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An efficient approach for improving the predictive understanding of dynamic mechanical system variability is developed in this work. The approach requires low model assessment time through the fitting of surrogate models. ML-based surrogate algorithms for finite element analysis (FEA) are developed in this study to accelerate FEA and prevent rerunning complex simulations. The research begins with an overview of the recent novelties in ML algorithms applied to finite element (FE) and other physics-based computational schemes. To predict the time-varying response variables, that is, the displacement of a two-dimensional truss structure, a surrogate FE technique based on ML algorithms is developed. In this work, several ML regression algorithms, including decision trees (DTs) and deep neural networks, are developed, and their efficacies are compared. In this study, the ML-based surrogate FE models are able to effectively predict the response of the truss structure in two dimensions over the entire structure. Extreme gradient-boosting DTs provide more precise outcomes and outperform other ML algorithms.