In this study, stochastic numerical treatment is presented for boundary value problems (BVPs) arising in nanofluidics for nonlinear Jeffery–Hamel flow (NJ-HF) equations using feed-forward artificial neural networks (ANNs) optimized with bio-inspired computing based on genetic algorithms (GAs) integrated with the active-set method (ASM). NJ-HF equations associated with both convergent and divergent channels, involving nanoparticles, are derived from the transformation of Navier–Stokes partial differential equations to nonlinear BVPs of third-order ordinary differential equations. The mathematical model of the transformed BVPs is developed with the help of ANNs in an unsupervised manner and the design parameters of these networks are trained with GAs, ASM, and GA–ASM. The design scheme is evaluated for NJ-HF by taking water as a base fluid containing three different types of nanomaterials: copper (Cu), alumina (Al₂O₃), and titania (TiO₂) under various scenarios based on the angle of the channels and Reynolds numbers. Accuracy and convergence of the designed scheme are validated through comparison with standard numerical results using the Adams method.

In this paper, a defused decision boundary which renders misclassification issues due to the presence of cross-pairs is investigated. Cross-pairs retain cumulative attributes of both classes and misguide the classifier due to the defused data samples’ nature. To tackle the problem of the defused data, a Tomek Links technique targets the cross-pair majority class and is removed, which results in an affine-segregated decision boundary. In order to cope with a Theft Case scenario, theft data is ascertained and synthesized randomly by using six theft data variants. Theft data variants are benign class appertaining data samples which are modified and manipulated to synthesize malicious samples. Furthermore, a K-means minority oversampling technique is used to tackle the class imbalance issue. In addition, to enhance the detection of the classifier, abstract features are engineered using a stochastic feature engineering mechanism. Moreover, to carry out affine training of the model, balanced data are inputted in order to mitigate class imbalance issues. An integrated hybrid model consisting of Bi-Directional Gated Recurrent Units and Bi-Directional Long-Term Short-Term Memory classifies the consumers, efficiently. Afterwards, robustness performance of the model is verified using an attack vector which is subjected to intervene in the model’s efficiency and integrity. However, the proposed model performs efficiently on such unseen attack vectors.