Abstract
We study an equation-free screen for finite-window Mittag-Leffler compatibility, in which multihorizon relaxation profiles are constructed out of sample by k-nearest-neighbor prediction from ensembles of scalar trajectories and compared with candidate temporal laws. The screen assesses compatibility, not the generating mechanism. In a matched, noise-free calibration, it reproduces the generating Mittag-Leffler behavior to numerical precision, while relaxation-rate heterogeneity shifts the fitted Mittag-Leffler order toward lower values. For noise-free classical distributed-rate ensembles, a Mittag-Leffler preference over a single exponential disappears when a biexponential alternative is included. Under observational noise, this recovery is incomplete: with three candidate families, the Mittag-Leffler law is still selected in 60% of runs for a classical ensemble, against 72% for a fractional reference. In the tested noise-free settings, simpler profile constructions reproduce the screening decisions, whereas kNN predicts individual trajectories far more accurately than a constant predictor. The screening interpretation of a single-record example, initially investigated as a chaotic test case, is withdrawn as evidence about the continuous system after numerical verification revealed a nonrobust simulated regime. Mittag-Leffler compatibility is therefore a comparative, condition-dependent screening outcome, not identification of fractional origin.
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BibTeX
@misc{ngbo2026equationfree,
title = {{Equation-Free Screening of Mittag-Leffler-Compatible Dynamics from Scalar Time Series via kNN Multi-Horizon Profiles}},
author = {N'Gbo N'Gbo and Andrei Velichko and Bruno Carpentieri},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2607.08588},
eprint = {2607.08588},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2607.08588},
}
RIS
TY - UNPB
TI - Equation-Free Screening of Mittag-Leffler-Compatible Dynamics from Scalar Time Series via kNN Multi-Horizon Profiles
AU - N'Gbo N'Gbo
AU - Andrei Velichko
AU - Bruno Carpentieri
PY - 2026
DA - 2026/10/29
PB - arXiv
DO - 10.48550/arxiv.2607.08588
UR - https://arxiv.org/abs/2607.08588
AB - We study an equation-free screen for finite-window Mittag-Leffler compatibility, in which multihorizon relaxation profiles are constructed out of sample by k-nearest-neighbor prediction from ensembles of scalar trajectories and compared with candidate temporal laws. The screen assesses compatibility, not the generating mechanism. In a matched, noise-free calibration, it reproduces the generating Mittag-Leffler behavior to numerical precision, while relaxation-rate heterogeneity shifts the fitted Mittag-Leffler order toward lower values. For noise-free classical distributed-rate ensembles, a Mittag-Leffler preference over a single exponential disappears when a biexponential alternative is included. Under observational noise, this recovery is incomplete: with three candidate families, the Mittag-Leffler law is still selected in 60% of runs for a classical ensemble, against 72% for a fractional reference. In the tested noise-free settings, simpler profile constructions reproduce the screening decisions, whereas kNN predicts individual trajectories far more accurately than a constant predictor. The screening interpretation of a single-record example, initially investigated as a chaotic test case, is withdrawn as evidence about the continuous system after numerical verification revealed a nonrobust simulated regime. Mittag-Leffler compatibility is therefore a comparative, condition-dependent screening outcome, not identification of fractional origin.
ER -