Physics-Informed Neural Networks for Three-Dimensional River Microplastic Transport: Integrating Conservation Principles with Deep Learning

Microplastic pollution in riverine systems poses critical environmental challenges, yet predictive modeling remains constrained by data scarcity and the computational limitations of traditional numerical approaches. This study develops a physics-informed neural network (PINN) framework that integrates advection–diffusion equations and turbulence modeling approaches with deep learning architectures to stimulate three-dimensional microplastic transport dynamics. The methodology embeds governing partial differential equations as soft constraints, enabling predictions under sparse observational conditions (requiring approximately three times fewer observation points than conventional numerical models), while maintaining physical consistency. Applied to a representative 15 km Yangtze River reach with 12 months of monitoring data, the model achieves improved performance with a root mean square error of 0.82 particles/m3 and a Nash–Sutcliffe efficiency exceeding 0.88, representing a 34% accuracy improvement over conventional finite volume methods. The framework successfully captures size-dependent transport behavior, identifies three primary accumulation hotspots exhibiting 3–5 times elevated concentrations, and quantifies nonlinear flux–discharge relationships with 6–8-fold amplification during high-flow events. This physics-constrained approach provides practical findings for pollution management and establishes an adaptable computational framework for environmental transport modeling in data-limited scenarios across diverse riverine systems.