As a promising strategy to mitigate carbon emissions, hydrogen enrichment of conventional fuels is gaining increasing interest, but can lead to increased propensity to damaging thermoacoustic instability. This paper demonstrates the ability of machine learning algorithms to reliably predict a key flame behavior relevant to thermoacoustic stability prediction – the flame’s nonlinear response to upstream acoustic forcing. Using computational simulations of a laminar premixed flame under difference hydrogen enrichment and equivalence ratio conditions, training data for machine learning are generated. The machine learning models are then used to predict the flame response under new test conditions, including extrapolating into new hydrogen enrichment regimes. The effect of algorithm choice, data structure, data size, and extrapolation distance on the performance of different machine learning models is investigated with particular attention to performance with sparse training data. It is found that a type of neural network known as the multi-layer perceptron (MLP) model outperforms the Gaussian process and random forest models in both interpolation and extrapolation tasks. A physics-informed preprocessing strategy, involving extracting the time delay of the flame response (which can be deduced from geometry and flow parameters) prior to applying machine learning, is found to remarkably improve the accuracy of machine learning models, especially in extrapolation tasks. When the extrapolation into new hydrogen content levels is strong enough, the MLP model no longer performs well. However, for small and intermediate extrapolation, the MLP model shows a commendable level of prediction, even with small data sets, fulfilling needs relevant to thermoacoustic stability prediction. Extending the MLP model to experimental data from turbulent flames, the gain fall-off frequency and phase lag are accurately predicted but not the secondary periodic fluctuations in gain.