A hybrid machine learning framework using fractional order dynamics to predict fish toxicity in aquatic ecosystems

Abstract

Accurate prediction of chemical toxicity to aquatic organisms remains a critical challenge in environmental risk assessment. Traditional machine-learning (ML) models capture static correlations but cannot represent time-dependent, memory-driven processes such as bioaccumulation and cumulative physiological damage. This study presents a hybrid framework that integrates an ensemble ML classifier with a system of fractional-order differential equations (FDEs) for both toxicity prediction and dynamic modeling. Using the QSAR Fish Toxicity dataset (908 compounds, six molecular descriptors), a LogitBoost classifier (MATLAB implementation of an XGBoost approximation) was trained after MRMR feature selection and SMOTE oversampling, achieving an AUC of 0.9015. The continuous probability output of this classifier serves as the external forcing function for six coupled Caputo-type FDEs that evolve the normalized molecular descriptors over a biologically motivated pseudo-time axis. The resulting hybrid model is validated by an existence-uniqueness theorem, Adams–Bashforth–Moulton numerical integration, and constrained nonlinear optimization. Risk assessment identifies compounds that exceed regulatory thresholds. The bidirectional ML–FDE architecture supplies both high predictive accuracy and explicit memory-aware mechanistic trajectories, thereby complementing purely data-driven or purely mechanistic approaches. Further experimental validation on independent datasets is warranted.