Mathematical vs. machine learning models for particle size distribution in fragile soils of North-Western Himalayas

Abstract Purpose Particle size distribution (PSD) assessment, which affects all physical, chemical, biological, mineralogical, and geological properties of soil, is crucial for maintaining soil sustainability. It plays a vital role in ensuring appropriate land use, fertilizer management, crop selection, and conservation practices, especially in fragile soils such as those of the North-Western Himalayas. Materials and methods In this study, the performance of eleven mathematical and three Machine Learning (ML) models used in the past was compared to investigate PSD modeling of different soils from the North-Western Himalayan region, considering that an appropriate model must fit all PSD data. Results and discussion Our study focuses on the significance of evaluating the goodness of fit in particle size distribution modeling using the coefficient of determination (R 2 adj = 0.79 to 0.45), the Akaike information criterion (AIC = 67 to 184), and the root mean square error (RMSE = 0.01 to 0.09). The Fredlund, Weibull, and Rosin Rammler models exhibited the best fit for all samples, while the performance of the Gompertz, S-Curve, and Van Genutchen models was poor. Of the three ML models tested, the Random Forest model performed the best (R 2 = 0.99), and the SVM model was the lowest (R 2 = 0.95). Thus, the PSD of the soil can be best predicted by ML approaches, especially by the Random Forest model. Conclusion The Fredlund model exhibited the best fit among mathematical models while random forest performed best among the machine learning models. As the number of parameters in the model increased better was the accuracy.