jats:titleAbstract</jats:title> jats:pThe application of machine learning to aerospace problems faces a particular challenge. For successful learning a large amount of good quality training data is required, typically tens of thousands of cases. However, due to the time and cost of experimental aerospace testing, this data is scarce. This paper shows that successful learning is possible with two novel techniques: The first technique is rapid testing. Over the last five years the Whittle Laboratory has developed a capability where rebuild and test times of a compressor stage now take 15 minutes instead of weeks. The second technique is to base machine learning on physical parameters, derived from engineering wisdom developed in industry over many decades.</jats:p> jats:pThe method is applied to the important industry problem of predicting the effect of blade damage on compressor operability. The current approach has high uncertainty, it is based on human judgement and correlation of a handful of experimental test cases. It is shown using 100 training cases and 25 test cases that the new method is able to predict the operability of damaged compressor stages with an accuracy of 2% in a 95% confidence interval; far better than is possible by even the most experienced compressor designers. Use of the method is also shown to generate new physical understanding, previously unknown by any of the experts involved in this work. Using this method in the future offers an exciting opportunity to generate understanding of previously intractable problems in aerospace.</jats:p>