We develop and demonstrate a computationally cheap framework to identify optimal experiments for Bayesian inference of physics-based models. We develop the metrics (i) to identify optimal experiments to infer the unknown parameters of a physics-based model, (ii) to identify optimal sensor placements for parameter inference, and (iii) to identify optimal experiments to perform Bayesian model selection. We demonstrate the framework on thermoacoustic instability, which is an industrially relevant problem in aerospace propulsion, where experiments can be prohibitively expensive. By using an existing densely sampled dataset, we identify the most informative experiments and use them to train the physics-based model. The remaining data are used for validation. We show that, although approximate, the proposed framework can significantly reduce the number of experiments required to perform the three inference tasks we have studied. For example, we show that for task (i), we can achieve an acceptable model fit using just 2.5% of the data that were originally collected.
