Application of Artificial Intelligence in Mathematical Modeling and Numerical Investigation of Transport Processes in Electromembrane Systems

To enhance desalination efficiency and reduce experimental costs, the development of ad-13 vanced mathematical models for EMS is essential. In this study, we propose a novel hy-14 brid approach that integrates neural networks with high-accuracy numerical simulations 15 of electroconvection. Based on dimensionless similarity criteria (Reynolds, Péclet num-16 bers, etc.), we establish functional relationships between critical parameters, such as the 17 dimensionless electroconvective vortex diameter and the plateau length of current-volt-18 age curves. Training datasets were generated through extensive numerical experiments 19 using our in-house developed mathematical model, while multilayer feedforward neural 20 networks with backpropagation optimization were employed for regression tasks. The resulting AI (artificial intelligence) -driven hybrid models enable rapid prediction and optimization of EMS design and operating parameters, reducing computational and experimental costs. This research is situated at the intersection of membrane science, artificial intelligence, and computational modeling, forming part of a broader foresight agenda aimed at developing next-generation intelligent membranes and adaptive control strategies for sustainable water treatment. The proposed methodology offers a scalable framework for integrating physics-informed modeling and machine learning into the design of high-performance electromembrane systems.