A data-based comparative review and AI-driven symbolic model for longitudinal dispersion coefficient in natural streams

A better understanding of dispersion in natural streams requires knowledge of longitudinal dispersion coefficient(LDC). Various methods have been proposed for predictions of LDC. Those studies can be grouped into three types: analytical, statistical and ML-driven researches(Implicit and explicit). However, a comprehensive evaluation of them is still lacking. In this paper, we first present an in-depth analysis of those methods and find out their defects. This is carried out on an extensive database composed of 660 samples of hydraulic and channel properties worldwide. The reliability and representativeness of utilized data are enhanced through the deployment of the Subset Selection of Maximum Dissimilarity(SSMD) for testing set selection and the Inter Quartile Range(IQR) for removal of the outlier. The evaluation reveals the rank of those methods as: ML-driven method > the statistical method > the analytical method. Whereas implicit ML-driven methods are black-boxes in nature, explicit ML-driven methods have more potential in prediction of LDC. Besides, overfitting is a universal problem in existing models. Those models also suffer from a fixed parameter combination. To establish an interpretable model for LDC prediction with higher performance, we then design a novel symbolic regression method called evolutionary symbolic regression network(ESRN). It is a combination of genetic algorithms and neural networks. Strategies are introduced to avoid overfitting and explore more parameter combinations. Results show that the ESRN model has superiorities over other existing symbolic models in performance. The proposed model is suitable for practical engineering problems due to its advantage in low requirement of parameters (only w and U* are required). It can provide convincing solutions for situations where the field test cannot be carried out or limited field information can be obtained.