Unraveling Microplastics in Lakes with a Mechanism-Informed, Few-Shot Data-Driven Liquid Neural Networks

Simulating microplastic (MP) transport in aquatic environments faces two persistent bottlenecks: error accumulation in purely physical models and the intrinsic difficulty of machine learning methods with sparse, discontinuous field observations. Here, we introduce a mechanism-informed, few-shot data-driven framework powered by Liquid time-constant networks, the first application of continuous-time neural ordinary differential equation models to pollutant transport prediction. The framework employs the MIKE21 hydrodynamic particle tracking model as a physics knowledge generator, whose high-resolution fields augment limited measurements to train a physically constrained closed-form continuous-time (CfC) neural network. With learnable time constants and nonlinear synaptic coupling, the networks assimilate sparse observations directly without interpolation, correcting spatial distortions in nearshore zones and suppressing long-term error propagation. Demonstrated on Poyang Lake using only sparse monitoring data, the model achieves R2 values of 0.867 and 0.895 for dry and wet seasons, respectively, markedly outperforming Random Forest and other benchmarks. SHAP analysis further identifies flow velocity, water depth, and suspended sediment concentration as dominant regional drivers. This paradigm offers both a transferable solution for lacustrine MP prediction and a new avenue for environmental simulation in data-sparse contexts.