This work presents a hybrid model that integrates a mechanistic multicomponent transport scheme in hollow-fiber membranes with an Adaptive Neuro-Fuzzy Inference System (ANFIS). The physical model incorporates pressure drops on the feed and permeate sides (Hagen–Poiseuille), non-ideal gas behavior (Peng–Robinson equation of state), and temperature-dependent viscosity; species permeances are treated as constant for model validation. After validation, a post-validation parametric exploration of permeance variability is carried out by perturbing the methane (CH₄) permeance by one decade up and down. From an initial set of 18 variables, 4 key parameters were selected through rigorous statistical analysis (Pearson correlation, variance inflation factor (VIF), and mean absolute error (MAE)); likewise, other physical criteria have been considered: permeance, retentate volume, retentate pressure, and retentate viscosity. Trained with 70% of the simulated data and validated with the remaining 30%, the model achieves a coefficient of determination (R²) close to 0.999 and a root mean square error (RMSE) below 8 × 10⁻⁸ m³/h in predicting the methane volume in the retentate, effectively responding to both steady and dynamic fluctuations. The combination of first-principles modeling and adaptive learning captures both steady-state and dynamic behavior, positioning the approach as a viable tool for real-time analysis and supervisory control in petrochemical membrane operations.

The separation of Natural Gas/CO₂ using hollow fiber membranes is essential for industrial applications, particularly in the oil and gas sector. Traditional modeling approaches, such as «black-box» models based on artificial neural networks (ANNs), offer high accuracy in parameter estimation but lack physical interpretability, making them unreliable for large-scale applications with variable operating conditions. Conversely, «white-box» models, grounded in physical laws and conservation principles, provide better scalability and physical insight but often require complex derivations and exhibit high uncertainty when experimental data is insufficient or when key parameters, such as gas permeabi- lity, must be inferred from empirical correlations.

This paper introduces a modified soft margin optimal hyperplane (MSMOH) model that integrates the kernel trick for heart disease classification. The optimal hyperparameters for each kernel are determined using particle swarm optimization (PSO), aiming to minimize the difference between desired and achieved test accuracy in a 5-fold cross-validation setup. The performance of MSMOH is compared against a random forest (RF) classifier. Results show that the MSMOH with radial basis function (RBF) kernel achieves the most balanced and accurate performance, outperforming RF and other MSMOH kernels in both accuracy and F1-score. These findings demonstrate the potential of MSMOH as a reliable support vector machine (SVM) variant for medical diagnosis tasks, particularly combined with metaheuristic optimization.