This research aims to model soil temperature (ST) using machine learning models of multilayer perceptron (MLP) algorithm and support vector machine (SVM) in hybrid form with the Firefly optimization algorithm, i.e. MLP-FFA and SVM-FFA. In the current study, measured ST and meteorological parameters of Tabriz and Ahar weather stations in a period of 2013–2015 are used for training and testing of the studied models with one and two days as a delay. To ascertain conclusive results for validation of the proposed hybrid models, the error metrics are benchmarked in an independent testing period. Moreover, Taylor diagrams utilized for that purpose. Obtained results showed that, in a case of one day delay, except in predicting ST at 5 cm below the soil surface (ST5_cm) at Tabriz station, MLP-FFA produced superior results compared with MLP, SVM, and SVM-FFA models. However, for two days delay, MLP-FFA indicated increased accuracy in predicting ST_5cm and ST _20cm of Tabriz station and ST_10cm of Ahar station in comparison with SVM-FFA. Additionally, for all of the prescribed models, the performance of the MLP-FFA and SVM-FFA hybrid models in the testing phase was found to be meaningfully superior to the classical MLP and SVM models.

本研究旨在使用多层感知器（MLP）算法的机器学习模型和支持向量机（SVM）与Firefly优化算法（即MLP-FFA和SVM-FFA）混合使用，对土壤温度（ST）进行建模。在本研究中，将大不里士和阿哈尔气象站2013-2015年期间测得的ST和气象参数用于对所研究模型的训练和测试，但要延迟一到两天。为了确定用于验证所提出的混合模型的结论性结果，在独立的测试期内对误差指标进行了基准测试。此外，泰勒图用于该目的。所得结果表明，在延迟一天的情况下，除了预测ST在土壤表面以下5 cm（ST5 _cm）在大不里士车站，与MLP，SVM和SVM-FFA模型相比，MLP-FFA产生了出色的结果。然而，与SVM-FFA相比，MLP-FFA延迟了两天，表明在预测大不里士站的ST _5cm和ST _20cm以及Ahar站的ST _10cm方面的准确性提高。此外，对于所有规定的模型，发现MLP-FFA和SVM-FFA混合模型在测试阶段的性能显着优于经典MLP和SVM模型。