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A better understanding of dispersion in natural streams requires knowledge oflongitudinal dispersion coefficient(LDC). Various methods have been proposedfor 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, wefirst 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 ofhydraulic and channel properties worldwide. The reliability andrepresentativeness of utilized data are enhanced through the deployment of theSubset Selection of Maximum Dissimilarity(SSMD) for testing set selection andthe Inter Quartile Range(IQR) for removal of the outlier. The evaluationreveals the rank of those methods as: ML-driven method > the statistical method> the analytical method. Whereas implicit ML-driven methods are black-boxes innature, explicit ML-driven methods have more potential in prediction of LDC.Besides, overfitting is a universal problem in existing models. Those modelsalso suffer from a fixed parameter combination. To establish an interpretablemodel for LDC prediction with higher performance, we then design a novelsymbolic regression method called evolutionary symbolic regressionnetwork(ESRN). It is a combination of genetic algorithms and neural networks.Strategies are introduced to avoid overfitting and explore more parametercombinations. Results show that the ESRN model has superiorities over otherexisting symbolic models in performance. The proposed model is suitable forpractical engineering problems due to its advantage in low requirement ofparameters (only w and U* are required). It can provide convincing solutionsfor situations where the field test cannot be carried out or limited fieldinformation can be obtained.

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