Hybrid nanofluids have gained significant attention for their superior thermal and rheological characteristics, offering immense potential in energy conversion, biomedical transport, and electromagnetic flow control systems. Understanding their dynamic behavior under coupled magnetic, rotational, and reactive effects is crucial for the development of efficient thermal management technologies. This study develops a neuro-fuzzy computational framework to examine the dynamics of a reactive Cu–TiO₂–H₂O hybrid nanofluid flowing through a squarely elevated Riga tunnel. The governing model incorporates Hall and ion-slip effects, thermal radiation, and first-order chemical reactions under ramped thermo-solutal boundary conditions and rotational electromagnetic forces. Closed-form analytical solutions are derived via the Laplace transform method to describe the transient velocity, temperature, and concentration fields. To complement and validate the analytical model, an artificial neural network (ANN) optimized using the Levenberg–Marquardt backpropagation algorithm (ANN-LMBPA) is trained on datasets generated in Mathematica. Regression and error analyses confirm the model’s predictive robustness, with mean squared errors ranging between ${10}^{-4}$ and ${10}^{-9}$. In addition, an Adaptive Neuro-Fuzzy Inference System (ANFIS) is developed to estimate the heat transfer rate (HTR), achieving a minimal RMSE of 0.011012 for the heat transfer coefficient (HTC). The findings reveal that rotational motion and Hall–ion slip effects suppress primary velocity but enhance secondary flow, while the modified Hartmann number (Lorentz force) accelerates both components. Thermal radiation increases fluid temperature, whereas higher Schmidt numbers and reaction rates diminish solute concentration. The HTR decreases with increasing radiation and nanoparticle volume fraction, while the mass transfer rate (MTR) improves under stronger chemical reactivity. Overall, the proposed hybrid analytical–AI framework demonstrates high accuracy and efficiency, offering valuable insights for the design and optimization of electromagnetic nanofluid systems in advanced thermal and process engineering applications.