Nano Fluid Dynamics Meets Artificial Intelligence: Bifurcation, Control, and Learning-Based Stability

Abstract

This work develops a reduced-order dynamical model for ion transport and electrohydrodynamics in nano fluidic channels derived from the coupled Poisson–Nernst–Planck–Stokes equations. Spatial averaging over the channel length yields a finite-dimensional nonlinear system describing the coupled evolution of ionic concentrations, charge imbalance, and electric potential under diffusion, electromigration, and electroosmotic advection. The reduced formulation preserves the essential nonlinear electrokinetic feedback mechanisms responsible for complex dynamic behavior. Bifurcation analysis using MATCONT reveals the existence of equilibrium branches and a supercritical Hopf bifurcation at ,(Q,S,V,I)=(1.514542,0.738483,0.278626,1.446676) leading to stable limit-cycle oscillations confirmed through eigenvalue crossing and time-domain simulations. To quantify stability, a dataset of equilibrium states and Jacobian-based spectral measures is constructed for analysis and surrogate modeling. A feedforward neural network is trained to approximate the dominant eigenvalue, enabling a smooth stability indicator suitable for gradient-based optimization. The resulting surrogate is embedded into a Pyomo.DAE optimal control framework solved using IPOPT, where a differentiable soft-penalty formulation is used to suppress unstable regimes. The proposed control strategy reduces the objective function value from 16.7424 to 4.776778, demonstrating significant improvement in performance and stability regulation. Overall, the study shows that combining physics-based model reduction, numerical bifurcation analysis, and machine-learning-assisted optimal control provides an effective framework for stabilizing nonlinear nano fluidic dynamics.