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Due to increasing volume of measurements in smart grids, surrogate based learning approaches for modeling the power grids are becoming popular. This paper uses regression based models to find the unknown state variables on power systems. Generally, to determine these states, nonlinear systems of power flow equations are solved iteratively. This study considers that the power flow problem can be modeled as an data driven type of a model. Then, the state variables, i.e., voltage magnitudes and phase angles are obtained using machine learning based approaches, namely, Extreme Learning Machine (ELM), Gaussian Process Regression (GPR), and Support Vector Regression (SVR). Several simulations are performed on the IEEE 14 and 30-Bus test systems to validate surrogate based learning based models. Moreover, input data was modified with noise to simulate measurement errors. Numerical results showed that all three models can find state variables reasonably well even with measurement noise.