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Viscosity ($η$) is one of the most important properties of disordered matter. The temperature-dependence of viscosity is used to adjust process variables for glass-making, from melting to annealing. The aim of this work was to develop a physics-informed machine learning model capable of predicting $η(T)$ of oxide liquids. Instead of predicting the viscosity itself, the NN predicts the parameters of the MYEGA viscosity equation: the liquid's fragility index, the glass transition temperature, and the asymptotic viscosity. With these parameters, $η$ can be computed at any temperature of interest, with the advantage of good extrapolation capabilities inherent to the MYEGA equation. The dataset was collected from the SciGlass database; only oxide liquids with enough data points in the high and low viscosity regions were selected, resulting in a final dataset with 17,584 data points containing 847 different liquids. About 600 features were engineered from the liquids' chemical composition and 35 of these features were selected using a feature selection protocol. The hyperparameter (HP) tuning of the NN was performed in a set of experiments using both random search and Bayesian strategies, where a total of 700 HP sets were tested. The most successful HP sets were further tested using 10-fold cross-validation, and the one with the lowest average validation loss was selected as the best set. The final trained NN was tested with a test dataset of 85 liquids with different compositions than those used for training and validating the NN. The $R^2$ for the test dataset's prediction was 0.97. This work introduces three advantages: the model can predict viscosity as well as the liquids' glass transition temperature and fragility index; the model is designed and trained with a focus on extrapolation; finally, the model is available as free and open-source software licensed under the GPL3.