Real-Time Monitoring and Control of Water Pollution Using a Fokker–Planck-Based Model

This study presents a groundbreaking approach to water pollution management in arid regions through the development of a symmetry-aware Fokker–Planck stochastic model. Unlike typical deterministic treatments, our method itself creatively combines probability-density-based regulation with immediate monitoring to achieve a (Formula presented.) reduction in contaminant concentrations in the Saudi coastal regions during practical validations. Utilizing the natural front-spatial symmetries of aquifer systems, we have reduced computation cost by half while maintaining their accuracy (error within (Formula presented.)). Through ensuring robust stability standards, the model produces control protocols that are tuned to address uncertain environmental conditions. Building on Saudi Vision 2030, this research—backed by detailed 21-day data in the field—presents a real and scalable approach to sustainable water management. The use of stochastic methods alongside symmetry analysis is a significant breakthrough in limiting water pollution in areas where water resources are minimal.