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

## TL;DR

This paper introduces a new AI-based method to improve desalination by combining mathematical models with neural networks for better efficiency and lower costs.

## Contribution

A novel hybrid approach integrating neural networks with electroconvection simulations for EMS optimization.

## Key findings

- Hybrid AI models predict EMS parameters with reduced computational costs.
- Functional relationships between electroconvective parameters were established using dimensionless criteria.
- The framework integrates physical modeling and machine learning for EMS design.

## Abstract

To enhance desalination efficiency and reduce experimental costs, the development of advanced mathematical models for EMS is essential. In this study, we propose a novel hybrid approach that integrates neural networks with high-accuracy numerical simulations of electroconvection. Based on dimensionless similarity criteria (Reynolds, Péclet numbers, etc.), we establish functional relationships between critical parameters, such as the dimensionless electroconvective vortex diameter and the plateau length of current–voltage curves. Training datasets were generated through extensive numerical experiments using our in-house developed mathematical model, while multilayer feedforward neural 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 methodology provides a scalable framework for integrating physically based modeling and machine learning into the design of high-performance electromembrane systems.