We propose an on-the-fly statistical learning method to make a qualitative reduced-order model of the dynamics of a premixed flame quantitatively accurate. This physics- informed data-driven method is based on the statistically optimal combination of (i) a reduced-order model of the dynamics of a premixed flame with a level-set method, (ii) high-quality data, which can be provided by experiments and/or high-fidelity simulations, and (iii) assimilation of the data into the reduced-order model to improve the prediction of the dynamics of the premixed flame. The reduced-order model learns the state and the parameters of the premixed flame on the fly with the ensemble Kalman filter, which is a Bayesian filter used in the data assimilation of high-dimensional dynamical systems, e.g., in weather forecasting. The proposed method and algorithm are applied to two test cases with relevance to reacting flow and instability. First, the capabilities of the framework are demonstrated in a twin experiment, where the assimilated data are produced from the same model as that used in prediction. Second, the assimilated data are extracted from a high-fidelity reacting-flow direct numerical simulation (DNS). The results are analyzed by using Bayesian statistics, which provide the uncertainties of the calculations. This method opens up new possibilities for on-the-fly optimal calibration of computationally cheap reduced-order models when experimental data become available, for example, from sensors.